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Agent-based computing / editors, Duarte Bouça and Amaro Gafagnão.
p. cm.
Includes index.
1. Intelligent agents (Computer software) 2. Distributed artificial intelligence. 3. Data mining. I. Bouça,
Duarte. II. Gafagnão, Amaro. QA76.76.I58A3176 2010
006.3--dc22
2009041926

Published by Nova Science Publishers, Inc. †New York
ISBN: 978-1-61122-576-1 (eEook)
Agent-Based Computing, edited by Duarte Bouca, and Amaro Gafagnao, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,
Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

CONTENTS

Preface ix
Chapter 1 Agent-Based Genetic Algorithm for Global Numerical
Optimization and Feature Selection 1
Yongming Li, Xiaoping Zeng and Pin Wang
Chapter 2 Multi-Agent Enterprise Sustainability Performance
Measurement System
51
Ismail Erol and Safiye Turgay
Chapter 3 A Modular Artificial Neural Network Based Decision Making
in a Multi-Agent Robot Soccer Systems 89
K. G. Jolly, R. Sreerama Kumar and R. Vijayakumar
Chapter 4 Security and Privacy in Track and Trace Infrastructures 109
Leonardo Weiss Ferreira Chaves and Florian Kerschbaum
Chapter 5 A Challenge to Develop Large-scale Agent Simulation Software 123
Hiroshi Arikawa, Sen-ichi Morishita and Tadahiko Murata
Chapter 6 A Framework of an Agent-Based Model Using Social and Physical
Interaction for Vulnerability Analysis on Flood Events
141
Sung-Jin Cho, Jinmu Choi and Chul-Sue Hwang
Chapter 7 Agent-Based Manufacturing System Innovation:
Fractal Approaches 155
Jungtae Mun, Moonsoo Shin, Kwangyeol Ryu
and Mooyoung Jung
Chapter 8 Agent-Based Discovery, Composition and Orchestration
of Grid Web Services
195
Dionysios D. Kehagias, Dimitrios Tzovaras
and George A. Gravvanis
Chapter 9 An Efficient Mobile-Agent-Based Platform for Dynamic Service
Provisioning in 3G/UMTS 225
Yuan-Lin Ko, Kuochen Wang and Hung-Cheng Shih
Agent-Based Computing, edited by Duarte Bouca, and Amaro Gafagnao, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,
Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

Contents viii
Chapter 10 An Investigation into the Issues of Multi-Agent Data Mining 247
Kamal Ali Albashiri, Frans Coenen and Paul Leng
Index 325

Agent-Based Computing, edited by Duarte Bouca, and Amaro Gafagnao, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,
Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

PREFACE

Multi-agent systems (MAS) often deal with complex applications that require distributed
problem solving. In many applications, the individual and collective behavior of the agents
depends on the observed data from distributed sources. This book discusses a number of
research issues concerned with the use of Multi-Agent Systems for Data Mining (MADM),
also known as agent-driven data mining. In addition, optimization algorithms are very
important in modern research and industrial areas. This book examines one multi-population
co-genetic algorithm (MPAGA) with double chain-like agent structure to realize parallel
optimization, combining chain-like agent structure and multi-population parallel searching.
Furthermore, this book proposes an efficient modular artificial neural network (ANN)
architecture for the intelligent decision making of a robot in a robot soccer systems with
different team configurations. Other chapters review the use of radio frequency identification
(RFID) technology with supply chain agents and then analyze the security requirements,
describe how to design and implement a large-scale multi-agent simulation software, and
provide a framework of evacuation simulation for urban hazards such as flooding with
effective agent's interaction tools with other agents and the physical environment.
Chapter 1 - This chapter discusses how to construct two kinds of agent-based genetic
algorithms (CAGA, MPAGA) for numerical optimization and feature selection. Firstly, this
chapter introduces recent works about numerical optimization and feature selection with
evolutionary computation algorithms especially genetic algorithm. The works’ contribution
and limitation are discussed. Based on the limitation, this chapter discusses the advantage of
the agent-based genetic algorithm over normal genetic algorithm in terms of global numerical
optimization and feature selection. Then the detailed construction and theoretical analysis of
agent-based genetic algorithm are involved. Thirdly, a lot of experiments are involved to
show the optimization capability of the agent-based genetic algorithms. In terms of global
numerical optimization, over ten benchmark test functions are used for testing. Over four
popular genetic algorithms are compared. In terms of feature selection, over 6 datasets will be
used for testing. Over 3 classifiers are used for comparison. The experimental results show
that the agent-based genetic algorithms are more attractive and promising than non agent-
based genetic algorithm for computing in terms of global numerical optimization and feature
selection.
Chapter 2 - Sustainability grounds the development debate in a global framework, within
which a continuous satisfaction of human needs constitute the ultimate goal. When
transposing this idea to the business level, corporate sustainability can accordingly be defined
Agent-Based Computing, edited by Duarte Bouca, and Amaro Gafagnao, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,
Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

D. Bouça and A. Gafagnão x
as meeting the needs of a firm’s direct and indirect stakeholders without compromising its
ability to meet the needs of future stakeholders as well. Based on the definition of corporate
sustainability, the goal of sustainable development is to integrate the economic, social and
ecological impacts of our patterns of production and consumption into forms of development
that are designed for long-term sustainability. But for the transition to sustainability,
performance must be assessed, which has posed important challenges to the researchers in
providing efficient but reliable tools. A number of principles, tools and reporting formats
have emerged, some of which are adopted by corporations to demonstrate their commitment
to sustainable development. In the context of sustainability measurement and management, to
the extent of our knowledge, no study has been performed to develop an agent based or multi
agent integrated decision making tool that can meet organizational needs at the decision
making level. Given the characteristics of a typical agent system and system requirements for
today’s organizational sustainability assessment, it is concluded that a multi-agent based
system can be a useful tool in such environments to put together a coordinated workflow of
collaborating agents. In this research, considering the need for multi-agent approach in the
context of sustainability assessment, a multi-agent system with integrated multi-criteria tools
is developed to measure, compare and communicate the sustainability performances of an
organization. The proposed system is designed consistent with the fact that no uniform agreed
multi-criteria methodology exists for aggregation of composite indicators for sustainability
evaluation. Therefore, in this study, several multi-criteria methods are used simultaneously
instead of selecting the best method for the situation. To test the proposed methodology, data
obtained from a grocery retailer is used. Finally, discussion, implications and some
concluding remarks are provided.
Chapter 3 - This chapter proposes an efficient modular artificial neural network (ANN)
architecture for the intelligent decision making of a robot in a robot soccer systems with different
team configurations. In conventional ANN based approaches, the decision making systems are
trained separately for different team configurations and which leads to an increased computational
overheads and learning time. The technique discussed in this chapter can alleviate this situation,
by making use of a flexible modular ANN architecture capable of accommodating different team
configurations without any repeated learning phase as the team configuration
changes. The basic
building block in this modular decision making system is an ANN developed for a MiroSot small
league system. Decision space of the MiroSot small league system is simple and two dimensional
so that its prediction accuracy is high. The simulation results indicates that the modular decision
making system developed for higher team configuration maintains the same level of prediction
accuracy as that of the smaller team configuration.
In the modular approach decision variables are
shared among the various ANN blocks so that it need not be trained again.
Chapter 4 - Radio Frequency Identification (RFID) has the potential to increase supply chain
efficiency in many track and trace scenarios. RFID tags are attached to the items forwarded by
agents in the supply chain. Each agent records the RFID data when processing each item. The
exchange of such data between different supply chain agents enables new forms of analytics, but
also raises new security and privacy concerns.
The authors show how to reconcile the two conflicting objectives using the example of batch
recalls. Especially in the food and in the pharmaceutical industry, producers are obliged to
implement recalls in order to comply with legislation. In extreme cases, non-compliance can cause
loss of life, e.g., when perished food or medicine reaches the consumer.
Current batch recall practice is expensive and difficult, since many different agents need to
combine their data. RFID can be used to efficiently implement batch recalls by storing data
Agent-Based Computing, edited by Duarte Bouca, and Amaro Gafagnao, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,
Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

Preface xi
produced by agents along the supply chain, e.g., batch numbers from parts/ingredients used in all
manufacturing steps. But this raises concerns regarding industrial privacy, since competitors could
use this information to gain insight into the whole supply chain.
The authors explore a novel, cryptography-based approach that stores encrypted track and
trace information on RFID tags, such that data are only available in the case of a recall. Our
method encrypts the information using identity-based encryption and, furthermore, allows
universal re-encryption along the supply chain to prevent information leaks from the ciphertexts.
Chapter 5 - This chapter describes how to design and implement a large-scale multi-agent
simulation software. Multi-agent simulation (MAS) is one of promising research fields in artificial
intelligences. The authors have proposed to implement a large-scale simulation software for MAS.
First, the authors illustrate that a way of implementing a multi-agent software with a huge number
of agents is to parallelize it using wide-area distributed computing environment. In this chapter,
they describe a method to implement a large-scale MAS software using two traditional
parallelization approaches: message-passing approach and remote procedure call approach. Next,
the authors illustrate the architecture of “ELASTIC.” ELASTIC is a large-scale MAS toolkit they
developed. Using our toolkit developers do not have to have knowledge to allocate a large-scale
memory space on a computer. In this chapter, the authors also show how to apply ELASTIC to a
simulation software with large amount of agents for policy-making assistance.
Chapter 6 - Urban hazards have become a matter of concern with both property damages and
human victims. For flood evacuation, the effective mechanism of residents’ communication with
other people and sensing methods for the environmental situations would be essential. In this
study, agents’ interactions with other agents and the physical environment were discussed for the
evacuation simulation of flood hazard using an agent-based model. The knowledge query
manipulation language (KQML) was used for a social interaction that is the communication
between agents. The reinforcement learning (RL) was used for a physical interaction that is the
agents’ perception of the physical situation. A physical interaction is an internal interaction since
the judgment is based on agent’s own experience and memory. A social interaction is an external
interaction since the judgment is based on the communication with other people. Therefore, this
study will provide a framework of evacuation simulation for urban hazard such as flooding with
effective agent’s interaction tools with other agents and the physical environment.
Chapter 7 - Today’s business environment demands a permanent alignment of enterprises
with the market. As the mass customized product development based on various emerging
technologies often exceeds what a single enterprise is able to accomplish, it has to achieve a
competitive synergistic advantage, i.e., mobilizing the best available internal/external resources.
Furthermore, the dynamic nature of today’s environment has forced the manufacturing system to
be more distributed and autonomous. Advances in the internet are accelerating the shift from self-
centered integration to networked collaboration. In a centralized management system, a supervisor
unit, either a human operator or a software system such as manufacturing resources planning
(MRP II) and enterprise resources planning (ERP) systems, maintains detailed information on all
the perceivable aspects of constituent resources. However, in the current distributed and
decentralized production environments, there is no central decision entity authorized to access all
the necessary information to solve the resource management problem. Thus, the centralized
approaches are no longer valid. This chapter introduces recent technological and organizational
perspectives of an agent-based distributed manufacturing system, which covers both intra-
enterprise and inter-enterprise operations based on fractal approaches.
Chapter 8 - A plethora of Web services exist today that produce a large amount of content
capable to fulfill the knowledge requirements of various application domains. These Web services,
appropriately annotated, may form a Grid of Services, capable to achieve high performance and
Agent-Based Computing, edited by Duarte Bouca, and Amaro Gafagnao, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,
Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

D. Bouça and A. Gafagnão xii
content availability on behalf of knowledge-intensive processes or applications. This chapter
provides a review of recent advances on service-oriented, agent-based discovery, composition and
orchestration of Grid services, as well as new research directions, based on recent findings and
experience derived from a relevant large-scale integrated project. The work presented in this
chapter is motivated by the development of an ambient intelligence framework for the provision of
content and services in order to fulfill the needs of mobility impaired users on the move. The
framework is coupled with a Grid services infrastructure that realizes a network of geographically
dispersed service providers.
Chapter 9 - An important key concept of the Virtual Home Environment (VHE) is dynamic
service provisioning. In 3G/B3G, the mobile network will have such a capability. The users can
dynamically subscribe new services anytime, and the system operator or service provider can
dynamically provide services to subscribed users immediately. Based on the UMTS CAMEL
(Customized Applications for Mobile Enhanced Logic) architecture, the authors propose an
efficient mobile-agent– based platform to provide services dynamically, which can greatly reduce
signaling traffic. To demonstrate the efficiency of our platform, the authors used the operations of
incoming and outgoing calls to illustrate the operation of mobile agents. In an existing approach, a
CORBA agent-based platform was deployed in a distributed processing environment, and it
requires a standard, OMG Mobile Agent System Interoperability Facility (MASIF), to be
interoperable between agent environments of different vendors or operators. However, there are
some problems in this approach, such as problems in the aspects of security and performance.
Analysis results have shown that the signaling traffic in our CAMEL mobile-agent-based platform
can be reduced 40% compared to that in the CORBA agent-based platform. Our platform can
provide efficient mobility management, and enhance network performance, security and
interoperability.
Chapter 10 - Multi-agent systems (MAS) often deal with complex applications that
require distributed problem solving. In many applications the individual and collective
behaviour of the agents depends on the observed data from distributed sources. The field of
Distributed Data Mining (DDM) deals with these challenges in analyzing distributed data and
offers many algorithmic solutions to perform different data analysis and mining operations in
a fundamentally distributed manner that pays careful attention to the resource constraints.
Since multi-agent systems are often distributed and agents have proactive and reactive
features, combining DM with MAS for data intensive applications is therefore appealing.
This Chapter discusses a number of research issues concerned with the use of Multi-
Agent Systems for Data Mining (MADM), also known as agent-driven data mining. The
Chapter also examines the issues affecting the design and implementation of a generic and
extendible agent-based data mining framework. An Extendible Multi-Agent Data mining
System (EMADS) Framework for integrating distributed data sources is presented. This
framework achieves high-availability and high performance without compromising the data
integrity and security.

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In: Agent-Based Computing ISBN 978-1-60876-684-0
Editor: D. Bouça and A. Gafagnão, pp.1-49 © 2010 Nova Science Publishers, Inc.

Chapter 1

AGENT-BASED GENETIC ALGORITHM FOR GLOBAL
NUMERICAL OPTIMIZATION AND FEATURE
SELECTION

Yongming Li, Xiaoping Zeng and Pin Wang
College of Communication Engineering of Chongqing University, P.R.China, 400030

1. INTRODUCTION

Optimization algorithms are very important in modern research and industrial areas.
Among the existing optimization algorithms, the genetic algorithm (GA) has received
considerable attention regarding its potential as a novel optimization technique for complex
problems and has been applied in various areas successfully. The main specific feature of the
GA as an optimization method is its implicit parallelism which is a result of the evolution and
the hereditary-like process. Besides, it is more likely to jump out of local optima to search for
global optima. However, the traditional GAs are not enough satisfying in optimization
precision since they are still easy to fall into local optima. Because of GA’s importance and
limitation, many researchers have done much research about the improvement of genetic
algorithm until now. These improvements relate to genetic operators (namely probability of
crossover, probability of mutation, and so on), population size, population structure, selection
strategy, and so on [Gaofeng Huang, et al].
Leung and Wang proposed an improved genetic algorithm- the orthogonal genetic
algorithm with quantization [Y.W.Leung, etl al]. The algorithm not only can find optimal or
close-to-optimal solutions but also can give more robust and significantly better results than
some other improved-GAs. Among the improved crossover operators and mutation operators,
adaptive crossover and mutation operator are welcomed mostly [M. Srinivas et al]. That is
because adaptive crossover operator and mutation operator can effectively keep the diversity
of population, avoiding premature convergence.
Some researchers proposed penalty function
to keep the diversity of population, the effect is satisfied to some extent [Yi-Bo Hu et al].
However, according to various applications, it is hard to set penalty function correctly.
Incorrect setting of penalty function will make performance of genetic algorithm fall down.
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Yongming Li, Xiaoping Zeng and Pin Wang 2
For adaptive crossover operator, incorrect setting of probability of crossover will be modified
with genetic evolution one generation after one generation. Moreover, additional introduction
of penalty function except crossover and mutation operation will lead to more computational
cost. Some researchers proposed hybrid genetic algorithm putting genetic algorithm and local
optimization method together in order to improve genetic algorithm [Sung-Hwan Min, et al].
Some other researchers proposed competitive selection strategy [Samya Elaouda et al]. The
strategy is a special selection, the individual sometimes is different from the individuals
selected, inheriting the good genes of individuals selected. It is seen that the strategy is
similar to local optimization method to some extent because they all can search the local
region. However, normally, the local optimization method is introduced between crossover
operation and mutation operation, so the competitive selection strategy can have less
computational cost because it functions as selection operation and local optimization at the
same time.
Except the improvements above, the improvement of population structure is important
too. For conventional genetic algorithm, the individuals live together, are selected,
crossovered and mutated together. The apparent disadvantage is some individuals with high
fitness value are very early to cover the whole population leading to premature convergence.
Besides, since the selection, crossover and mutation process need to be done within the whole
population, the fitness value of the whole population and the individuals need to be
calculated, the computational cost is much high. Kai Cao [Kai Cao et al] and Weicai Zhong
[Weicai Zhong et al] proposed a lattice-like agent population structure to solve the problem.
The individuals are thought as agents living in lattice-like agent population structure, they do
genetic operations just with neighboring agents. The relevant experimental results show the
structure can effectively keep the diversity of the population. It is seen that this kind of
structure is two dimensional structures; the agent needs to do genetic operations with four
neighboring agents. If one dimensional structure is introduced, one agent just needs to do
genetic operations with two neighboring agents, the computational cost will be reduced, and
premature convergence will be avoided better.
Based on the analysis of the relevant papers above, one novel genetic algorithm is
proposed here, and it is called as dynamic chain-like agent genetic algorithm (CAGA)
[Yongming Li, et al]. This genetic algorithm adopts chain-like agent structure as population
structure. This population structure is simpler than lattice-like agent structure; the
corresponding computational complexity is reduced; it can more effectively avoid premature
convergence. Adaptive genetic operators (including adaptive crossover operator and mutation
operator) are introduced in CAGA to effectively search the global optima and keep the
diversity of the population. Besides, the dynamic neighboring competitive selection strategy
is introduced to replace conventional selection operator to enhance the searching capability.
The applications with GA can be divided into two categories: numerical optimization and
feature selection, though the latter can be looked as the variant of the former. The difference
of the two kinds of applications is: 1, the coding strategy is different. Normally, the coding
strategy of the numerical optimization is real coding because real coding can have better
faster searching speed, is more suitable for optimization problems with continuous variables
than binary coding and it can avoid the “binary cliff”. 2, the corresponding operations are
different. The former is the searching of the gl
obal optima of object functions. With practical
optimization projects, the designed is asked to build up the optimization model, namely object
functions needing to be optimized, and then the GA can be applied into the object functions.
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Agent-Based Genetic Algorithm for Global Numerical Optimization… 3
The latter is no so. It is the selection of the best features combination among the features
being selected for the classification. The object functions correspond to concrete evaluation
criteria, and vary with different evaluation criteria for the same feature selection problem. 3,
the former is continuous, the latter is discrete. Generally, one kind of GA can be used both in
numerical optimization and in feature selection through different coding strategies. So, the
discussion with numerical optimization and feature selection can evaluate the performance of
the GA more comprehensively. However, very few papers about GA’s study involve the two
aspects within one paper.
During the research of CAGA, the authors found that the improvement on time cost is
still limited. For the complex optimization problems, even if we combine the characteristics
of search space into optimization algorithm
to reduce the algorithm’s time cost, the
improvement on time cost is still limited and is not very apparent. In order to reduce the time
cost and improve the optimization speed greatly, multi-population genetic algorithm is a good
choice to be applied to realize parallel optimization. We can adopt multi-CPUs (Computing
Processing Unit, CPU) to realize the multi-population genetic algorithm, each CPU realize
one population. Apparently, the time cost will be reduced greatly.
Currently, there are two realization modes for multi-population genetic algorithm. One
kind of realization mode is to decompose the optimization problem into many sub-problems;
every sub-problem uses one GA with single population. The shortcomings of the mode are in:
firstly, it is hard to know whether the decomposition is reasonable. Secondly, because the
optimization result of every genetic algorithm is optimal partial solution, the assembly of the
optimal partial solutions into one optimal full so
lution is necessary. However, the assembly is
very hard and skillful for the corresponding designer. Usually, the simple combination of all
optimal partial solutions is not one optimal full solution for the whole optimization problem.
Another kind of realization mode is to design one multi-population genetic algorithm, every
sub-population searches optimal full solution in parallel, and the sub-populations exchange
evolution information each other during genetic operation to search for global optimal full
solution. Bjoin Olsson [9] proposed the co-evolutionary search algorithm in asymmetric
space, obtaining satisfying results to some extent, but the searching speed and precision for
complex searched space are not satisfying enough. Mitchell A Potter et.al. [Mitchell A Potter
et al] proposed one collaboration co-genetic algorithm. They introduced multi-population idea
into genetic algorithm to improve GA’s optimization performance. However, it still has some
drawbacks: firstly, the algorithm divides whole population into several independent
populations with fewer variables, so the mode belongs to the first realization mode discussed
above. Secondly, the algorithm just considers collaboration between sub-populations but does
not consider competition between sub-populations
. Thirdly, the division of population into
sub-populations is very challenging; maybe the division needs enough relevant prior
knowledge, so it is not convenient for practical application. Besides, the false or not precise
division will lead to false or not precise optimization result. Chi-Hung Su and Tung-Hsu Hou
[Chi-Hung Su et al] proposed another multi-population genetic algorithm for parameter
optimization problem. The GA has two sub-populations, each sub-population optimizes
different object function and two optimization results within one generation are obtained.
After that, the two results are put together to make an optimal full solution. So it still belongs
to the first realization mode discussed above.
Based on the analysis above, this chapter will discuss one multi-population co-genetic
algorithm (MPAGA) with double chain-like agent structure (close chain-like agent structure
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Yongming Li, Xiaoping Zeng and Pin Wang 4
and cycle chain-like agent structure) to realize parallel optimization, combining chain-like
agent structure and multi-population parallel searching. In this algorithm, inside every sub-
population, close chain-like agent structure is applied; the individuals of some sub-population
are connected with one close chain as agents. Every sub-population is connected with one
cycle chain and shares some common agents (they are called shared agents). The sub-
populations evolve themselves and cooperate and compete with each other. Inside each
subpopulation, the genetic operators are similar as CAGA.
As we know, feature selection problems are optimization problems in essence. But
generally, the coding strategy is binary code strategy. Therefore, the normal agent genetic
algorithms are needed to be modified to suit the problems. In order to further study the
parallel optimization capability of MPAGA in feature selection problems. For clarity, the
MPAGA means the MPAGA for global numerical optimization; the MPAGAFS means the
MPAGA for feature selection.
Currently, feature selection problems always are large scale, apparently one processor is
not enough for running feature selection to meet the requirement of time cost often.
Therefore, for GA based feature selection, parallelism is needed to be introduced into the
genetic algorithm of feature selection algorithm to speed it up. Currently, some researchers
did works on parallel feature selection based on genetic algorithm [Li Chen et al].
Nordine Melab proposed one kind of parallel wrapper feature selection based on genetic
algorithm [Melab, N et al]. But strictly, just the evaluation of individuals is about parallelism.
The authors classify the individuals into several groups, each group of individuals are
assigned to one classifier to ev
aluate their fitness value. But the rest of genetic operations are
done within one population in one processor. Chih-Ming Chen proposed another kind of
parallel feature selection based on genetic algorithm [Chih-Ming Chen et al]. The algorithm is
similar to that by Nordine Melab, just evaluate the individuals in parallel. Punch et al.
proposed a similar algorithm too [Punch, W. F et al]. Although the computational cost of
evaluation of individuals is too large compared with other operations (including selection,
crossover, mutation and so on), when the scale
of feature selection problems becomes very
huge, the computational cost of the genetic operations except evaluation of individuals cannot
be negligible. If the genetic operations can be done in parallel, the computational cost will be
reduced apparently. As in the above discussion, the feature selection problem is essentially an
optimization problem. Currently, there are two realization modes for parallel optimization
based on genetic algorithm.
One kind of realization mode is to decompose the optimization problem into many sub-
problems; every sub-problem uses one GA with single population. The shortcomings of the
mode are in that it is hard to know whether the decomposition is reasonable, incorrect
decomposition will lead to bad performance usually. Hugo Silva and Ana Fred proposed one
parallel feature selection based on genetic algorithm [Hu, Y.-B et al]. They divided the whole
feature space (i.e. search space) into several
sub-feature spaces; each sub-feature space is
searched by one GA. The experimental results show that the method can effectively reduce
computational cost. However, the method has the following drawbacks: firstly, the correct
division of whole feature space is difficult. Secondly, when the feature space is very complex,
the distribution of local optima is not even. The feature space for each GA is not different, so
the search load for each processo
r is not even, the efficiency of parallel processing is not high.
Potter and De Jong [Potter, M. A et al] proposed one collaboration co-genetic algorithm.
They introduced a multi-population idea into the genetic algorithm to improve GA’s
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Agent-Based Genetic Algorithm for Global Numerical Optimization… 5
optimization performance. The algorithm divides whole feature space (search space) into
several sub-feature spaces and divides whole population into several independent
subpopulations with fewer variables. Each subpopulation searches for one optimal solution of
one sub-feature space independently. After that
, the optimal solutions of each sub-feature
space are combined together to construct a final solution (i.e. feature subset). However, it still
has some drawbacks: firstly, the algorithm only considers collaboration between
subpopulations but does not consider competition between subpopulations. Secondly, the
division of population into subpopulations is very challenging; maybe the division needs
enough relevant prior knowledge, so it is not convenient for practical application. Besides, the
false or not precise division will lead to false or not precise optimization result. Su and Hou
[Su, C.-H et al] proposed another multi-population genetic algorithm for the parameter
optimization problem. The GA has two subpopulations, each subpopulation optimizes
different object functions and two optimization results within one generation are obtained.
After that, the two results are put together to make an optimal full solution. The division
of population is dependent on the object function. If the object function can be divided into
two parts only, the population must be divided into two subpopulations and cannot be divided
into more than two subpopulations. The reduction of time cost is very limited. Another kind
of realization mode is to design one multi-population genetic algorithm, every subpopulation
searches for optimal full solution of whole search space in parallel. The method has the
following advantages: firstly, it is not necessary to divide the whole search space into several
sub search spaces. Secondly, the algorithm can make use of multi-population to search for
solution in parallel to reduce the computational cost. However, since it is not necessary to
divide the search space, for the same search
space, smaller population will lead to worse
precision. Apparently, the size of subpopulation is smaller than that of whole population.
Therefore, it is necessary to enhance the inte
raction between subpopulations to improve their
cooperation for optimization.
Based on the analysis above, MPAGAFS is very suitable for parallel feature selection
problems. The major reasons are as follows: firstly, it can have multiple subpopulations
according to different requirements. Secondly
, it can obtain satisfying feature selection
precision based on agent technology. Thirdly, based on shared agent, it can realize parallel
feature selection to speed up feat
ure selection speed. Fourthly, it is not necessary to divide the
feature space into feature subspace. As a matter of fact, it is very hard to correctly divide the
feature space into feature subspace.

2. CHAIN-LIKE AGENT GENETIC ALGORITHM FOR GLOBAL
NUMERICAL OPTIMIZATION AND FEATURE SELECTION

2.1. Analysis of Algorithm

2.1.1. Chain-Like Agent Structure
In the chain-like agent genetic algorithm, all the agents live in a chain-like
environment,L, which is called an agent chain. The size of L is1
size
L× , where
size
L is an
integer, 1 means one dimensional agent structure. Each agent is fixed on a chain-point and it
can only interact with its neighbors.
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Yongming Li, Xiaoping Zeng and Pin Wang 6
Definition: Assuming that the agent that is located at ()1,i is represented
as
1,
,1,2,,
isize
Li L=L , the neighbors of
1,i
L,
1,i
Neibors are defined as follows:

{ }
12
1, 1, 1,
,
iii
Neibors L L= (2-1)

where
1
11
1
size
ii
i
Li
−≠⎧
=⎨
=
⎩
，
2
1
1
size
size
iiL
i
iL
+≠⎧
=⎨
=
⎩
.

The agent chain can be described as the one in Figure 2.1. Each circle represents an
agent, the data in a circle represents its position in the chain, and the agent can interact with
the left neighboring one and the right neighboring one.
In traditionalGAs, those individual that will generate children are usually selected from
all individuals according to their fitness value. But in nature, a global selection does not exist,
and the real natural selection only occurs in a local environment, and each individual can only
interact with the neighboring ones. That is, the natural evolution is like a kind of local
phenomenon. The information can be shared globally only after a process of diffusion. For
description, the search algorithm is called as CAGA because of its chain-like agent structure.

Figure 2.1. Chain-like agent structure.

2.1.2. Selection Process Based on Dynamic Neighboring Competition Strategy
Definition of the energy: an agent, a, represents a candidate solution to the optimization
problem in process. The value of its energy is defined as follows:

()1, 1,
()
ii
Eng L fitness L= (2-2)

where ()fitness means the fitness value of some individual in the population. For
numerical optimization, ()fitnessmeans the corresponding function needing to be
optimization; for feature selection, it corresponds to some evaluation criteria.
As can be seen, each agent stands for an individual. In order to realize the local
perceptivity of agents, the environment is constructed as a chain-like structure as mentioned
above.
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Agent-Based Genetic Algorithm for Global Numerical Optimization… 7
Suppose that the current agent is located at()1,i, ()1, ,1 ,2 ,
,,,
iii in
Lll l= L .
()1, ,1 ,2 ,
,,,
iii in
Max m m m= L is the agent with maximum energy among the neighbors
of
1,i
L, where nmeans the number of genes.
,in
l means the nth gene of ith individual
1,i
L(that is chromosome),
1,n
m means the nth gene of
1,i
Max. That is,
1, 1,ii
Max Neibors∈ ,
and
1,i
a Neibors∀∈ , then () ( )1,i
Eng a Eng Max≤ .
If
1,i
L satisfies the formula (3), then it still live in the agent chain. Or else, it will die, and
its chain-point will be occupied by
1,i
New.

() ( )1, 1,ii
Eng L Eng Max≥ (2-3)

Dynamic competition strategy: during competition process,
the ()
12
1, 1, 1,
max ,
iii
Max L L= . The competition process is done in ascending order, after the
competition of the 1st agent, the 1st agent is updated. Assuming the ith agents before
competition and after competiton are
1,
pre
i
L and
1,
post
i
L respectively, so
1,i
Max is determined
by
()
()
()
1, 1, 1
1, 1, 1 1,1
1, 1 1, 1
max , 1
max ,
max ,
size
size
pre pre
Li
post post
i L size
post pre
ii
LL i
Max L L i L
LL else
+
−
−+
⎧ =
⎪
⎪
==⎨
⎪
⎪
⎩
(2-4)

with different coding strategy, the concrete selection process is a little different.

a) Discussion on Selection Process with Real Coding
Normally, the processs with real coding is for numerical optimization and is described as
follows:
For formula (3),
1,i
Max has two strategies to occupy the chain-point, and the strategies
vary based on competition probability
co
P. If ()0,1
co
UP <, the strategy 1 is selected; else,
the strategy 2 is selected.
Here, the ‘()0,1U ’ means a random number generator, it is realized with ‘rand’
generator. Regardless of the different ways,
1,i
Max first generates a new
agent, ()1, ,1 ,2 ,
,,,
iii in
New ne ne ne= L , and then
1,i
Max is put on the chain-point.
In strategy 1,
1,i
New is determined by

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Yongming Li, Xiaoping Zeng and Pin Wang 8
()( )
() ()
() ()
,,,,,
,,,,,,
,,,
1,1
1,1
1,1
ilk ik ik ik ilk
ik iuk ik ik ik iuk
ik ik ik
B mU ml B
ne B m U m l B
mU ml else
⎧ +−× − <
⎪⎪
=+−×−>⎨
⎪
+−× −
⎪⎩
(2-5)

where i means which agent in whole population; k means which dimension; l means the
lower bound; u means the upper bound;
,ik
m means the biggest value in the neighboring
agents of kth dimension;
,ik
l means the value of the current agent of kth dimension.
In strategy 2,
1,i
New is determined by

()
()
()
1
, ,
2
1
N
j
ik match match match com ik
j
ne p p p p m
−
=
⎛⎞
=+ ×− +×⎜⎟
⎝⎠
∑
, 2, ,j N=L (2-6)

where the
match
p means the inoculation probability, it is realized with
2
rand
;
com
p is
determined by ()
()
()
1
2
11
N
j
com match match match
j
pp pp
−
=
⎡⎤
=− + −⎢⎥
⎣⎦
∑
. During the concrete
realization, the corresponding formula is simplified, the number of parts is 2, that
is:
12
,,,
stnd
ik ik ik
ne ne ne=+ , where
1
,,
st
ik match ik
ne p m=× , ( )
2
,,
1
nd
ik match ik
ne p m=− ×
Here, two strategies play different roles. When
1,i
L is a loser, it perhaps has some useful
information, so occupying strategy 1 in favor of reserving some information of a loser. It puts
emphasis on exploitation. Strategy 2 aims to disassemble the
,ik
m into some parts, and
assemble the parts back into
,ik
ne. It has the function of random searching, but is better than
random searching in that it makes use of the information of a winner. It puts emphasis on
exploration.

b) Discussion on Selection Process with Binary Coding
Normally,the processs with binary coding is for feature selection and is described as
follows:
For formula (4), the way of
1,i
Max to occupy the chain-point is: compare
1,i
Max
and
1,i
L one gene bit by one gene bit. If
,,in in
lm= , the gene bit has no change, else, the value
of this gene bit is generated randomly, that means the value is 1 or 0 randomly.
The pseudo code is as follows:

for (
i=1:
size
L)
evaluate ()1,i
Eng L and ( )1,i
Eng Max;
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Agent-Based Genetic Algorithm for Global Numerical Optimization… 9
if () ( )1, 1,ii
Eng L Eng Max<
compare the gene bits of
1,i
L and
1,i
Max;
for (j=1: L) % assuming the number of genes is L
if the value of jth gene of
1,i
L and
1,i
Max is same
the value has no change;
else the value of the gene is generated randomly;
end
end
else
1,i
L has no change
end
end

From the procedure,
1,i
L is updated through the competition and cooperation of
1,i
L and
1,i
Max. If () ( )1, 1,ii
Eng L Eng Max< , to combine the good gene of both sides is helpful to
find the good chromosome, and to generate randomly the value of gene is helpful to keep
diversity and jump out of local trap. If () ( )1, 1,ii
Eng L Eng Max≥ ,
1,i
L no changes. That
shows the survival of the fittest. All of the operation is very similar to natural evolution.

2.1.3. Neighboring Crossover Process
Two crossover operators for binary coding and real coding are described here
respectively. Orthogonal crossover operator is used for real coding, and adaptive crossover
operator is used for binary codi
ng. Both the two operator is used between some agent and its
neighboring agents.

a) Neighboring orthogonal Crossover Operator with Real Coding
The orthogonal crossover operator was described in [8]. An orthogonal array can specify
a small number of individuals that are scattered uniformly in the search space; the orthogonal
crossover operator can generate a small but representative sample of potential individuals. In
CAGA, this operator is performed between
1,i
L and
1,i
Max to achieve the both sides’
cooperation. Combing this paper, the design of this operator is described briefly as follows,
and for details, please see [5]. The brief description can be found in appendix.
Assuming that the search space defined by
1,i
L and
1,i
Max is
,,
,
il iu
xx⎡ ⎤
⎣ ⎦
as follows:

() ( ) ( )()
()( ) ( )()
,,1,1,2,2 ,,
,,1,1,2,2 ,,
min , ,min , , ,min ,
max , ,max , , ,max ,
il i i i i in in
iu i i i i in in
xlmlm lm
xlmlm lm
⎧=
⎪
⎨
=⎪
⎩
L
L
(2-7)

The domain of the bth dimension is quantized into
2
,1 , 2 ,
,,
bb bQ
βββL as follows:

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Yongming Li, Xiaoping Zeng and Pin Wang 10
()
() ()
()
,,
,,
,,, 2
2
,, 2
min , 1
min , 1 2 1
1
max ,
ib ib
ib ib
b j ib ib
ib ib
lm j
lm
lm j jQ
Q
lm jQ
β
⎧ =
⎪
⎪ ⎛⎞−⎪
=+−⋅ ≤≤− ⎜⎟⎨
⎜⎟−
⎪ ⎝⎠
⎪
=
⎪⎩
(2-8)

Specially, we randomly generate 1F− integers
12 1
,,,
F
kk k
−
L such
that
12 1
1
F
kk k N
−
<<<< <L , and then create the following F factors for any
chromosome()
12
,,
n
axx x= L :

()
()
()
1
12
1
11
21
1
,
,
,
F
k
kk
kn
fxx
fxx
fxx
−
+
⎧=
⎪
⎪=⎪
⎨
⎪
⎪
=
⎪⎩
L
L
L
L
(2-9)

The
fth factor
f
f with
2
Q factor is determined as follows:

()( )
()()
()()
22 2
1 1,1 1 2 ,1 ,1
1 1,2 1 2,2 ,2
211,12, ,
1,,,
2,,,
,,,
ii i
ii i
ii i
fkk k
fkk k
fkQkQkQ
f
f
fQ
ββ β
ββ β
ββ β
−+ −+
−+ −+
−+ −+
⎧ =
⎪
⎪ =⎪
⎨
⎪
⎪
=
⎪⎩
L
L
L
L
(2-10)

The orthogonal matrix
()
2
2
2,
F
Mij
MF
LQ b
×
⎡⎤=
⎣⎦
is used to generate the following
2
M
chromosomes (here they are called as agents).

() () ()()
()() ( )()
()() ( )()
22 2
11,1 21,2 1,
12,1 22,2 2,
1,12,2 ,
,,
,,
,,
FF
FF
MMFMF
fb fb f b
fb fb f b
fb fb f b
⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
L
L
L
L
(2-11)

Finally, among the
2
M agents, the one with the biggest energy is selected to replace
1,i
L.
For simplicity and fast speed, in CAGA,
2
Q, F and
2
M are fixed at 2, 3 and 4, which is
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Agent-Based Genetic Algorithm for Global Numerical Optimization… 11
seen in [8]. Therefore, no parameter needs to be adjusted for this operator, and the orthogonal
array is()
3
4
2L , which is shown as follows:

()
3
4
111
122
2
212
221
L
⎡⎤
⎢⎥
⎢⎥=
⎢⎥
⎢⎥
⎣⎦
(2-12)

b) Adaptive Neighboring Crossover Operator with Binary Coding
In the crossover process, the crossover probability
,ci
p is calculated adaptively. The
corresponding formula is as follows:

'
1
'
(, )
'max
,
max
'
1
GH i i
i
ave
ci
ave
ave
ff
ff
p
ff
ff
⎧
⎛⎞−
⎪
⎪ ≥⎜⎟
=⎨ −
⎝⎠
⎪
<⎪⎩
(2-13)

here,
,ci
p means the probability of crossover about the crossover operation between the
1,i
L
and
1,i
Max,
'
(, )GH i i means the distance between the
1,i
L and
1,i
Max,
'
f means the
maximum value of both the individuals,
max
f means the maximum value of all the
individuals in the current population,
ave
f mean the average fitness value of all the
individuals. The crossover procedure is as follows:

if ()
,
0,1
ci
Up <
do single point crossover processing between
1,i
L and
1,i
Max
else keep
1,i
L no change.

2.1.4. Adaptive Mutation Process

a) Adaptive Mutation Operator with Real Coding
A new agent, ()
1, 1 2
,,,
in
New ne ne ne= L is generated as

()
,
,
1
0, 0,1
ik m
k
ik
lG U p
tne
lelse
⎧ ⎛⎞
+<⎪ ⎜⎟
= ⎝⎠⎨
⎪
⎩
(2-14)

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Yongming Li, Xiaoping Zeng and Pin Wang 12
where
m
p means mutation probability, ( )
10,G
t
is a Gaussian random number generator, t
is the evolution generation. According to [7], the suitable
m
p is advised to be set as1
n
.

b) Adaptive Mutation Operator with Binary Coding
In the crossover process, the mutation probability
m
p is calculated adaptively based on
the length of chromosome [Zbigniew Michalewicz et al]. The
m
p is determined by:
1
m
p
n
=,
where n means number of genes, namely the length of chromosome.
The crossover procedure is as follows:

if ()0,1
m
Up <
do single point mutation processing between
1,i
L (namely, some gene changes its value
from 1 to 0 or vice versa randomly)
else keep
1,i
L no change

2.1.5. Stop Criterion
ave
f can reflect the evolution of the current population.
best
f stands for the best average
fitness value since beginning.
stop
k means a counter, it counts the number that
best
f has no
change. If
stop
kk>, the search stops. The setting of k is described in section 3.

2.1.6. Elitism Strategy
Agents have knowledge which is related with the problem that they are designed to solve.
With elitism strategy, the agent can inherit the good solution from the former generation. This
method can make the best solution within ith generation better than or equals to the best
solution in the former ()1i−generations. In order to avoid repetition, the detailed operation
is omitted here; it can be found in section 2.6.

2.1.7. Realization of Algorithm
In CAGA, the neighborhood competition operator is performed on each agent. As a
result, the agents with lower energy are cleaned out from the agent chain so that there is more
developing space for the promising agents. The neighboring crossover operator and the
mutation operator are performed on each agent respectively. At the end of ith generation, the
best agent in this generation competes with the best agent in ()1ith− generation, and
t
best
ind(the best agent during t generations’ evolution) is updated. The algorithm in this
paper is described as follows:
Algorithm for dynamic chain-like agent genetic algorithm %
t
L represents the agent
chain in the tth generation, and
13t
L
+
and
23t
L
+
are the mid-chains between
t
L and
1t
L
+
,
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Agent-Based Genetic Algorithm for Global Numerical Optimization… 13
t
end
Lis the agent chain after mutation processing in the tth generation.
t
best
ind is the best
agent among { }
01
,,
t
LL LL , and
ct
best
ind is the best agent in
t
L.
c
p and
m
p are the
probabilities to perform the neighboring crossover processing and the mutation processing.
Step1: initialize
0
L, update
0
best
pop, and0t←;
Step2: do dynamic neighboring competitive selection processing and update
t
L,
obtaining
13t
L
+
;
Step3: for each agent in
13t
L
+
, do crossover processing on it, obtaining
23t
L
+
;
Step4: for each agent in
23t
L
+
, do mutation processing on it, obtaining
t
end
L;
Step5: find
ct
best
ind in
t
end
L, and compare
ct
best
ind and
1t
best
ind
−
, if
() ()
1ct t
best best
Engind Engind
−
> , then
tct
best best
ind ind← , else,
1tt
best best
ind ind
−
← ,
1tt
end
LL
+
← .
Step6: if stop criterion is satisfied, then output
t
best
ind and stop, else1tt←+ , go to
Step 2.

2.2. Experimental Results

In order to verify the performance of CAGA pr
oposed in this paper, the authors realized
the algorithm with MATLAB and organized two groups of experiments. They include global
numerical optimization experiments and feature selection experiments of CAGA.

2.2.1. Global Numerical Optimization Experiments

a) Tested Functions
Numerical experiments are conducted to test the effectiveness and efficiency of the
CAGA.11 test functions from [23] are selected, for the purpose to demonstrate the robustness,
reliability and fast convergence capability of the presented algorithm.
Table 2.1 lists the eleven test functions and their key properties. These functions can be
divided into two categories approximately.
16
ff− are unimodal functions.
711
ff− are
multimodal functions with many local optima, and they represent the most difficult class of
problems for many optimization algorithms. General speaking, for unimodal functions the
convergence rates are of main interest while optimizing such functions to a satisfactory
accuracy is not a major issue.
However, for multimodal functions, the quality of the final results is more crucial since it
reflects the CAGA’s ability in escaping from local deceptive optima and locating the desired
global solution or near-global solution.

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Yongming Li, Xiaoping Zeng and Pin Wang 14
Table 2.1. List of 11 test functions (
min
f= minimum function value, SD = prescribed
search domain)

Test functions SD
min
f
()
2
1
1
n
i
i
fxx
=
=∑
[ ]100,100
n
− 0
()
2
1 1
nn
ii
i i
fxxx
= =
=+∑ ∏
[ ]10,10
n
− 0
() ()
2
3
11
nn
j
ij
fxx
==
=∑∑
[ ]100,100
n
−
0
() { }
4
max ,1
ii
fxxin=≤≤ [ ]100,100
n
− 0
() () ()
21 2
2
51
1
100 1
n
ii i
i
fx x x x
−
+
=
⎡⎤
=−+−
⎢⎥⎣⎦
∑
[ ]30,30
n
− 0
() ( )
2
6
1
0.5
n
i
i
fx x
=
=+∑
[ ]100,100
n
− 0
()
()
()
12
2
1
7 2
2
1
sin 0.5
0.5
1
1
1000
n
i
i
n
i
i
x
fx
x
=
=
⎛⎞
−
⎜⎟
=− +⎜⎟
⎜⎟ +
⎝⎠
∑
∑
[ ]100,100
n
− -1
() ()8
1
sin
n
ii
i
fxxx
=
=−∑
[ ]500,500
n
−
-
418.95n
() ( )
2
9
1
10cos 2 10
n
ii
i
fx x x π
=
⎡⎤=− +
⎣⎦∑
[ ]5.12,5.12
n
− 0
()
2
10
11
11
20exp 0.2 exp cos 2
nn
ii
ii
fxxx
nn
π
==
⎛⎞ ⎛⎞
=− − −⎜⎟ ⎜⎟⎜⎟
⎝⎠⎝⎠
∑∑

20e++
[ ]32,32
n
− 0
()
2
11
1 1
1
cos 1
4000
nn
i
i
i i
x
fx x
i
= =
⎛⎞
=− +
⎜⎟
⎝⎠
∑ ∏

[ ]600,600
n
−
0

Figure 2.2 shows some test functions listed in Table 1. As the figure shows, the function
3 and function 5 has one global optima. It is not hard to find out the global optima, however,
the searching speed is an important index to tell which algorithm is better. The function 8 and
function 9 has a lot of local optima, which trap optimization method. It is hard to find out the
global optima or near-global optima. The closer to the global optima, the better the algorithm
will be.

b) Optimization Results and Analysis
The compared genetic algorithms are genetic algorithm with elitism strategy (SGAE)
[24], adaptive genetic algorithm (AGA) [6], survival of the fittest genetic algorithm (FSGA)
[25] and lattice-like agent genetic algorithm (MAGA) [13].

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Agent-Based Genetic Algorithm for Global Numerical Optimization… 15

(a)

(b)
Figure 2.2. Some tested functions: (a) unimodal functions; (b) multimodal functions.
CAGA is realized to compare with some popular genetic algorithms. It is note that the
CAGA here adopts genetic operators for real coding, they are: selection operator for real
coding, crossover operator for real coding, mutation operator for real coding.
The operation platform is a CPU with main frequency of 1.54GHz, memory of 256 MHz.
Besides, the stop criterion is that if30k>, then quit optimization. Here, k means the times
that the difference between ith generation and ()1ith+ generation is smaller than
5
10
−
.
Initial population has 64 individuals. Here, for CAGA, the initial 0.95
c
p= ,
initial0.05
m
p= . The number of dimensions is 2, though it is low, but the advantage of
CAGA over some other algorithms is apparent.
Table 2.2 shows the optimization performances of the SGAE, SFGA, AGA, MAGA and
CAGA. For showing the optimization capability of the algorithms statistically, we compared
the average optimization results of the different algorithms for different benchmark functions,
the corresponding performance indices are average global optima (AGO), the number of
generation when global optima occurs (NGO), the average number of generation when
optimization stops (AOS), average running time (ART), respectively. The functions and
indices include expression of functions, corresponding prescribed search domain, and normal
global optima.
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Yongming Li, Xiaoping Zeng and Pin Wang 16
Table 2.2. The comparison of the optimization performances of the SGAE, SFGA, AGA,
MAGA and CAGA

SGAE MAGA CAGA AGA SFGA
F1=x1^2+x2^2
[-100,100]
0
1.3740 0 0 1.1137 1.4767
122.9000 43.7143 52.4600 9.3600 3.9200
148.9600 73.7143 82.4600 38.3600 32.9200
1.3475 6.30968 8.0372 0.24594 1.3153
F2=|x1|+|x2|+x1*x2
[-10,10]
0
0.1449 0 0 1.2310 1.6935
114.7600 44.5918 61.6000 12.9000 5.6000
143.6400 74.5918 91.6000 41.9000 34.6000
1.28594 6.42312 8.91626 0.22374 1.0428
F3=x1^2+(x1+x2)^2
[-100,100]
0
1.0563 5.1505e-
010
0 1.1074 1.6654
102.4600 45.6735 56.1400 7.0400 4.3200
131.4600 75.6735 86.1400 36.0400 33.3200
0.76968 6.53782 8.445 0.22688 1.32718
F4=maxi{|xi|} 1<i<2
[-100,100]
0
4.6885 0 0 4.8838 5.9008
41.2000 45.1224 57.5600 23.1400 15.7600
70.2000 75.1224 87.5600 52.1400 44.7600
0.38156 6.51314 7.86438 0.33312 1.7072
F5=100*(x2-x1^2)^2+(x1-1)^2
[-30,30]
0
0.2573 0 0 4.3024 4.6860
80.5600 75.4286 86.2800 20.5200 7.4600
109.5600 105.4286 116.2800 49.5200 36.4600
0.62406 9.1722 11.3547 0.35814 75.1560
F6=(x1+0.5)^2+(x2+0.5)^2
[-100,100]
0
1.3329 0 0 1.0087 1.4367 3.5000 45.6531 59.8400 7.6000 3.3000
32.5000 75.6531 89.8400 36.6000 32.3000
0.2047 6.52812 8.7497 0.23468 1.21314
F7=-[0.5+[sin((x1^2+x2^2)^0.5)-0.5]/
[1+0.001*(x1^2+x2^2)]^2]
[-100,100]
-1
-0.9352 -0.9846 -0.99755 -0.9371 -0.8603
56.8500 94.8163 74.8400 43.0200 50.9400
80.7500 124.8163 104.8400 66.4600 71.0200
0.46906 10.9375 10.37626 0.39782 2.75156
F8=-x1*sin(sqrt(abs(x1)))
- x2*sin(sqrt(abs(x2)))
[-500,500]
-837.9
-706.0390 -828.2973 -837.8658 -747.7160 -737.0889
44.9800 117.7143 112.2200 65.5200 68.4400
73.4200 147.7143 142.2200 93.6800 95.8000
0.5575 12.93406 14.07406 0.65468 4.13062
F9=x1^2-10*sin(2*pi*x1)+10
+x2^2-10*sin(2*pi*x2)+10
[-5.12,5.12]
0
5.5149 0.0406 1.5298e-
008
4.4161 5.5959
22.7200 86.2653 92.7400 20.1800 25.3200
51.7200 116.2653 122.7400 49.1800 54.3200
0.4325 10.26564 12.24624 0.42312 2.43094
F10=-20exp(-0.2*sqrt(0.5*(x1^2+x2^2)))
-exp(0.5*(cos(2*pi*x1)+cos(2*pi*x2)))
+20+exp(1)
[-32,32]
0
1.3519 9.0894e-
006
8.8818e-
016
4.2009 5.3490
122.4600 65.6939 76.9400 41.2000 55.2800
151.3400 95.6939 106.9400 70.2000 84.2800
1.1022 8.35094 10.57626 0.52532 3.47064
F11=0.00025*(x1^2+x2^2)
-cos(x1/sqrt(1))*cos(x2/sqrt(2))+1
[-600,600]
0
0.1578 0.0195 0 1.9650 2.5915
103.3600 115.2857 53.6400 6.9200 4.9800
131.3200 145.2857 83.6400 35.9200 33.9800
1.0397 12.8275 8.29532 0.36874 1.58
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Agent-Based Genetic Algorithm for Global Numerical Optimization… 17
As can be seen from Table 2.2, the optimization results of CAGA is better than those of
SGAE, AGA, and SFGA very much, is better than those of MAGA apparently. Since the
optimization results are the average values under 50 times run of algorithms, they can show
the robustness and reliability of CAGA are strong. For most of the functions, the convergence
of CAGA is the fastest. The subsequent experimental results can support this point.
Figure 2.3 shows the evolution curves (the best individual versus number of generations)
of different algorithms for part of tested functions. In the figure, ‘chain’ stands for CAGA,
‘lattice’ stands for MAGA, ‘adaptiveSGA’ stands for SGAE, ‘adaptive PCPM’ stands for
AGA, ‘haiming’ stands for SFGA.
Figures 3 shows, regardless of unimodal and multimodal functions, the convergence of
CAGA is the fastest among the five algorithms. The optima that CAGA can reach is closest to
the global optima, and CAGA usually is the fastest one to reach the global optima or near
global optima.

(a) (b)

(c) (d)
(Abscissa = number of generations; Vertical axis=function value).
Figure 2.3. The evolution curves of different algorithms for different functions: (a) function 4; (b) the
magnification effect of function 4; (c) function 8; (d) the magnification effect of function 8.
Besides, the number of generation when CAGA reach the desired near-global optima is
the smallest among the algorithms. The convergence capabilities of MAGA and CAGA are
close, but the latter is better than the former apparently.
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Yongming Li, Xiaoping Zeng and Pin Wang 18
2.2.2. Feature Selection Experiments

a) Tested Databases and Experimental Conditions
The authors adopt two databases for comparison of feature selection capability of CAGA,
SGAE, AGA, and SFGA. We know that the feature selection means the search of the optimal
features combination through optimization method. Its essence is optimization, but the
difference between it and numerical optimization is apparent as we discussed in section 1.
Feature selections with genetic algorithm usually adopt binary coding; the kind of experiment
can verify the performance of genetic algorithms at another point. Because the MAGA was
described for real coding optimization, so this algorithm is not used for the comparison of
feature selection here. It is noted that the four genetic algorithms need to be coded using
binary coding strategy for being used for feature selection.
The databases are selected from popular international UCI database. The database 1 is
letter- recognition database; the number of features is 16, so it is a low dimensional database.
The class a and b are used, there are 789 specimens belonging class a, 766 specimens
belonging class b. The database 2 is waveform data
base; the number of features is 40, so it is
a high dimensional database. The class wave 0 and wave1 are used, there are 2000 specimens
belonging to class wave0 and wave1 respectively. The position of the database 1 is in
http://www.ics.uci.edu/~m
learn/databases/letter-recognition/ .The position of the database 2
is in http://www.ics.uci.edu/~mlearn/databases/waveform/ .
The corresponding experimental condition is: CPU: 3GHz, memory: 504MHz; for
comparison, the size of the populations of the four algorithms is 30; for SGAE,
initial0.65
c
p= , initial0.05
m
p= ; for SFGA, initial0.05
m
p
= , the
c
pis adaptive; for
AGA and CAGA, the
c
p and
m
p are adaptive. The stop criterion is 10k>.
The fitness function is determined by the evaluation criterion, and is made up of two parts
here, it is: discriminability-correlationfitness= . The fitness function below is adopted
for feature selection here:
Fitness function (evaluation criterion):
1
() 2
N
b
i
w
i
S
fitness corr
S
=
=−∑
, where, N is the
number of the features;
b
Smeans between-classes variance, ()
2
12b
Smm=− ;
1
m means the
first class specimens under some feature;
2
m means the second class specimens under the
same feature; ()()
22
12wclass class
Sσσ=+ ;2corr is correlation between features selected, and
is called as within-classes variance. Here, the 2corr is to calculate the correlation of the
features matrices of the two classes. 2corr is initialized as 0. The first step is to calculate the
correlation of the first feature vector and the second feature vector within the first class
p_corr1, then calculate the correlation of the first feature vector and the second feature vector
within the second class p_corr2, after that, the correlation of the first feature and the second
feature p_corr can be obtained with the formula: p_corr=(p_corr1+p_corr2)/2. The p_corr is
added to 2corr. With the same processing, the correlation of the second feature and the third
feature can be gotten and be added to the 2corr. The processing lasted until the correlation
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Agent-Based Genetic Algorithm for Global Numerical Optimization… 19
of the ()1Nth− feature and the Nth feature is obtained and is added to the 2corr. At this
time, the 2corr is obtained.

b) Comparison of Feature Selection Capability
Figure 2.4 shows that the searching capability of the four algorithms according to the
database 1. For showing the searching capability of them, the initial population is same. In the
figure, sga means SGAE，sga_zsypc means AGA，sga_haimin means SFGA，sga_chain
means CAGA.

Figure 2.4. The comparison of the searching capability for database 1.
Abscissa means number of generations, Vertical axis means fitness value. From the
figure, as can be seen, CAGA is the fastest one to get the near global optima, and the search
result through CAGA is most precise. The corresponding number of generations needed is the
smallest.

b-1). Comparison of CAGA and SGAE
Tables 2.3 and Table 2.4 show the feature selection capability of CAGA compared with
SGAE based on database 1 and database 2 respectively.
In these tables, ET means experimental times, NG means number of generations, NF
means number of selected features, SF means the selected features, BF means the best fitness
value, and RT means running time for feature selection. The abbreviation is suitable for the
latter tables. It is noted that practical experimental times is much more than 4, but because of
length problem of this paper, four of them ar
e listed in Table 3 and Table 4, the latter Tables
5,6,7 and 8 are the same case.

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Yongming Li, Xiaoping Zeng and Pin Wang 20
Table 2.3. Comparison of feature selection capability of SGAE and CAGA based on
database 1

ET SGAE CAGA
NG NF SF BF RT(s) NG NF SF BF RT(s)
1 15 10 1,7-12,14-
16
17.6629 13.7970 25 10 5,7-
12,14-
16
17.9449 33.2650
2 10 9 5,7-
9,11,12,14-
16
17.8082 7.6570 18 10 5,7-
12,14-
16
17.9449 21.5150
3 13 10 5-11,14-16 17.2461 11.5000 23 10 5,7-
12,14-
16
17.9449 30.1410
4 24 10 5,7-9,11-16 17.7079 17.9850 18 10 5,7-
12,14-
16
17.9449 22.3430

Table 2.4. Comparison of feature selection capability of SGAE and CAGA based on
database 2

ET
SGAE CAGA
NG NF SF BF RT(s) NG NF SF BF RT(s)
1 10 18 1,2,6,9-
12,14,17,18
,20,24,25,2
8,30,33-35
-0.1269 18.4060 60 14 9-
11,18,21,22
,27,28,31,3
3,34,36,37,
40
1.5467 92.391
2 10 22 6,8-
12,15,18,20
,22,24-
28,30,32-
35,37,38
-0.1596 20.1400 70 9 9-
11,20,21,28
,31,33,35
1.6144 81.157
3 10 17 1,4,9,11-
13,18,20,22
,24,26,28,3
1,34,38-40
0.0138 19.9690 16 14 2,10,11,17,
21-23,27-
29,33-
35,38
0.9615 25.313
4 10 23 8,10-12,17-
20,22-
34,36,37
0.0481 18.7810 76 7 9-
11,20,32,35
,38
1.6469 90.156

From these tables, we can see: for low dimensional feature selection, although the
number of features selected by two algorithms is similar, but the selection result of CAGA
has higher fitness value than that of SGAE, it is same and very stable all the 4 times
experiments. For high dimensional feature selection, the advantage of CAGA is very
apparent. The selection result of CAGA is much better than that of SGAE all the 4 times
experiments. The number of features of CAGA is much less than that of SGAE all the 4 times
experiments. It is noted that for the dimensional feature selection, the NG is 10. Because the
stop criterion is10k>, that means SGAE ends searching from the beginning, falling into
premature convergence.

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Agent-Based Genetic Algorithm for Global Numerical Optimization… 21
b-2) Comparison of CAGA and AGA
Table 2.5 and Table 2.6 show the feature selection capability of CAGA compared with
AGA based on database 1 and database 2 respectively.
From these tables, we can see: for low dimensional feature selection, although the
number of features from two algorithms is similar, but the selection result of CAGA has
higher fitness value than that of AGA, it is same and very stable all the 4 times experiments.
For high dimensional feature selection, the advantage of CAGA is very apparent. The
selection result of CAGA is much better than that of AGA all the 4 times experiments. The
number of features of CAGA is much less than that of AGA, even half of that of AGA all the
4 times experiments. It is noted that for the dimensional feature selection, the NG is 10.
Because the stop criterion is10k>, that means SGAE ends searching from the beginning,
falling into premature convergence.

Table 2.5. Comparison of feature selection capability of AGA and CAGA based on
database 1

ET AGA CAGA
NG NF SF BF RT(s) NG NF SF BF RT(s)
1 37 9 7-12,14-
16
17.6897 41.031 25 10 5,7-
12,14-16
17.9449 33.2650
2 44 10 5,7-
12,14-16
17.9449 50.078 18 10 5,7-
12,14-16
17.9449 21.5150
3 30 9 5-
9,11,12,
14,15
17.1921 19.484 23 10 5,7-
12,14-16
17.9449 30.1410
4 25 10 1,7-
12,14-16
17.6629 27.641 18 10 5,7-
12,14-16
17.9449 22.3430

Table 2.6. Comparison of feature selection capability of AGA and CAGA based on
database 2

ET AGA CAGA
NG NF SF BF RT(s) NG NF SF BF RT(s)
1 10 21 1-3,6,9-
11,13,16,18,20,
22,24-
27,29,31,33,34,
39
-
0.5034
18.531 60 14 9-
11,18,21,2
2,27,28,31
,33,34,36,
37,40
1.5467 92.391
2 10 21 1,3,8,10,11,17-
21,23,24,26,28,
30,31,34,36,38-
40
0.0130 19.859 70 9 9-
11,20,21,2
8,31,33,35
1.6144 81.157
3 11 17 6,9,11,13,14,17
,20,22,23,25-
27,33,35,37,39,
40
-
0.2093
20.500 16 14 2,10,11,17
,21-23,27-
29,33-
35,38
0.9615 25.313
4 10 14 6,7,9,11,12,17,
22,23,29,32,34,
36,37,39
-
0.0493
17.453 76 7 9-
11,20,32,3
5,38
1.6469 90.156
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Yongming Li, Xiaoping Zeng and Pin Wang 22
b-3). Comparison of CAGA and SFGA
Table 2.7 and Table 2.8 show the feature selection capability of CAGA compared with
SFGA based on database 1 and database 2 respectively.
From these tables, we can see: for low dimensional feature selection, although the
number of features from two algorithms is similar, but the selection result of CAGA has
higher fitness value than that of SFGA, it is same and very stable all the 4 times experiments.
For high dimensional feature selection, the advantage of CAGA is very apparent. The
selection result of CAGA is much better than that of SFGA all the 4 times experiments. The
number of features of CAGA is much less than that of SFGA, even half of that of SFGA all
the 4 times experiments. It is noted that for the dimensional feature selection, the NG is 10.
Because the stop criterion is10k>, that means SGAE endS searching from the beginning,
falling into premature convergence.

Table 2.7. Comparison of feature selection capability of SFGA and CAGA based on
database 1

ET SFGA CAGA
NG NF SF BF RT(s) NG NF SF BF RT(s)
1 24 10 5,7-12,14-
16
17.9449 29.9220 23 10 5,7-12,14-
16
17.9449 33.2650
2 20 8 7-11,13-15 16.7284 21.2970 18 10 5,7-12,14-
16
17.9449 21.5150
3 37 9 7-12,14-16 17.6897 40.3600 23 10 5,7-12,14-
16
17.9449 30.1410
4 23 10 5,7-12,14-
16
17.9449 29.7030 18 10 5,7-12,14-
16
17.9449 22.3430

Table 2.8. Comparison of feature selection capability of SFGA and CAGA based on
database 2

ET SFGA CAGA
NG NF SF BF RT(s) NG NF SF BF RT(s)
1 10 14 6,9,10,12,15,1
8,20,27-
30,32,36,37
-0.2151 32.0630 60 14 9-
11,18,21,2
2,27,28,31
,33,34,36,
37,40
1.5467 92.391
2 10 15 1 ,4 ,6 ,9
,11,13,19 ,21
,24 ,27,28 ,33
,37 ,38 ,40
-0.0087 25.5780 70 9 9-
11,20,21,2
8,31,33,35
1.6144 81.157
3 10 18 6,9,10,11,15,1
6,21-
27,30,32,36,3
7,40
0.4300 32.0630 16 14 2,10,11,17
,21-23,27-
29,33-
35,38
0.9615 25.313
4 10 18 1,3,5,6,9-
11,18,21,24,2
7,28,31-
33,35,38,40
0.2469 30.5460 76 7 9-
11,20,32,3
5,38
1.6469 90.156

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Agent-Based Genetic Algorithm for Global Numerical Optimization… 23
From the comparison of SGAE, AGA, SFGA and CAGA, we can know the major
advantages of CAGA. They are: CAGA can attain the best selection result, which is crucial
for numerical optimization and has much relationship with classification capability. The
selection result is the best stable. Usually, for many kinds of practical optimization problems
and pattern recognition problems, stable search
ing result is always agreeable. The number of
features selected by CAGA is much less than other genetic algorithms. The less the features
is, the simpler the complexity of the classifier will be, and the less the time of classification
will be.

c) Classification Experiments on the Feature Subset from Four Genetic Algorithms
Classification experiments on the feature subset from genetic algorithms are necessary.
Some parameters about classification can evaluate the performances of feature subsets.
Because the feature subsets are got from genetic algorithms, so these parameters can evaluate
the feature selection capability of the genetic algorithm.
BPNN is a kind of popular classifier. It has simple structure, fast classification speed, and
is easy to be realized, so it is widely applied in various kinds of feature selection researches.
Based on this, it is used in this paper for evaluating the feature subsets from the four genetic
algorithms.

c-1). Comparison of Classification Results Based on Database 1
Many times experiments of comparison of classification results of four genetic
algorithms based on database 1 are done. Table 2.9 lists two of them with same feature subset
to show the corresponding performance of the genetic algorithms.

Table 2.9. Comparison of classification results of four genetic algorithms based on
database 1

ET Parameters SGAE AGA SFGA CAGA
Number of features 10 10 9 10
Time for feature
selection (s)
11.500 27.641 40.3600 30.141
BPNN’s complexity 10*21*2 10*21*2 9*19*2 10*21*2
1 Training time 2.844 13.765000 3.828000 5.525
Test time 0.031 0.016000 0.032000 0.016
Total time 2.875 13.781 3.86 5.541

Classification rate R1 = 0.9100
R2= 0.9450
R
1 = 0.9100
R2 = 0.9900
R
1= 0.9050
R2 = 0.9950
R
1 = 0.9600
R2 = 1
Training step 4 29 7 10
2 Training time 5.219 3.953000 5.187000 3.218
Test time 0.016 0.016000 0.032000 0.016
Total time 5.235 3.969 5.219 3.281
Classification rate R
1 = 0.8850
R2 = 0.9900
R
1 = 0.9200
R2 = 0.9600
R
1 = 0.8600
R2= 0.9850
R
1 = 0.9250
R2= 0.9900
Training step 10 7 10 5

From Table 2.9, although the number of features from SGAE, AGA and CAGA is same,
but during two times experiments, the classification rate from CAGA is better than SGAE and
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Yongming Li, Xiaoping Zeng and Pin Wang 24
AGA. The test time from CAGA is shorter than the other three algorithms. As we know, the
two parameters (classification rate and test time) are very essential to pattern classification.
The better the classification rate is, the better the classification result will be; the shorter the
test time is, the faster the classification process will be. In the second experiment, under the
same training object(0.01)MSE= , the training step from CAGA is half of that of SGAE.
During the two times experiments, the training time, test time and training step of CAGA is
better than those of AGA. The training time and test time from CAGA and SFGA is similar,
but the classification rate of CAGA is better than that of SFGA. In the second experiment,
under the same training object, the training time, training step and test time of CAGA is half
of those of SFGA.

c-2). Comparison of Classification Results Based on Database 2
Many times experiments of comparison of classification results of four genetic
algorithms based on database 2 are done. Table 2.10 lists two of them with same feature
subset to show the corresponding performance of the genetic algorithms.
The data in Table 2.10 confirms the analysis on Table 9. Besides, the dimensional
reduction of CAGA is the best apparent among the four algorithms, the reduction is from 40
features to 15 features. The corresponding BPNN’s complexity of CAGA is the simplest
among the four genetic algorithms. During the two times experiment, the training time,
classification rate of BPNN based on the feature subset from CAGA is the best. It is noted
that with features increasing, from database 1 to database 2, the classification rates of the four
genetic algorithms fall down compared to databa
se 1, but for CAGA, the speed of decline of
classification rate is the slowest.

Table 2.10. Comparison of classification results of four genetic algorithms based on
database 2

ET Parameters SGAE AGA HMGA LAGA Number of features 22 22 18 15
Time for feature selection
(s)
20.1400 21.906 30.5460 53.3910
BPNN’s complexity 22*45*2 22*45*2 10*37*2 15*31*2
1
Training time 132.328 160.344000 125.203 45.797
Test time 0.016 0.015000 0.078 0.031
Total time 132.344 160.359 125.281 45.828
Classification rate R
1 = 0.7350
R
2= 0.8700
R
1 = 0.7150
R
2 = 0.7700
R
1 = 0.7600
R
2= 0.8450
R
1 = 0.8100
R
2 = 0.7850
Training step 21 27 37 25
2
Training time 126.407 153.109000 78.578 43.735
Test time 0.015 0.172000 0.016 0.015
Total time 126.422 153.181 78.594 43.75
Classification rate R
1 = 0.6850
R2 = 0.8800
R
1 = 0.7250
R2 = 0.8800
R
1 = 0.7600
R2 = 0.8300
R
1 = 0.8050
R2 = 0.8000
Training step 19 23 21 24

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Agent-Based Genetic Algorithm for Global Numerical Optimization… 25
2.3. Conclusions

In this section, one novel chain-like agent genetic algorithm (CAGA) has been proposed
based on chain-like agent structure and adaptive neighboring genetic operators. In order to
verify the performance of this kind of genetic algorithm, systematic global numerical
optimization experiments and feature selection experiments are done to show the CAGA can
be used both for real coding and binary coding. In the global numerical optimization
experiments, 11 benchmark functions was tested and compared with four popular genetic
algorithms, SGAE [Zbigniew Michalewicz et
al], AGA [M. Srinivas et al], SFGA [GONG
Dun-wei et al], and MAGA [Weicai Zhong et al]. The experimental results show that CAGA
can attain the more precise result than the four genetic algorithms. As we know, for numerical
optimization problems, the optimization result is of most importance. In the feature selection
experiments, two databases from UCI database are used for verifying the performance of
CAGA.
The compared genetic algorithms are SGAE, AGA, and SFGA. The experimental results
show that the feature subset from CAGA has higher and more stable classification rate than
other three GAs. At the same time, the corresponding classifier’s complexity is simpler. As
we know, for feature selection problems, the higher and stable classification rate will lead to
more precise and more reliable pattern recognition performance. The simpler classifier’s
complexity will lead to more reliable and more efficient pattern recognition algorithm. From
another point, the feature selection experiments show the satisfying optimization capability of
CAGA indirectly.
To summarize, CAGA obtains a good performance for both numerical optimization and
feature selection problems. This mainly benefits from chain-like agent structure and dynamic
neighboring genetic operators. The future work may include: 1, improve the CAGA itself to
get faster and more precise searching capabil
ity; 2, apply the CAGA in more applications.

3. MULTIPLE-POPULATION CHAIN-LIKE AGENT GENETIC
ALGORITHM FOR GLOBAL NUMERICAL OPTIMIZATION AND
FEATURE SELECTION

3.1. Analysis of Algorithm

3.1.1. Multi-Population Cycle Chain-Like Agent Structure
Multi-population cycle chain-like agent structure means that in terms of the position
information of agents, the whole population is divided into some sub-populations. The agents
inside sub-population are located in close chain-like agent structure and cooperate with each
other.
Each sub-population is connected with other sub-population through “shared agents” and
in the form of cycle chain-like agent structure; they cooperate with each other though sharing
the information of “shared agents”. Suppose the number of shared agents is S, the agent that
is located in the
jth node in the ith sub-population is expressed as
,ij
L, where
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Yongming Li, Xiaoping Zeng and Pin Wang 26
1, 2, ,iM=⋅⋅⋅ ，1, 2, ,j L=⋅⋅⋅ . The neighborhood domain of
,ij
L is defined
as: { }
12
,,,
,
ij ij ij
Neibors L L= , where

12
,,1
,,
,1 ,1
1
,
1
iL i
ij ij
ij ij
LLj jL
LL
LLj jL
−+
⎧⎧ ==⎪⎪
==⎨⎨
≠≠⎪⎪⎩⎩
(3-1)

Figure 3.1 shows the multi-population cycle chain-like agent structure with 6 agents per
sub-population and 2 shared agents. The motivation of the agents for evolution is to augment
their power, so they cooperate and compete with each other. Finally, the agent with low
power will die, and new agent will occupy its position.
Inside the sub-population, the cooperation and competition take place between the agent
and its neighbors, the introduction of the shared agents will supply the genetic information of
other sub-populations, thereby improving the efficiency of the evolution. Within the structure,
each ring represents a ring-like agent structure.
In the ring-like agent structure (close chain-like agent structure), all the agents live in a
close chain-like environment,L, which is called an agent ring. The size of L is1
size
L× ,
where
size
L is an integer, 1 means one dimensional agent structure. Each agent is fixed on a
ring-point and it can only interact with its neighbors.

3.1.2. Genetic Operators
The genetic operators within each subpopulation are similar to those in CAGA in section
2. Therefore, the corresponding description is omited.

Figure 3.1. Multi-population cycle chain-like agent structure.

3.1.3. Realization of Algorithm
The MPAGA algorithm can be described as follows. Please note, the algorithm can be
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Agent-Based Genetic Algorithm for Global Numerical Optimization… 27
Procedure of MPAGA
Notes: Suppose the best individual in the whole population in the ith generation is
_
i
best whole
ind , the
number of evolution counter is
_cnt whole
k , the upper boundary of
_cnt whole
k is TIMEs_OUT. The
stopping criterion here is as follows: compare the
_
i
best whole
ind and
1
_
i
best whole
ind
−
, if the difference of
them is lower than ε, the
_cnt whole
k is added with 1, or else, the
_cnt whole
k is updated with 0. When
the
_cnt whole
k equals to TIMEs_OUT, quit the whole evolution and output the final optimization.
Begin
Initialization: Randomly generate an initial population; (real coding for numerical optimization, binary
coding for feature selection)
Sub-population division: divide initial population into Msub-populations based on the size of L;
While(stopping criteria are not satisfied)
Each sub-population evolves respectivel
y based on principle of MPAGAFS_IN;
Judge whether all the sub-populations finish their one generation evolution, if so, the
M best
individuals are
obtained;
Judge the M best individuals and obtain the best individual in the whole population in the current
generation;
Implement Elitism strategy;
End While
End
Procedure of MPAGA_IN
Notes: In MPAGAFS_IN, the nei
ghborhood competition operator is applied on each agent. As a result,
the agents with lower energy are cleaned out from the agent chain so that there is more developing
space for the promising agents. The neighboring crossover operator and the mutation operator are
applied on each agent respectively. At the end of ith generation, the best agent in this generation
competes with the best agent in ()1ith− generation, and
t
best
ind(the best agent during t
generations’ evolution) is updated.
Begin
initialize
0
L, update
0
best
pop, and0t←;
While(stopping criteria are not satisfied)
If self adaptability enabled, then automatic change size of subpopulation; else do not change size of
subpopulation
do dynamic neighboring competitive selection processing and update
t
L, obtaining
13t
L
+
;
for each agent in
13t
L
+
, do crossover processing on it, obtaining
23t
L
+
;
for each agent in
23t
L
+
, do mutation processing on it, obtaining
t
end
L;
find
ct
best
ind in
t
end
L, and compare
ct
best
ind and
1t
best
ind
−
, if ( )()
1ct t
best best
Engind Engind
−
> ,
then
tct
best best
ind ind← , else,
1tt
best best
ind ind
−
← ,
1tt
end
LL
+
← .
Implement Elitism strategy;
End While
End
Comment:
t
L represents the agent chain in the tth generation, and
13t
L
+
and
23t
L
+
are the mid-
chains between
t
L and
1t
L
+
,
t
end
Lis the agent chain after mutation processing in the tth generation.
t
best
ind is the best agent among { }
01
,,
t
LL LL , and
ct
best
ind is the best agent in
t
L.
c
p and
m
p
are the probabilities to perform the neighboring crossover processing and the mutation processing.
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Yongming Li, Xiaoping Zeng and Pin Wang 28
used for both global numerical optimization and feature selection based on different coding
strategy and different genetic operators. But the agent genetic structure is same. For clarity, in
the experimental part, the MPAGA means the MPAGA algorithm for global numerical
optimization; the MPAGAFS means the MPAGA algorithm for feature selection.
The optimization precision and time cost are two important indices to show the
performances of optimization algorithms. Whether MPAGAFS can have better optimization
precision is still unknown. We did many modifications to enhance its optimization
performance: Dynamic neighborhood competition operator is similar to as the principle of
“good ones win and bad ones lose” in the nature. The individuals with high fitness values are
kept, the individuals with low fitness values are not kicked out simply, but are improved with
their neighbors to obtain new individuals, and the diversity of the whole population is kept
and enhanced. Neighborhood orthogonal operator can obtain different individuals as possible,
thereby keeping and enhancing the diversity of the population. Besides, with the shared
agents, the sub-populati
ons can share genetic information with each other, the optimization
precision can be assured. Besides, the optimization result obtained by any sub-population is a
full solution, so it is not necessary to consider how to combine the partial solutions into a full
solution, and the error occurred during combination of a full solution can be avoided.
However, the modifications can not prove its advantage of optimization precision directly.
Therefore, it is very necessary to verify
the optimization precision of the algorithm and
compare it with other popular GAs through empirical insights.

3.1.4. Computational Complexity
As we know, the MPAGAFS can realize parallel optimization. Suppose each CPU
(Computing Processing Unit) implements one sub-population, CPU shares genetic
information with other CPUs through shared agents. Compared with the time cost needed for
genetic operation, the time cost for exchanging genetic information is little and can be
neglected. Suppose the time cost needed by each sub-population is equal, the time cost with
each CPU should be average time costTimeAvg:
_nsub
Time
TimeAvg
k
= , where Time means the
time cost of whole population with MPAGAFS,
_nsub
k means number of sub-populations.
Suppose the time complexity of MAGA is()Ogp, if MPAGAFS is realized by multi-CPUs
in parallel, the time complexity of MPAGAFS is
_
()
nsub
gp
O
k
approximately, where g means
the generations of iteration, pmeans the size of whole population.

3.2. Experimental Results

3.2.1. Global Numerical Optimization Experiments
For the MPAGA, The size of sub-population and the number of shared agents are
adjustable. For fixed size of whole population, with the size of sub-population and the number
of shared agents changes, the number of sub-population changes. Table 3.1 shows the
possible number of sub-populations with different shared agents and size of sub-population.
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Agent-Based Genetic Algorithm for Global Numerical Optimization… 29
Here, we discuss the number of sub-populations, size of sub-population, and number of
shared agents based on one premise. The premise is that the whole population is same
(however, the size of whole population in the experiments in this paper varies from 63 to 66
because the number of sub-populations should be integer.).

Table 3.1. Number of sub-populations with different shared agents and size of sub-
population

Size of sub-population
4 6 8
Number
of shared agents
1 21 13 9
2 32 16 11
3 63 21 13

In the following experiments with section a), b), c), we set 6 as the size of sub-population
and 2 as the number of shared agents. The setup of the other parameters is as follows: the size
of whole population is 66, the probability of crossover is0.95
c
p= , the probability of
mutation is 0.05
m
P= , the upper limit of evolution generation is 1000T= ,
TIMEs_OUT=10. The relevant condition about PC platform is: CPU (central processing unit,
CPU) with mainframe of 2.8GHz, memory of 0.99GB.
In the experiments with section d), the size of whole population is 63-66; the size of sub-
population and the number of shared agents are adjustable. The other parameters of MPAGA
are same as those in section a),b) and c).
Some popular test functions were used in Table 3.2 for comparing MPAGA and MAGA
[Weicai Zhong et al].
15
ff− are unimodal functions,
69
ff− are multimodal functions with
many local optima (traps). The functions have a lot of local optima, which trap optimization
method. It is not easy to find out the global optima or near-global optima. It means that the
closer to the global optima, the better the algorithm will be.

a) Low Dimensional Optimization Experiments for MPAGA and MAGA
We used MPAGA and MAGA to optimize the tested functions listed in Table 3.2
respectively under 2 dimensions, the statistical results were obtained after 50 running times
and are listed in Table 3.3. The correspondi
ng performance indices are as follows: ‘Fave’
means average global optima, ‘Generation’ means the average number of generation when
optimization stops, ‘Time’ means average running time, ‘Time_Avg’ means average running
time for each sub-population or for each CPU (here, the Time_Avg is obtained by the
formula: Time_Avg = Time/kn_sub, where ‘Time’ means the time cost of whole population
with MPAGA, ‘kn_sub’ means number of sub-populations.)

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Yongming Li, Xiaoping Zeng and Pin Wang 30
Table 3.2. Test functions (
min
f is the relevant global optima，n is dimensions of test
functions, SD is searched domain)

Test functions SD
min
f
2
1
1
()
n
i
i
fxx
=
=∑
[ ]100,100
n
− 0
()
2
1 1
nn
ii
i i
fxxx
= =
=+∑ ∏
[ ]10,10
n
− 0
() ( )
2
3
11
nn
j
ij
fxx
==
=∑∑
[ ]100,100
n
− 0
() () ()
21 2
2
41
1
100 1
n
ii i
i
fx x x x
−
+
=
⎡⎤
=−+−
⎢⎥⎣⎦
∑
[ ]30,30
n
− 0
() ( )
2
5
1
0.5
n
i
i
fx x
=
=+∑
[ ]100,100
n
− 0
() ()6
1
sin
n
ii
i
fxxx
=
=−∑
[ ]500,500
n
− -418.95n
() ( )
2
7
1
10cos 2 10
n
ii
i
fx x x π
=
⎡⎤=− +
⎣⎦∑
[ ]5.12,5.12
n
− 0
()
2
8
11
11
20exp 0.2 exp cos 2
nn
ii
ii
fxxx
nn
π
==
⎛⎞ ⎛⎞
=− − −⎜⎟ ⎜⎟⎜⎟
⎝⎠⎝⎠
∑∑

20e++
[ ]32,32
n
− 0
()
2
9
1 1
1
cos 1
4000
nn
i
i
i i
x
fx x
i
= =
⎛⎞
=− +
⎜⎟
⎝⎠
∑ ∏
[ ]600,600
n
− 0

Table 3.3. The comparison of optimization performances of MPAGA and MAGA under
2 dimensions

Functions Fave Generati on Time(s) Time_Avg(s)
F1 MAGA 0 21.56 0.2889 0.2889
MPAGA 0 18.74 0.1715 0.0107
F2 MAGA 0 18.88 0.2643 0.2643
MPAGA 0 17.34 0.1531 0.0096
F3 MAGA 0 31.58 0.4313 0.4313
MPAGA 0 23.25 0.2754 0.0172
F4 MAGA 0 24.02 0.3182 0.3182
MPAGA 0 21.56 0.1912 0.0120
F5 MAGA 0 33.14 0.3665 0.3665
MPAGA 0 23.86 0.1902 0.0119
F6 MAGA -830.7986 23.02 0.3579 0.3579
MPAGA -837.9655 21.06 0.1881 0.0118
F7 MAGA 0 19.06 0.2682 0.2682
MPAGA 0 16.40 0.1332 0.0083
F8 MAGA 1.3546E-04 20.52 0.3268 0.3268
MPAGA 8.8818E-16 19.40 0.1596 0.010
F9 MAGA 6.3531E-06 33.14 0.3617 0.3617
MPAGA 0 22.82 0.1882 0.0118

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Agent-Based Genetic Algorithm for Global Numerical Optimization… 31
From Table 3.3, we can find that under low dimensions, the optimization of these
functions is not hard, so both the MPAGA and MAGA can find similar optimization
precision. For some test functions, the average optimization precision of MPAGA is better
than MAGA slightly. For most of test functions, the average running time of MPAGA is
shorter than that of MAGA. These advantages of MPAGA are mainly in that: firstly, the
whole population is divided into several sub-populations, the genetic operation becomes
simpler, the relevant time is shortened. Secondly, within each sub-population, the number of
neighboring individuals is changed from 4 to 2, the relevant genetic operation becomes less,
the relevant time cost will become less, besides, the possibility of some individuals with high
fitness value occupying the whole population over early becomes lower, that means the
average optimization precision will become higher. Thirdly, the ring-like agent structure
allows the genetic information propagate along the ring, which means for each sub-
population, all the individuals in the sub-population communicate with other individuals. Just
with some individuals, the whole sub-population can exchange genetic information with other
sub-populations; the relevant genetic operation becomes less. Besides, if multi-CPU is used
for realizing MPAGA, the time cost can be reduced greatly. For example, for test function 1
in Table 3, the time cost by MAGA is 0.2889s, but the time cost by MPAGA can be reduced
to 0.0107s.

b) Middle and high dimensional optimization experiments for MPAGA and MAGA
The following experiments will increase the relevant dimensions: 10 dimensions (see
Table 3.4), 50 dimensions (see Table 3.5) and 100 dimensions (see Table 3.6) respectively.
The experimental conditions are similar as the low dimensional optimization experiments
(section a)).

Table 3.4. The comparison of optimization performances of MPAGA and MAGA under
10 dimensions

Functions Fave Generation Time(s) Time_Avg(s)
F1 MAGA 0.0348 170.12 34.5610 34.5610
MPAGA 0 103.74 33.3356 2.0845
F2 MAGA 5.6284E-03 98.80 47.5678 47.5678
MPAGA 0 60.24 9.6899 0.6056
F3 MAGA 0 223.80 41.3884 41.3884
MPAGA 0 96.18 17.0630 1.0664
F4 MAGA 0.0487 35.34 5.6720 5.6720
MPAGA 0 25.88 5.0711 0.3169
F5 MAGA 6.2090E-04 121.80 27.5191 27.5191
MPAGA 3.6997E-04 69.06 11.0977 0.6936
F6 MAGA -4142.4523 55.96 8.7537 8.7537
MPAGA -4189.8288 26.26 5.1152 0.3197
F7 MAGA 2.8199 19.38 3.8778 3.8778
MPAGA 0 19.02 3.2012 0.2001
F8 MAGA 2.6645E-15 32.06 5.0166 5.0166
MPAGA 2.6645E-15 27.10 4.9408 0.3088
F9 MAGA 9.0790E-05 88.64 14.6815 14.6815
MPAGA 1.3125E-15 33.76 6.5163 0.4073

Agent-Based Computing, edited by Duarte Bouca, and Amaro Gafagnao, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,
Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

Yongming Li, Xiaoping Zeng and Pin Wang 32
Table 3.5. The comparison of optimization performances of MPAGA and MAGA under
50 dimensions

Functions Fave Generation Time(s) Time_Avg(s)
F1 MAGA 0. 2701 137.21 77.0603 77.0603
MPAGA 0 131.74 43.9468 2.7467
F2 MAGA 0.2308 115.22 58.2455 58.2455
MPAGA 0.0458 71.24 10.1208 0.6326
F3 MAGA 0.1829 256.80 72.3721 72.3721
MPAGA 0.0857 120.18 27.1920 1.6995
F4 MAGA 0.4902 85.56 12.6649 12.6649
MPAGA 0.2189 42.58 9.8881 0.6180
F5 MAGA 0.0826 132.55 34.5729 34.5729
MPAGA 8.5706-03 76.02 12.9335 0.8083
F6 MAGA -18242.8878 328.74 49.7018 49.7018
MPAGA -20949.1382 27.82 6.0478 0.3780
F7 MAGA 2.6436 102.46 16.0618 16.0618
MPAGA 0 19.22 4.2118 0.2632
F8 MAGA 0.7002 108.68 16.7660 16.7660
MPAGA 2.6645E-15 27.22 5.0971 0.3186
F9 MAGA 0.6658 270.70 42.2037 42.2037
MPAGA 0.3342 35.66 6.8683 0.4293

Table 3.6. The comparison of optimization performances of MPAGA and MAGA under
100 dimensions

Functions Fave Generation Time Time_Avg(s)
F1 MAGA 0.2885 189.25 89.1607 89.1607
MPAGA 0.0016 181.87 58.4607 3.6538
F2 MAGA 0.3826 151.22 58.1181 58.1181
MPAGA 0.3431 121.30 37.5848 2.3491
F3 MAGA 0.2436 355.80 104.5901 104.5901
MPAGA 0.0969 128.18 42.8617 2.6789
F4 MAGA 0.5569 626.12 224.9085 224.9085
MPAGA 0.0699 96.53 30.0899 1.8806
F5 MAGA 0.3086 161.23 60.3687 60.3687
MPAGA 0.0107 81.20 17.5182 1.0949
F6 MAGA -33803.1422 339.96 128.5109 128.5109
MPAGA -40608.4975 28.10 10.6249 0.6641
F7 MAGA 0.6903 145.40 61.2187 61.2187
MPAGA 0 19.26 8.4375 0.5273
F8 MAGA 1.5877 127.26 43.4392 43.4392
MPAGA 2.6645E-15 28.32 9.9617 0.6226
F9 MAGA 0.7911 356.60 158.0647 158.0647
MPAGA 0.4087 48.54 13.7845 0.8615

With dimensions increasing, the coupling degree of variables becomes stronger, the
relevant optimization becomes more and more complex. The advantage of MPAGA becomes
more and more apparent. It means that for those high dimensional complex test functions,
MPAGA can obtain better optimization performance.
Agent-Based Computing, edited by Duarte Bouca, and Amaro Gafagnao, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,
Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

Agent-Based Genetic Algorithm for Global Numerical Optimization… 33
From the tables, it is seen that for high dimensional functions, MPAGA has satisfied
optimization precision. With dimensions increasing, the optimization precision falls down to
some degree. It is because the increase of dimensions will lead to the increase of coupling
degree of variables, at the same time, the search space will increase in positive proportion,
approximately as
1
()
n
ii
i
ul
=
−∏
. However, MPAGA still can find the more precise optimization
results than MAGA. For example, for high dimensional multimodal functions
678
,,fff, the
results can show that MPAGA can have good global optimization capability for those high
deceptive and multi-trap optimization problems. The reasons for the improvement are the
similar as the analysis in section a). The ring-like (that is close chain-like) agent structure
decreases the number of the neighboring individuals from 4 to 2, thereby reducing the
probability of some individuals with high fitness value occupying the whole population over
early, the diversity of population is kept. The structure is more effective for those functions
with multi-local optima than lattice-like agent structure adopted in [Weicai Zhong et al].
Besides, the dynamic neighboring selection operator, neighboring crossover operator and
adaptive mutation operator can contribute to th
e improvement. As similar as the section a), if
multi-CPU is used for realizing MPAGA, the time cost can be reduced greatly.

c) Analysis of Convergence Performance
In order to show the convergence performance of MPAGA and compare it with MAGA,
several test functions listed in Table 3.2 were tested under several dimensions. Figure 3.2
show the convergence performance of MPAGA and MAGA for function
7
f, the experimental
condition is similar to section a) and section b). The function
7
f is complex high deceptive
multimodal function, and very suitable for testing optimization performance. In Figure 3.2,
lattice means MAGA, cell means MPAGA.
From Figure 3.2, convergence curve can be divided into two parts: the fast falling part
(part 1) that can be looked as global searching part and the slow falling part (part 2) that can
be looked as local searching part. In the part 2, the diversity of population is very strong; the
major task is to fix the optimal area. If the global searching capability of some algorithm is
not strong, it is easy for this algorithm to fall into local trap.
If the diversity of population can be kept well, it is easy to jump out of local trap to locate
the global optima or near global optima. In the part 1, more strongly the fitness value
changes, the better the global searching capab
ility of this algorithm will be. From Figure,
under several dimensions, MPAGA show its good convergence performance. Taking Figure
5(d) as example, the part 1 is within 5 generations, but the part 1 of MAGA is extended to be
50 generations. The speed of converging of MPAGA is faster than that of MAGA in part1. It
means MPAGA can have better global searching capability, especially for those high
deceptive mulitmodal functions. For function
7
f, there are many local optima, and the local
optima are very close, so the optimization of the function belongs to high deceptive problem.
From the experimental results, MPAGA shows its good global searching capability. Part 2
can be looked as local searching part, good algorithm should can tell different local optima
within local searched area. For MPAGA, its
neighboring selection operator and crossover
operator keep the individuals different each other as much as possible, thereby effectively
Agent-Based Computing, edited by Duarte Bouca, and Amaro Gafagnao, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,
Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

Yongming Li, Xiaoping Zeng and Pin Wang 34
distinguish different optima. Besides, the adaptive mutation operator can reduce the search
area gradually, thereby improving the searching precision and saving searching time. For
7
f
under 100 dimensions, the part 2 of MPAGA is 15 generations (from 5
th
generation to 20
th

generation), but the part 2 of MAGA is 45 generations (from 50
th
generation to 95
th

generation). It means MPAGA has better local searching capability than MAGA.

(a) (b)

(c) (d)
Figure 3.2. The comparison of convergence performance of MPAGA and MAGA under different
dimensions (a)2 dimensions; (b)10 dimensions; (c)50 dimensions; (d)100 dimensions.

d) The study of the Number of Shared Agents and Size of Sub-Populations
Through the experiments above, the optimization capability of MPAGA have been
verified. The major reason that sub-populations can co-evolve is that they can exchange
genetic information each other through shared agents, so it is necessary to study the number
of shared agents. In order to study the relationship between the number of shared agents and
optimization capability, different numbers of shared agents are adopted; they are 1, 2 and 3.
The size of sub-population is 6; the setup of the other parameters is similar to the experiments
above. The test functions are
6, 7 8 9
,,ffff (100 dimensions). The relevant data can be seen in
Agent-Based Computing, edited by Duarte Bouca, and Amaro Gafagnao, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,
Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

Agent-Based Genetic Algorithm for Global Numerical Optimization… 35
Table 3.7. Time_Avg means the average running time for each CPU if the MPAGA is
realized by multi-CPUs in parallel. From Table 3.7, it can be seen that with the number of
shared agent increasing, the optimization result doesn’t change apparently.

Table 3.7. The study of the number of shared agents (
6789
,,,ffff) under 100
dimensions

Test
functions
Number of
shared agents
Fave Generation Ti me (s) Time_Avg(s)
6
f
1 -39579.9123 27.36 8.2950 0.6381
2 -41898.2764 27.96 10.0545 0.6284
3 -41898.2764 24.3 11.9221 0.5677
7
f
1 0 19.04 6.5301 0.5023
2 0 19.28 7.4118 0.4632
3 0 19.06 9.5652 0.4555
8
f
1 2.6645E-15 27.4 8.2002 0.6308
2 2.6645E-15 25.3 9.6714 0.6045
3 2.6645E-15 25.3 12.0773 0.5751
9
f
1 0 32.3 6.2574 0.4813
2 0 40.3 7.6745 0.4797
3 0 40.3 9.8522 0.4692

Within the sub-population, the genetic information is propagated along ring, so any
individual can obtain the information, so theoretically, one shared agent can exchange genetic
information between different sub-populations. That is why different number of shared agent
leads to similar optimization precision. Secondly, from the Time_Avg, we can find out, with
the number of shared agents increasing, the time cost needed by each sub-population
decreases. For example, for test function
6
f, when number of shared agents increases from 1
to 2, the Time_Avg decreases from 0.6381s to 0.6284s. When number of shared agents
increases from 2 to 3, the Time_Avg decreases from 0.6284s to 0.5677s. It is because the
increase of shared agents can quicken the propagation of genetic information between sub-
populations. However, from Table 3.1, we know that with number of shared agents
increasing, number of sub-populations increases accordingly. It means more CPUs are
needed, more computational resource is needed. Therefore, number of shared agents can not
be too many or too few; suitable number of shared agents should be made certain based on
practical application. Figures 3.3, 3.4, 3.5 show the convergence performance of MPAGAs
with different number of shared agents and compare them with MAGA.
In the figures, lattice stands for MAGA, cellga-6-1 stands for MPAGA whose size of sub-
population is 6 and whose number of shared agents is 1, cellga-6-2 stands for MPAGA whose
size of sub-population is 6 and whose number of shared agents is 2, cellga-6-3 stands for
MPAGA whose size of sub-population is 6 and whose number of shared agents is 3.

Agent-Based Computing, edited by Duarte Bouca, and Amaro Gafagnao, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,
Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

Yongming Li, Xiaoping Zeng and Pin Wang 36
0 5 10 15 20 25 30 35 40 45 50
-4500
-4000
-3500
-3000
-2500
-2000
-1500

lattice
c ellga-6-1
c ellga-6-2
c ellga-6-3

0 10 20 30 40 50 60
0
10
20
30
40
50
60
70

lattice
cellga-6-1
cellga-6-2
cellga-6-3

(a) (b)
0 5 10 15 20 25 30 35 40 45 50
0
2
4
6
8
10
12
14
16
18
20

lattice
cellga-6-1
cellga-6-2
cellga-6-3
0 10 20 30 40 50 60 70
0
20
40
60
80
100
120
140
160
180

lattice
cellga-6-1
cellga-6-2
cellga-6-3

(c) (d)
Figure 3.3. Comparison of different shared agents according to test functions
6789
,,,ffff under 10
dimensions: (a)
6
f; (b)
7
f; (c)
8
f; (d)
9
f.
From the figures, it can be seen: firstly, with the number of shared agent increasing, the
optimization result doesn’t change apparently. Both the three kinds of MPAGAs can obtain
the global optima or near global optima better than MAGA. Secondly, with number of shared
agents increasing, the conver
gence speed quickens. In other words, in most cases, the
convergence speed of the MPAGA whose number of shared agents is 3 is fastest; it can reach
the near global optima area most quickly. It is because the increase of shared agents can
quicken the propagation of genetic information between sub-populations.
Tables 3.8, 3.9 and 3.10 show the optimization performance with different number of
sub-population under two kinds of dimensions. The relevant test functions are
6, 7 8 9
,,
ffff .
From the tables, we can see that: firstly, with size of sub-population increasing, the time
cost needed by each sub-population increases. It is because the individuals within one sub-
population increases, time complexity increases accordingly. Secondly, with size of sub-
population increasing, the optimization precision does not change apparently. It is because for
different size of sub-population, the size of whole population is same or similar. Thirdly,
when the number of shared agents is fixed, with size of sub-population increasing, average
time needed by each CPU increases, but number of CPUs decreases accordingly. Therefore,
Agent-Based Computing, edited by Duarte Bouca, and Amaro Gafagnao, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,
Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

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Parlando della Sicilia (scrive l'avv. Locatelli), «È impossibile
immaginare l'immoralità che dovevano spargere nelle classi povere
quelle parecchie migliaia di religiosi, provvisti di ricchezze, di
influenza, oziosissimi, e dotati dello spirito ardente e della vivissima
sensualità dei popoli meridionali. Per essi erano peccati perdonabili la
seduzione, l'adulterio, e persino anche l'incesto. L'assassino, che
rivelava al confessionale il proprio misfatto, e che cercava scusarsi
adducendo l'offesa ricevuta, il danno patito, la estrema sua miseria,
veniva non solo assolto, ma per di più esonerato dal darne scarico
alla giustizia umana, quand'anche questa avesse colpito per isbaglio
un innocente invece sua. Il testimone che taceva al giudice la verità,
per evitarsi un pericolo, per non compromettere il prossimo, era del
pari sicuro di riconciliarsi con Dio coll'intermezzo del confessore. Il
ricco, che teneva le proprie donne in continua clausura per una
gelosia veramente turca, era compatito se attentava alla onestà della
figlia del popolo. Un uomo infine potea francare la coscienza di un
falso, di un peculato, pagando alla chiesa 32 lire e 80 cent.
Pochi secoli sono i grandi vicari generali delle più cospicue città
concedevano il permesso di commettere adulteri per un anno intero:
in altre si potea aver licenza di fornicare impunemente per tutta la
vita: pagando un quarto di vino all'officiale vescovile, che ne
attingeva il diritto nelle decretali del papa: nel canone De
Dilectissimis. Si ebbe l'audacia di presentare supplica a papa Sisto IV
per ottener la permissione di commettere l'infame peccato nei mesi
canicolari.
Nei nostri tempi, a Palermo—e propriamente fino all'anno 1868—
vigeva pubblicamente una bolla di composizione, annullata con
decreto del Proc. del Re Tajani, 23 dic. 1368, con cui si era assoluti
dalla restituzione di crediti di un male guadagno in qualsivoglia
maniera con falso, o scritto, con corruzione di ufficio, pagando
determinate somme alla Chiesa ecc.
[118]
Dupin di St. André ripubblicò, nel 1879, Les Taxes de la pénitencerie
apostolique (edizione già stampata, nel 1520 da Toussaint Denis e
nel 1741 a Roma), in cui sono lo tariffe pei reati stabilite da papa

Giovanni XII e Leone X. Così, per es., un laico che avesse ucciso un
prete era assolto pagando 7 grossi, e 5 se avesse ucciso un altro
laico.
«Se un chierico fornicasse con monache nel monastero o fuori,
quanto con nipoti, cugini o figliocci, non verrebbe assolto che
mediante la pena di 67 lire, 11 soldi e 6 denari.»
«Se contro natura 219 lire e 14 soldi.»
«Una monaca che avesse fornicato con molti uomini, dentro o fuori
del monastero 131 lira, 14 s. e 6 d.»
«L'adultera viene assolta con lire 87,3. Un laico, per adulterio, solo
con 4, però, per adulterio e incesto 10.»
«Sotto Giovanni XII l'incesto colle sorelle e colla madre costava 40
soldi»
[119].
Chi non conosce le massime dei Gesuiti del secolo passato, del
Lacroix (1775), p. e., in cui si dichiara che «quantunque la legge
naturale vieti la bugia e l'uccisione, tuttavia, in date circostanze,
sono permesse» e del Buzenbraun «Colui che è estremamente
povero può prendere ciò che gli occorre. Un povero può anche
uccidere chi gli impedisca di prendere le somme che gli sono
necessarie». E di Maiorca che autorizzava il regicidio.
E del Padre Longuet: «Non si pecca contro giustizia e non si è
obbligati a restituire quando si riceve danaro per uccidere o per
ferire».
Però due fatti mi paiono sicuri che la civiltà avanzandosi appiani e
scancelli tutte le influenze religiose, e che quanto più le religioni
sono fresche e in istato nascente, esercitano un potere moralizzatore
molto maggiore perchè allora la lettera non invade lo spirito e perchè
l'ebbrezza delle nuove idee preoccupa il sentimento e lo distrae dal
delitto; e perchè qualunque siane la derivazione, l'organismo allora è
più sciolto dai simboli e dalle formole che ne arrugginiscono e
irrigidiscono l'attività.

Ciò si notò col Savonarola, coi Valdesi fra noi: e fin i negri degli Stati
Uniti quando si convertono al metodismo abbandonano l'ozio,
l'infanticidio, sicchè in quei distretti ove avviene la conversione ne
aumenta notevolmente la popolazione. È un fatto curioso che perfino
le nuove sêtte religiose create da puri paranoici, come i Lazzarettisti
in Italia, i Quaccheri in Inghilterra, irradiarono un miglioramento nei
costumi e una diminuzione nel delitto.
Così gli Skopzi che hanno per religione la castrazione reciproca sono
celebrati per onestà. Nella Russia settentrionale pure i Bialoriztzi
(Revue des Revues, 15 ottobre 1895) non bevono alcool, non
fumano, si vestono di abiti bianchi da loro tessuti, non praticano che
la virtù, e così i Soutasewtzy, che rigettano i preti, le immagini, le
servitù militari: soffrendo perciò fin il martirio; essi predicano la
guerra alla violenza; uno giunse a perseguire i ladri per cambiar loro
in buona la farina cattiva rubatagli.
I Figli di Dio credono che ognuno essendo il proprio Dio, basti offrir
preghiere a un qualunque vicino: si riuniscono e ballano
furiosamente, in onore del Dio, finché cadono estenuati e sono
onestissimi.
I Weriginski o Tolstoiani non vivono che di tè e spesso si lasciano
battere dai conterranei senza dir altro che «Dio aiutami«, finchè i
persecutori cadono ai loro piedi ammirati.
Sono dunque queste nuove sette, vere epidemie di santità e di virtù.
Anzi è curioso che nella Russia del Sud dove nascono (certo per
effetto del clima caldo che, come sappiamo, fa più incline l'uomo
all'omicidio) delle sette sanguinarie, anch'esse in mezzo ai più feroci
costumi hanno degli scopi altamente morali; così i Douchobortzi
uccidevano tutti i fanciulli anormali di corpo o di spirito per rispetto
allo spirito divino che li dovrebbe abitare: un loro capo, Kapoustine,
faceva seppellire vivi tutti quelli che tradivano i dogmi della setta, e
in un processo intentatogli si rivelarono a suo carico 21 omicidi
religiosi. Tuttociò parrebbe più che criminale; eppure questa setta è
contraria alla guerra e predica: lo czar non regnare che sui tristi e sui

criminali, sicchè le genti oneste, i veri Douchobortzi non sanno che
farsi delle sue leggi e della sua autorità.—E da essi pullularono i
Molokani, bevitori di latte, nemici dei preti, dei riti inutili, degli
ornamenti; tutti colti, onestissimi, che si aiutano fra loro, non hanno
alcun povero, alcun mendicante, e ovunque vengon deportati
trasformano in giardini i luoghi più inospitali (Revue des Revues,
1895).
E i Mormoni in America erano notorî per l'attività e probità. Gli è che
i nuovi settari, sien pure pazzi e fanatici, sono monoteizzati da
un'idea che fa loro da inibitrice da vaccino dalle passioni più ignobili.
Ma sopra tutto influisce favorevolmente la religione che più si spoglia
delle forme e bada alla morale.
La contraddizione, insomma, dell'influenza, ora grande ora nulla,
della religione si toglie se concludesi che la religione è utile, e
quando si fonde veramente colla morale, e abbandona il culto delle
formule, il che ora non può darsi che nelle religioni nuove, perchè
tutte in principio sono morali, e poi a poco a poco si cristallizzano, e
le pratiche rituali sopranuotano e annebbiano il nucleo morale, meno
facile a concepirsi e ritenersi dal volgo: quindi si nota una minore
propensione al crimine, anche là dove solo il senso etico e non il
religioso è in onore come fra gli uomini atei ma colti, perchè ci vuole
un'energia intellettuale per resistere al consenso universale, una
forza inibitrice, che come resiste all'imitazione, resiste anche agli
impulsi istintivi; ragione questa forse unica dei vantaggi dell'alta
coltura.
Analogamente si spiega perchè certi popoli protestanti in cui il
fervore religioso è più caldo e più ardente, come Ginevra e Londra,
sono i soli in cui malgrado la aumentata civiltà, e la popolazione
addensata (Londra da sola è più popolata di una intera regione
italiana), il delitto sia in ribasso.
Qui, non è in giuoco l'inibizione, ma invece una grande passione
religiosa, che neutralizza e doma gli istinti più ignobili, e combatte
con tanto accanimento i vizi e le tendenze immorali, da debellarle.

In Inghilterra la religione recluta migliaia di fanatici, che sotto i nomi
e le teorie più diverse si agitano febbrilmente per salvare le anime
umane dalla perdizione. Essi hanno un campo immenso in cui
agitarsi, organizzando chiese, processioni, opere pie, predicazioni,
ecc., ecc. Nei paesi latini, invece, dove la chiesa cattolica stende la
sua dominazione, la religione non può che molto meno essere un
parafulmine del vizio; e ciò non tanto in ragione della irreligiosità e
dello scetticismo del popolo—molto minore di quanto si crede, anche
nella patria di Voltaire—ma per l'organizzazione stessa della sua
chiesa. La chiesa cattolica è una grande istituzione disciplinare e
quasi un esercito fondato sulla obbedienza e subordinazione; in cui
ogni uomo ha il suo posto, la sua linea di condotta, le sue idee già
fissate da leggi fortissime. I fanatici attivi, come il Bernardo, che
sono naturalmente indipendenti e un po' rivoltosi, non possono
quindi trovarcisi che a disagio; salvo nelle missioni l'unico
dipartimento della chiesa che ridona all'individuo una certa
indipendenza e autonomia (Ferrero); mentre si trovano benissimo tra
la indipendenza un po' anarchica delle varie sêtte protestanti, libere
ed autonome come tanti piccoli clans di tribù barbare, quali p. es. la
Salvation Army, i Baptisti
[120].
«Un altro sfogo al fanatismo, potentissimo nelle nazioni germaniche
e specialmente in Inghilterra, ma che manca quasi del tutto nelle
nazioni latine è la filantropia. Londra è la capitale di questi fanatici
della filantropia; sono uomini o donne di tutte le classi e le posizioni
sociali, ricchi o poveri, istruiti o ignoranti, normali o matti, che si
sono fitti in mente di guarire la malattia sociale e di sradicare dalla
società una forma speciale di miseria e dolore. Uno si è preso a
cuore i bambini torturati dai genitori; l'altro i vecchi diventati ciechi;
un terzo i pazzi maltrattati nei manicomii; un quarto i prigionieri
usciti dal carcere; e tutti lavorano senza requie, stampano giornali,
tengono discorsi, organizzano società e talora riescono a promuovere
grandiose epidemie sentimentali e movimenti dell'opinione pubblica
intensissimi, che conducono a qualche importante riforma
umanitaria. Questo genere di attività può essere un succedaneo

eccellente di quel fanatismo politico, che finisce agli attentati
dinamitardi.
«Ma nei paesi latini queste agitazioni non sono promosse perchè
cadrebbero nel vuoto; la tradizione della carità amministrativa ed
esercitata per mezzo dell'autorità pubblica o della chiesa è così forte
profonda che nessuno vuole occuparsi personalmente delle miserie
sociali. Se i bambini sono spesso maltrattati nelle grandi città e se i
giornali protestano energicamente scuotendo un poco l'opinione
pubblica, questa domanda una legge dello Stato, che non sarà
nemmeno applicata e se ne contenta; ma nessuno penserà a
fondare società private, come ce ne sono tante in Inghilterra, che
spiino i genitori crudeli e giungano in tempo a strappar loro di mano
le piccole vittime» (Ferrero).
E ciò è naturale. Nelle religioni che sopravvissero molti secoli
l'elemento morale svanisce perchè meno adatto al sentimento delle
masse e sopravvive e sempre sovrabbonda il cerimoniale; su 73
norme capitali delle regole di S. Benedetto, 9 sole appartengono alla
morale; nelle regole di S. Colombano 1 anno di penitenza è indetto a
chi perde un'ostia e 6 mesi a chi lascia mangiare due ostie.
Le sole religioni, insomma, che ponno impedire il delitto sono le
fanaticamente, passionatamente, morali o le nuovissime; le altre
giovano forse tanto quanto o meno dell'ateismo.

CAPITOLO XI.
Educazione.—Illegittimi.—Orfani.
Illegittimi.—Quanto l'educazione entri come fattore del delitto, ci è
dimostrato indirettamente dalla quota (che si fa sempre più grossa,
pur troppo, nelle nazioni più civili e nelle epoche più recenti) dei rei
illegittimi.
In Prussia i delinquenti illegittimi, che costituivano nel 1858 il 3% del
totale, crebbero al 6, e le donne dal 5 all'8. In Francia gli 8006
minorenni arrestati nel 1864 contavano un 60% tra bastardi ed
orfani, il 38% di figli di prostitute o di delinquenti. In Austria nel
1873 gli illegittimi delinquenti sommavano: i maschi al 10 e le donne
al 21% (Oettingen, o. c.); In Amburgo il 30% delle prostitute era
fornito dalle bastarde (Hugel, op. cit.); ed a Parigi il quinto delle
cittadine, l'ottavo delle campagnuole (Parent-du-Chatelet, op. cit.). A
Nuova-York in un anno si arrestarono 534 figli naturali, 222 esposti.
I bastardi erano nelle carceri del Würtemberg: nel 1884-85 il 14,3%;
nel 1885-86 il 16,7%; nel 1886-87 il 15,3%; mentre sono negli
onesti l'8,76%. Sichart anzi
[121] sui 3181 esaminativi ne trovò la
cifra elevarsi al 27%, quasi al doppio, così diviso:
Su 100 ladri 32,4
Su 100 truffatori23,1
Su 100 rei di libidine21,0
Su 100 spergiuri13,0
Su 100 incendiarii12,9
E trovò 30,6% di illegittimi nei rei d'abitudine, il doppio, dunque,
17,5%, dei rei d'occasione.
Egli pure nota:

Ribrezzo del lavoroMendicantiVagabondi
Su 1248 ladri legittimi 52% 32% 42%
Su 600 ladri illegittimi 52,3% 39% 49%
Tutti avran notato come gran parte dei camorristi di Napoli ha nome
di Esposito, come molti grassatori lombardi e bolognesi di Colombo;
tale essendo il soprannome che si usa dare ai trovatelli.
In Italia la statistica carceraria ci dà dal 3 al 5% di illegittimi fra i
minorenni maschi, dal 7 al 9 nelle femmine minorenni
[122].
S'aggiunga che un 36% dei recidivi in Italia è fornito da figli naturali
ed esposti.
Per comprendere il grande significato di queste cifre bisogna
ricordare, che una gran parte degli illegittimi soccombe nei primi
mesi o nei primi 18 anni, per lo meno il 60, e spesso l'89%
[123], per
cui si può benissimo non trovare esagerata la espressione di
Marbeau, che sopra 4 trovatelli, 3 muoiono avanti 12 anni, ed il
quarto è sacrato alla colpa.
Per meglio assicurarmi dell'importanza di quella quota, ho fatto fare
ricerche sopra 3787 entrati, quasi tutti maggiorenni, nei manicomi di
Imola (dott. Lolli), di Padova (prof. Tebaldi), di Pavia, e sopra 1059
entrati nell'Ospedale Civico di Pavia nel 1871, ed ho rinvenuto una
proporzione di esposti pei primi di 1,5, pei secondi di 2,7%. Eppure
la mortalità fra gl'illegittimi di Pavia è minore di molti altri paesi
[124].
—A pari età e condizione, dunque gli esposti dànno venti volte più
delinquenti che pazzi.
Si può, dunque, con tutta certezza, assicurare, che la maggior parte
dei trovatelli che sfuggono alla morte, si abbandona al delitto. Forse
in ciò entra, per buona parte, anche l'influenza ereditaria; perchè
nascono i più da una colpa; e vi si aggiungono, certo, la difficoltà di
trovar un mezzo di sussistenza, e più di tutto l'abbandono. Senza un
nome da difendere, senza un freno che li arresti nel pendio delle
passioni, senza una guida che con cura diligente e con un tesoro di

affetti e di sacrifici faccia sviluppare i nobili istinti e contenere i
selvaggi, questi prendono facilmente il sopravvento.
Forse, anche, quelli che non hanno tendenze malvagie vi sono tratti
per imitazione; e probabilmente vi influisce sinistramente anche
quello stesso benefico ricovero dell'orfanotrofio, e del brefotrofio per
la ragione già sopra citata della maggior criminalità nelle occasioni di
maggiori contatti.
Orfani.—Che l'abbandono, che la mancanza di ogni educazione vi
influiscano di molto, lo dimostrerebbe, secondo alcuni, anche il
notevole numero di orfani e di figli di secondo letto che si
rinvengono nelle carceri. In Italia si contarono fra i rei minorenni nel
1871-72 dall'8 al 13% i figli di secondo letto. Il Barce (op. cit.), narra
che a New-York vennero arrestati 1542 ragazzi orfani e 504 figli di
seeondo letto; aggiunge che il 55% dei degenti nei penitenziari era
dato da orfani di padre e di madre; il 60% dei ragazzi arrestati aveva
perduto uno dei genitori, o ne era stato separato. Secondo il
Marbeau, su 100 minorenni carcerati, 15 erano stati abbandonati
dalle loro madri.—Per amore del vero, devo però fare notare che
molti statisti esagerano la portata di questi fatti, del resto innegabili,
per aver ommesso il confronto colla popolazione onesta, e per non
aver considerato che l'età media non sorpassando i 32 anni, pochi
possono essere i rei adulti che abbiano vivi ambedue i genitori.
In Italia noi ebbimo in 10 anni fra i delinquenti una media di 33 a
35% di orfani; ma sopra 580 alienati della mia clinica, gli orfani
fornirono il 47% ed il 78% ne offersero 1059 entrati nell'Ospedale di
Pavia, sicché la proporzione degli orfani rei viene ad essere inferiore,
probabilmente, alla normale.
Più importante, forse, è il trovare una media dell'8 al 12% di orfani
fra i minorenni, poiché la popolazione libera minorenne è, con tutta
probabilità, in proporzioni inferiori; e ciò vale anche per i minorenni
rei (23 a 30%) che perdettero od il padre o la madre (18%).

Non posso parlare, con certezza, degli orfani di padre, che avrebbero
dato nelle statistiche italiane circa il 26 di delinquenti, mentre
davano il 23% quelli di madre; poichè negli alienati notammo 51 dei
primi e 10 dei secondi.
Certo è invece, che fra gli orfani e gli esposti condannati si vede
predominare il sesso femminile, ma sopratutto fra gli esposti. E ciò
anche al difuori di quella subcriminalità che è la prostituzione;
cosicchè Oettingen riesce a questo calcolo singolare: che mentre
ogni 5 maschi si trova una femmina delinquente, invece per 3
esposte delinquenti si trova un maschio.
Educazione.—La femmina, più debole e più passionata degli uomini,
ha più bisogno dell'appoggio e del freno della famiglia per durare nel
retto sentiero, da cui la devia più facilmente che negli uomini la
sempre aperta e lubrica strada del meretricio; e in ciò entra
essenzialmente l'influenza ereditaria; chè le figlie di un traviamento
sessuale più facilmente vi sono trascinate esse medesime, e da
quello, alle colpe più gravi.
La maggior frequenza degli esposti fra delinquenti, spiega la
prevalenza de' minorenni delinquenti fra le popolazioni urbane che si
nota da noi (Cardon, op. cit.), essa ci dà la misura dell'azione,
massime dell'abbandono e del danno della mancata educazione.
Parenti viziosi.—È cosa naturale che, ancor più dell'abbandono,
debba influirvi sinistramente l'educazione malvagia.
Ricordiamo qui quell'eredità morbosa che secondo Sichart va fino al
36% e secondo Marro al 90%, il 6,7% di parenti epilettici, il 4,3% di
suicidi, il 16% di beoni
[125], il 6,7 di pazzi (vedi cap. seguente), cifre
che s'elevano nei parenti dei rei più gravi a 27% di beoni secondo
Penta, di 41% secondo Marro, e di 27% di criminali o viziosi secondo
Virgilio, di 45% secondo Marro.

Come può l'infelice ragazzo difendersi dal male, quando questo gli
venga rappresentato con rosei colori e, peggio, imposto coll'autorità
e coll'esempio dai parenti od istruttori?
La V. era sorella di ladri; fu educata dai suoi come un maschio;
vestita da maschio, prese aspetto virile e maneggia coltelli con
vigore; ruba per istrada un mantello ed arrestata ne incolpa i suoi
parenti.
La famiglia Cornu era composta di assassini e di ladri, abituati al
delitto dai parenti fino dalla più tenera infanzia. Di cinque fratelli e
sorelle, una sola avea mostrato ripugnanza invincibile al crimine: era
la più piccola; ma essi ve la iniziarono, facendole portare, per due
leghe, nel grembiale la testa di una loro vittima; scorso breve tempo
ella si era così spogliata d'ogni rimorso, da mostrarsi la più feroce
nella masnada, da volere praticare le torture più crudeli ai
passeggieri. Crocco, che a tre anni colpiva a sassi i compagni e
spennava gli uccelli, era stato dal padre lasciato quasi sempre solo in
mezzo ai boschi fino a diciannove anni.—Il Fregier racconta di un
ragazzo che era l'orgoglio del padre ladro, perchè a tre anni sapeva
cavare in cera l'impronta delle serrature.—Le mogli degli assassini,
scrive Vidocq, sono più pericolose dei mariti. Esse avvezzano i bimbi
al delitto, dando loro regali per ogni assassinio che si commette.
Noi abbiamo visto, e vedremo nel capitolo seguente, la quota
approssimativa dei genitori e delle famiglie immorali dei rei, azione
ereditaria che non può disgiungersi dalla educativa.
Anche qui, come nell'abbandono, e per la solita ragione della
prostituzione e della maggiore tenacità al delitto nelle donne, appare
assai più grande il numero delle femmine soggette a questa
influenza, che non dei maschi.
A molti parrà ancora scarsa l'influenza dell'educazione, come ci viene
rapportata da queste cifre. Ma, oltre che vi dobbiamo aggiungere
quelle quote surriferite di figli esposti, bisogna però ricordare che
moltissimi delitti hanno origine autonoma; che molti tristi nascono e
si conservano tali, malgrado gli sforzi ed i tentativi disperati delle loro

famiglie. Dei nostri delinquenti minorenni dell'anno 1871-72
[126],
l'84% dei maschi avrebbe avuto famiglie morali, e il 60 delle
femmine. Questa contraddizione si spiega colle prime debolezze dei
parenti onesti, i quali, quando più tardi vogliono farsi ubbidire sul
serio, non riescono più, si trovano impotenti. È il caso che accade,
come da relazioni ufficiali, in non meno del 20% delle persone
benestanti che ricoverano i figli nei riformatori; vedremo, più sotto,
quanto sinistramente influiscano, su questo proposito, le associazioni
infantili.
Noel, Vidocq, Donon, Demarsilly, Lacenaire, Abbado, Hessel, Fra
Diavolo, Cartouche, Trossarello, Troppman, Anzalone, Demme
appartenevano a famiglie moralissime. Rosati raccontavami essere
stato più volte battuto dal padre dopo i primi suoi furti, e di avere
visto piangere dirottamente la madre, e di avere loro promesso
sempre, ben inteso, senza mantenerla, la restituzione delle somme
che rubava.
Ed è noto, d'altronde, dalle rivelazioni di Parent-du-Chatelet e di
Mayhew, che molti ladri e prostitute arricchiti cercano ogni via per
educare sulla strada della virtù i loro figliuoli.

CAPITOLO XII.
Eredità.
Statistica dell'influenza ereditaria.—Su 104 rei da me esaminati
71 avevano fenomeni ereditarii
20 avevano padre alcoolista
11 avevano madre alcoolista
8 avevano padre criminale
2 avevano madre criminale
3 avevano padre pazzo o meningit.
5 avevano madre pazza od epilettica
3 avevano madre prostituta
6 avevano fratelli e sorelle pazzi
14 avevano fratelli e sorelle rei
4 avevano fratelli e sorelle epilettici
2 avevano fratelli e sorelle suicidi
10 avevano sorelle prostitute.
Tuttavia, non avendo mezzi ufficiali d'indagini, e dovendomi
accontentare delle asserzioni dei condannati, io era nelle peggiori
circostanze.
Il Virgilio, che si trovava in condizioni ben più favorevoli, trovò il
crimine nei parenti nei rapporto del 26,80%, quasi sempre, come
l'alcoolismo (21,77), dal lato paterno, senza contare un 6% di
collaterali
[127].
Meglio di tutti Penta
[128] su 184 criminali-nati di S. Stefano notò:
Età avanzata dei genitori 29volte, cioè16,0%
Ubbriachezza dei genitori 50volte, cioè27,0%
Tisi dei genitori 17volte, cioè9,2%

Apoplessia cerebrale dei genitori20volte, cioè11,0%
Pellagra dei genitori 3volte, cioè1,6%
Pazzia dei genitori 12volte, cioè6,5%
Pazzia (negli ascendenti e collaterali)27volte, cioè14,5%
Isterismo dei genitori 25volte, cioè13,5%
Epilessia dei genitori 17volte, cioè9,2%
Emicrania dei genitori 17volte, cioè9,2%
Solo nel 4 a 5% i genitori erano perfettamente sani. Più tardi ci
diede una nuova statistica dell'eredità morbosa in altri 447 casi
distinti in 2 serie:
1ª serie2ª serie
su 232 casisu 215 casi

Criminalità 30 58
Isterismo 17 38
Epilessia 11 22
Altre neuropatie 20 65
Alcoolismo 40 95
Pazzia 35 50
Tubercolosi polmonari 25 80
Età avanzata dei genitori 23 55
Apoplessia cerebrale 10 20
Diatesi gravi 12 20
Malaria cronica 5 20
Marro trovò nelle cause di morte di 230 genitori di rei e di 100
onesti:
nel padrenella madre
reionestireionesti
Alcoolismo 7,22,42,1 —
Suicidio 1,4 —— 3,7
Pazzia 6,52,45,3 —
Malattie cerebrospinali 21,114,618,27,4

Malattie di cuore 6,514,63,218,5
Idropisia 4,32,46,43,7
Tisi 5,12,410,7 —
Dispiaceri o scosse nervose2,12,44,3 —
Se poi, invece di esaminare separatamente i singoli gruppi, si
riuniscono insieme le morti per alcoolismo, suicidio, alienazione
mentale e malattie cerebrali, troviamo che fra i delinquenti queste
cause contano fra le morti dei 230 genitori nella proporzione del
32,1% mentre fra i normali esse stanno nel rapporto di 16,1; circa la
metà.
Se il numero degli ascendenti delinquenti è scarso anzichè no molto
più considerevole è il numero dei fratelli delinquenti.
Marro trovò 68 su 500 i delinquenti con uno o più fratelli rei essi
pure; di questi ebbero
Parenti alienatiNº17
Parenti epilettici»4
Parenti delinquenti»6
Parenti alcoolisti»34(4 anche la madre)
Parenti invecchiati»33(4 entrambi i genitori)
Studiando poi i parenti vivi di 500 criminali Marro trovò nel 41%
l'alcoolismo nel padre, il 5% nella madre, mentre nei normali si ha
solo il 16% nel padre; la pazzia fra gli ascendenti o collaterali nei
genitori nel 42,6% dei criminali (13% dei normali); l'epilessia nel
5,3% (2%); la delinquenza 19,7% (1%); carattere immorale e
violento 33,6%; computando nell'eredità morbosa la discendenza da
genitori alienati, apopletici, alcoolisti, epilettici, isterici e delinquenti,
la trovò nel 77%, e nel 90% comprendendo ancora le anomalie del
carattere e dell'età dei genitori (o. c.).
Sichart studiò nelle prigioni del Wurtemberg (Liszt, Archiv f. Rechtw.,
1890) 3881 carcerati per furti e truffe confrontandoli colla
popolazione onesta dello stesso paese.

Il complesso dell'azione ereditaria, secondo Sichart, secondo i reati
darebbe:
negli incendiariiil 36,8%
nei ladri il 32,2%
nei libidinosiil 28,7%
nei truffatoriil 23,6%
negli spergiuriil 20,5%col massimo nei ladri ed incendiarii.
Tenendo conto del solo alcoolismo, pazzia, epilessia e suicidio negli
ascendenti diretti, l'eredità morbosa gli risultava del 71% negli
incendiarii; del 55% nei ladri; del 43% nei libidinosi, e del 37% nei
truffatori.
Sichart e Marro trovarono:
Suicidio
(Sichart)(Marro)
% %
Ladri 5,0 —
Incendiarii 8,2 —
Libidinosi 3,9 5,1
Spergiuri 2,1 —
Truffatori 1,5 —
Omicidi — —
Totale 4,3%
Studiando la quota dei parenti viziosi nei 3000 rei di Sichart e
confrontandola con quelli di Marro così appaiono ripartiti:
Parenti viziosi
(Sichart)(Marro)
% %
Ladri 20,945,0
Incendiarii 11,014,2
Truffatori 10,832,4
Rei contro il buon costume 9,428,2

Spergiuri 6,0 —
Falso giuramento 12,0 —
con cifre massime in ambedue pei ladri e grandi pei falsari e
truffatori, minime per gli incendiari e spergiuri.
Su 3580 rei minorenni di Mettray, 707 erano figli di condannati, 308
figli di viventi in concubinato (Barce, Op. cit.).
I detenuti al riformatorio di Elmira, avevano un 13,7% i cui parenti
erano pazzi o epilettici, un 38,7% con parenti ubbriaconi.
Le nostre statistiche ufficiali ci dànno su 2800 rei minorenni del
1871-72 un 3% di genitori carcerati. Anche qui il padre rappresenta
la peggiore influenza (2,4), in confronto alla madre (0,5): il che si
spiega per la minore criminalità, apparente almeno, delle donne. Si
notò pure il 7% di genitori alcoolici, di cui il 5,3% il padre e 1,7 la
madre e pochi amendue.
La statistica medesima ci insegna, ancora, che un 28% delle famiglie
dei condannati minorenni aveva fama dubbia, e 26 cattiva, rapporti
questi ultimi che vengono a coincidere, con molta esattezza, coi dati
del Virgilio.
Thompson, sopra 109 condannati, ne trovò 50 imparentati, 8, fra gli
altri, membri di una stessa famiglia, che discendevano da un
condannato recidivo; egli osservò pure 3 fratelli e 2 sorelle ladre, il
cui padre era un assassino, e assassini erano altresì gli zii, le zie, i
cugini; in una famiglia di 15 membri di cui 14 falsi monetari, il 15º
parve onesto, ma alla fine mise il fuoco alla propria casa dopo averla
4 volte assicurata.
Mayhew ne notò, su 175, ben 10 che avevano il padre, e 6 che
avevano la madre, e 53 che avevano i fratelli condannati.
La stessa influenza si avvera nelle prostitute. Su 5583, Parent D. ne
avrebbe trovato 252 sorelle, 16 madre e figlia, 22 cugine, 4 zie e
nipoti. Nè senza ribrezzo si può leggere in Lacour un discorso che gli
teneva una di queste sciagurate: «Mio padre è in prigione, mia

madre vive con colui che mi sedusse, e n'ebbe un figliuolo che io e
mio fratello manteniamo».
DONNE

criminali di
Salsotto
criminali
di Marro
prostitute di
Grimaldi
ladre prostitute
di Tarnowsky
% % % % %
Padre
alcoolista 6,6 40 4,23 49 82
Alienazione
del padre 6,6 7,6 — — 3
Genitori
vecchi 17 26 — — 8
Parenti
epilettici 2,6 — — — 6
Genitori
tubercolotici — — — 19 44
Parenti
delinquenti ? 19,7 — — —
Nelle oneste la Tarnowsky trovò solo il 10% di genitori tubercolitici.
Prove cliniche.—A Pavia studiai, nelle carceri, un ragazzo, con
prognatismo enorme, con capelli folti, sguardo strabico, fisionomia
femminea; egli ch'era stato a 12 anni assassino, indi per 6 volte
imprigionato per furto, aveva 2 fratelli ladri, una madre
manutengola, 2 sorelle prostitute.
Sei dei Fossay furono condannati per associazione brigantesca,
erano 5 fratelli e un cognato; essi aveano avuto il nonno e il padre
appiccati; due zii ed un nipote nei bagni.
Una prova più curiosa dell'influenza ereditaria è offerta dall'Harvis
che osservando ad Hudson i crimini spesseggiarvi e quasi tutti gli
arrestati esservi omonimi, consultò i registri e vide che una gran
parte degli abitanti derivava da certa Motgare, donna di pessima

fama vissuta due secoli sono, che contava, su 900 suoi discendenti,
200 malfattori e 200 altri tra alienati e vagabondi (Atl. Monthl.,
1875).
E un'altra prova ne l'offre il Despine riportando la genealogia dei
Lemaire e Chretien che io ora riassumerò qui graficamente perchè
d'un colpo si possa abbracciare.
Anche i Fieschi erano assassini ereditari.

Straham (Instinctive criminality, Londra, 1892) ci dà la prova
dell'eredità criminale colla storia di una famiglia criminale. I
capostipiti di questa famiglia sono due sorelle, la prima delle quali
morì nel 1825. La loro progenie consta di 834 individui, di 709 dei
quali è stata tracciata una storia abbastanza accurata.
Fra questi 709 vi sono 106 figli illegittimi, 164 prostitute, 17 ruffiani,
142 mendicanti, 64 ricoverati per malattie croniche, 76 criminali i
quali insieme hanno passato 166 anni di prigione.
Aubry (Annales médico psycologiques, 1892) ci diede uno studio
curiosissimo su una famiglia di criminali.
La famiglia K..... occupava, nei secoli scorsi, un posto elevato nella
società: ma già al principio di questo secolo era completamente
decaduta; oramai non si componeva più che dei figli di due fratelli,
Lu... e Ren...: Ren... aveva passato tutta la vita in contatto coi
criminali, senza essere egli stesso mai stato condannato: era molto
originale, appassionatissimo pei combattimenti dei galli, gran
donnaiuolo, con un numero infinito di amanti e di figli, tanto che tutti
i bambini del quartiere lo chiamavano papà; da una delle sue amanti
nacque un gran numero di criminali. La famiglia di suo fratello Lu...
non presenta nulla di notevole, salvochè suo figlio, il giorno dopo
della morte dello zio Ren..., saputosi diseredato da questo, si uccise,
lasciando un testamento dove scriveva: «Non si accusi nessuno della
mia morte; io mi uccido per fuggire i nemici insopportabili,
procacciatimi dalla mia sciocchezza, e per non essere stato
abbastanza in guardia contro la furberia di certa gente.
Le due amanti di Ren..., che gli diedero una prole di degenerati,
erano Z..., moglie d'un carnefice, da cui nacque una femmina morta

tisica a 24 anni e F...., pure maritata, cui l'opinione pubblica accusava
di avere avvelenato il marito!
F..... ebbe 5 figli, dei quali 2 dal marito e 3 dall'amante. I figli avuti
dal marito furono:
1. Z..., che visse separata dal marito, era una mattoide querulante;
tutto era per essa occasione di far questioni: ma perdeva
regolarmente i suoi processi; ebbe parecchi amanti, un oratore, tra
gli altri, di gran talento da cui ebbe parecchi figli, uno dei quali
poeta, un pittore, ecc., celebri. 2. Fi..., proprietaria d'un postribolo;
ha due figli, di cui uno cieco e affetto da paralisi del Parkinson.
Tra i figli, che F... ebbe dall'amante Ren..., sono da notarsi:
1. Em..., che, vegliando il cadavere del padre, si ubbriacava colla
cognata, e ch'ebbe una figlia di condotta immorale; una nipote
prostituta (a 15 anni) e ladra.
2. Em..., contadino, tentò di suicidarsi strozzandosi; sposò una Fe...,
donna estremamente dissoluta, nota per rapporti incestuosi col figlio
maggiore, ladra in complicità con sua figlia, sospettata gravemente
di aver ucciso il genero, ubbriacona; sua figlia la chiamava: Vecchia
carica di delitti.
Da questo triste matrimonio nacquero due figli:
1. Maria, che in un periodo mestruale uccide il marito aiutata dalla
madre, benché al Tribunale siano state assolte entrambe; la Maria,
che aveva parecchie relazioni adultere si mostrò molto allegra dopo
la morte del marito, e dopo quella dell'unica bambina morta di
difterite.
2, Am..., che ebbe rapporti colla madre, ed uccise il marito della
amante.
In uno dei rami collaterali della Fl... (figlia di F...), si trovavano: molti
negozianti falliti; una madre, con prole numerosa, che fuggì,
portando via la cassa, coll'ultimo amante; un marito che consuma,
lontano dalla famiglia, le risorse della casa, e che quando non

possiede più nulla, vive a carico della moglie; un fratello del secondo
marito di Maria che si uccide dopo assassinata la moglie adultera.
In questa famiglia, adunque, quasi tutti i membri, hanno commesso
uno o più delitti; quelli che non sono criminali sono suicidi; ma un
ramo collaterale, quello di Ze..., è formato da persone che occupano
un posto elevato nell'arte, e che hanno realmente un grande
ingegno.
Questa famiglia costituisce anche una conferma dell'intimo rapporto
che esiste tra il genio e il delitto.
Laurent (Les habitudes des prisons), ci fa la storia di tutta una
famiglia di delinquenti-nati che conferma a meraviglia i dati di Marro,
di Aubry e di Sichart.
«Il nonno paterno morto di affezione cardiaca a 67 anni, era di
carattere debole completamente dominato dalla moglie: la quale
nervosa e strana, batteva il marito ad ogni occasione. Irascibilissima,
provava piacere a sferzare la sorella quand'era ammalata.
«Il padre era nervosissimo, violento, ma poltrone, e quantunque
conoscesse la vita disordinata della moglie, non aveva il coraggio
d'intervenire. Morì di un'insufficienza aortica.
«Uno zio paterno viziosissimo e violento percuoteva i suoi parenti
per avere denaro. Approffittò della loro assenza per vendere una
parte dei mobili, tentò uccidere suo fratello per gelosia. Un cugino
germano dei due precedenti si abbandonò alla pederastia.
«Il nonno materno era intelligente, ma ubbriacone, subì due anni di
prigione per furto. Capitano sotto la Comune, fu ancora punito per
cattiva condotta. Egli era disquilibrato, brutale e grossolano. Nel
primo matrimonio ebbe 4 figlie delle quali descriveremo lo stato
mentale più sotto. La nonna materna abbandonava i bimbi e
sprecava in compagnia del marito la paga settimanale. Morì di
cancro uterino.
«La madre viziosissima, pigra, impetuosa si marita a venti anni ed ha
due figliuoli; a 23 anni abbandona il marito, si unisce con un giovane

e dà alla luce una bimba. In seguito ritorna al letto maritale ed ha un
quarto bimbo, durante questo tempo è l'amante di un negoziante di
vino.
«A quest'amante ne succedono altri. A 35 anni partorisce un quinto
bimbo. Lasciando la famiglia ed i fanciulli senza cura ella passa la
vita nelle stamberghe (bouges) giuocando alle carte e disputando
cogli ubbriachi. Tentò più volte in stato di ubbriachezza d'uccidere il
marito. A 37 anni ha da un suo amante un sesto figlio che muore di
meningite. Resta incinta un'altra volta ed abbandona allora
decisamente il tetto maritale attirando con sè le figlie, che poi lascia
in balia del primo capitato mentre ella si ubbriaca. A 39 anni è
incinta per la nona volta, e dal suo amante essa si lascia maltrattare.
«Questa donna aveva tre sorelle.
«La prima era viziosa fin dall'infanzia. Corrotta, a 16 anni si dà alla
prostituzione. Irascibile, ella in un momento di gelosia strappò
un'orecchia ad una donna. La seconda sorella ha 38 anni, è
maritata; alcoolista lasciva et ottusa. Ha tre fanciulli dei quali uno
all'età di nove anni per un futile motivo si precipitò dalla finestra ed
un'altra volta senza ragione apparente si gettò sotto una vettura.
«Soffrì di meningite e guarì.
«La terza sorella, ottusa e lussuriosa, si ubbriaca in compagnia del
marito.
«Passiamo ora all'esame della 3ª generazione, che comprende otto
fanciulli.
«1º Una giovane di diciannove anni, poco intelligente, capelli
biondissimi, ha volta palatina ogivale e sviluppo esagerato delle
protuberanze frontali. Il sistema pilifero è sviluppatissimo sul corpo e
di un color nero carico. Cattiva, gelosa, ella metteva delle spine nella
minestra del fratello. A 10 anni la si trovava nelle cantine con dei
giovinetti abbandonandosi ad una crapula precoce. Ha sempre
rifiutato l'unione sessuale coi componenti la famiglia. «Io non ne so il
perchè, diceva, vorrei, ma non posso, ciò è più forte di me, e mi
ripugna».

«A quindici anni si dà alla prostituzione pubblica ed è incarcerata a
S. Lazare, poi nel convento delle Dame di S. Michele: ma quindici
giorni dopo l'uscita ricomincia la vita disordinata prostituendosi e
vivendo in compagnia dei souteneurs.
«2º Un giovane di 18 anni, lavoratore, economo, onesto, ma nervoso
e caparbio e di carattere debole come il padre.
«3º Una figlia adulterina di 15 anni, viziosa, beona e ghiotta.
Frequenta gli spacci di vino e s'ubbriaca spesso. Ruba nelle vetrine
dei droghieri.
«4º Una giovane di 14 anni pigra, bugiarda, ladra, irascibile, ha la
faccia costantemente contratta da un tic nervoso e la fisonomia non
è che una smorfia continua. Senz'alcun rispetto per la famiglia, ella
approfitta di notte del sonno della nonna per pizzicarle le gambe e
vendicarsi in questo modo delle punizioni avute. È egoista, civetta,
lasciva.
«5º Un ragazzo di 8 anni, rachitico, scrofoloso, nervosissimo,
irascibile. Prepotente, ha degli accessi con tendenza a rompere
qualsiasi oggetto. È dolicocefalo e d'intelligenza comune.
«6º Una figlia adulterina, morta a 16 anni di meningite.
«7º e 8º Due ragazzi in tenera età».
Il Sighele ha studiato tutti i processi intentati contro gli Artenesi dal
1852, e vi ha trovato sempre gli stessi nomi; il padre, il figlio, il
nipote si seguivano a distanza come spinti da una legge fatale.
Nell'ultimo processo v'erano due famiglie, già celebri negli annali
giudiziari: l'una di 7 persone, l'altra di 6: padre, madre e figli; non
uno mancava. Sighele notava come si potessero ben ripetere a
questo proposito le parole di Vidocq: «Il existe des familles dans
lesquelles le crime se transmet de génération en génération, et qui
ne paraissent exister que pour prouver la vérité du vieux proverbe:
Bon chien chasse de race« (Arch. di psich., 1894).
Mai—io credo—la legge d'eredità ebbe una conferma più splendida.

Nel 1846 si condannarono in Francia per 45 furti due famiglie che
erano legate insieme per parentela e per tendenza al brigantaggio:
C. Iegl capo della prima avea sposata la figlia di Ruch... capo della
2ª; dell'uno si condannarono il padre, la madre, il figlio, i generi, e
dell'altro il padre e il figlio.
Affinità elettive.—Il Locatelli ci spiega come questi fatali intrecci che
dànno luogo alle bande e sono il sustrato più saldo del brigantaggio
—prova ne siano il Chretien e Lemaire—nascano per una specie di
affinità elettiva che spinge la donna delinquente a scegliere l'amante
e lo sposo tra i più inclini allo stesso delitto.
È da ricordarsi nella famiglia K... sopra studiata l'affinità elettiva che
spinse Renato a scegliere le amanti tra le prostitute e le delinquenti,
e che rende possibile la esistenza di criminali e di persone immorali
anche nei rami solo indirettamente legati al principale.
La famosa ladra Sans Refus era figlia di un ladro Comtois, morto, nel
1788, sulla ruota, e della ladra Lempave.
La Marianna, la complice più abile della banda Thiebert, nacque da
una ladra e un ladro recidivo cinque volte e nacque anzi sulla
pubblica strada entro un carretto rubato (Lucas, De l'hérédité
naturelle, pag. 487).
Virginia P., amante di un beccaio tratto in giudizio per aver
assassinato una bambina, saputone l'arresto, rimase un giorno intero
sulla porta del carcere per aver sue notizie, e naturalmente invano;
tornatasene a casa ad ora tarda della sera, col cuore in tempesta,
sentendosi rimproverare dalla madre, le balzò al collo come una tigre
ferita, e l'avrebbe indubbiamente strangolata, senza il pronto aiuto
del vicinato, accorso alle grida della povera donna (Locatelli, p. 18).
Un esempio più celebre l'offrono le simpatie fatali della marchesa di
Brinvilliers col S. Croix, e della Pochon e della Catella, ladra,
truffatrice e prostituta con Rossignol, la prima delle quali si sentì,
quando era in carcere, attratta a lui, solo al racconto delle sue
imprese fattole dalla rivale; notisi che quest'ultima, nata da una

famiglia nobilissima, già perduta a 14 anni, a 15 anni avea
commesso i delitti di grassazione appunto in complicità con
Rossignol. A Torino, la Camburzano, quasi impubere, si dà prima ad
un ladro, e messa, perciò, in un riformatorio ne fugge, e nel giorno
stesso che n'esce si innamora e si unisce col sicario Tomo e se ne fa
complice e istigatrice di feroce omicidio e ride quando se ne sente
rimproverare; liberata, ruba di nuovo ad un amante e si
riprostituisce.
Eredità ataviche di Juke.—Ma la prova più importante della
ereditarietà del delitto e dei suoi rapporti colle malattie mentali e
colla prostituzione viene offerta da quel singolare studio fatto or ora
da Dugdale nella famiglia Juke
[129] divenuta in America sinonima di
criminale.
I capi stipite di questa sciagurata progenie sono Ada Yallkes nata nel
1740, ladra e beona, e Max Juke cacciatore e pescatore, beone e
donnaiuolo, che in tarda età divenne cieco, e nacque circa nel 1720,
lasciando numerosa discendenza legittima, 540, ed illegittima, 169;
non tutte le diramazioni di questa si poterono seguire fino ai dì
nostri; sì bene quella di 5 figlie, 3 delle quali eran prostitute prima di
maritarsi, e di alcuni rami collaterali, il tutto per 7 generazioni—Le
riassumeremo in questa tabella:

NB.—Per X si intendono i collaterali o imparentati coi Jìke ma non derivati
originalmente da questo.
Vedesi già da questo prospetto la singolare connessione della
prostituzione, del delitto e della malattia, perché per le stesse cause
ereditarie si hanno:
1º ceppo MAX
/ | \
76 delinquenti e 142
vagabondi, mendicanti,
64 poveri
181 prostitute, 18
tenenti postribolo, 91
illegittimi
181 impotenti,
idioti o sifilitici, 46
sterili
Con istrana progressione vediamo i delinquenti appena rappresentati
nella 2ª generazione, moltiplicarsi a 29 nella 4ª, a 60 nella 5ª
[130],
precisamente come le prostitute, da 14 crescono a 35, ad 80, ed i
vagabondi da 11 a 56, a 74; nè scemano nella 6ª e 7ª, se non
perchè la natura, che si direbbe provvida anche nel delitto come
nelle mostruosità, ponvi termine colla sterilità delle madri, che da 9

della 3ª generazione aumenta a 22 nella 5ª generazione, e colle
morti precoci dei bimbi che aumentano a 300 negli ultimi anni.
Passarono tutti insieme in carcere 116 anni; furono intrattenuti 734
individui a spese dello Stato.—Alla 5ª generazione, tutte le femmine
erano prostitute e gli uomini rei. Alla 6ª l'anziano dei discendenti
aveva solo 7 anni, eppure 6 individui erano stati raccolti all'asilo degli
indigenti.
In 85 anni la manutenzione loro costò allo Stato 5 milioni di dollari.
Si osservò che in tutti o quasi tutti i rami la tendenza al delitto,
all'inverso di quella al pauperismo, si presentava più intensa nel figlio
più anziano, seguendo, poi, sempre la linea maschile più che la
femminile; e si accompagnava ad eccessi di vitalità, di fecondità e di
vigore; che essa si sviluppava assai più nelle linee illegittime che non
nelle legittime, il che si ripete anche in tutte le altre note di
immoralità.
Così confrontando i 38 illegittimi sorti dalla 5ª generazione e dalle
primogenite delle 5 sorelle con gli 85 legittimi, troviamo nei:
38 illegittimi
/ | \
4 ubbriaconi
11 mendicanti, idioti o
prostitute
16 condannati
di cui
6 per gravi
delitti
85 legittimi
/ \
5 condannati
13 mendicanti
o prostitute
E la cifra della prostituzione qui accennata non è che una sottile
quota in confronto alle risultanze di altre indagini che mostrano
l'irruenza degli accessi venerei come il numero enorme di illegittimi,
91: di bastardi, 38; in totale 21% dei maschi e 13 delle femmine;

delle sifilitiche, 67, e specialmente delle donne immorali, che dal
60% ch'erano nella 1ª generazione e dal 37 ch'erano nella 2ª
crebbero a 69 nella 3ª, a 48 nella 5ª, a 38% nella 6ª, in totale al
52,40% e ciò nella generazione diretta, toccando al 42% nelle
collaterali.
I dati della fecondità eccessiva e della prostituzione dimostrerebbero
come gli eccessi sessuali siano una delle cause più gravi del
pauperismo, che par anch'esso d'indole ereditaria specialmente nella
donna, e che coglie di preferenza il più giovane. Il pauperismo si
lega poi al delitto ed al morbo pei molti casi d'individui che sono ad
un tempo colpiti da sifilide, o da deformazione degli arti e da
tendenze al delitto, al vagabondaggio.
Nelle tavole parziali si osserva poi che nelle famiglie, ove i fratelli si
dànno al delitto le sorelle si dànno alla prostituzione, essendo
arrestate solo per delitti contro al pudore. Una nuova prova, dice
Dugdale (p. 152), che l'una carriera è nel sesso femminile il
corrispettivo dell'altra—avendo origine comune.
La prostituzione si vede sorgere per causa ereditaria, senza che si
possa spiegare colla miseria, nè con speciali accidenti, nè si arresta
che quando avvenga un matrimonio in età precocissima.
I bastardi ammontarono al 21% dei maschi e 13% delle femmine:
questo indica una prevalenza nel sesso maschile, che è curiosa
perchè accade il contrario per i legittimi; esaminando i primogeniti di
queste razze si osserva che nei maritati predominano le femmine,
nei bastardi i maschi.
La cifra del pauperismo ci mostra il legame del delitto e della
prostituzione colle malattie del sistema nervoso e colle mostruosità;
essa ci viene assai bene spiegata da questa tabella
[131], che ci
mostra la tisi, l'epilessia, alternarsi colla cecità e pazzia e sifilide.
Facendo poi il riassunto complessivo del risultato di questi dati,
Dugdale trova che furono 200 i ladri e criminali; 280 i poveri o
malati; 90 le prostitute o donne infette discendenti da un solo
ubbriacone; e che senza contare i 800 ragazzi morti precocemente, i

400 uomini contaminati da sifilide, e le 7 vittime degli assassini, lo
Stato in 75 anni, per cotesta infame famiglia, perdette un milione e
più di dollari.
Nè questi casi sono i soli.
Il feroce Galetto di Marsiglia era nipote di Orsolano, lo stupratore
antropofago; Dumollard era figlio di un assassino; Patetot aveva il
nonno ed il bisnonno assassini; i Papa ed i Crocco, Serravalle,
avevano avuto il nonno nelle carceri, Cavalante il nonno e il padre. I
Cornu erano assassini di padre in figlio, come i Verdure, i Cerfbeer, i
Nathan, ch'ebbero in un giorno 14 membri della famiglia accolti nello
stesso carcere. La Mocc..., avvelenatrice del marito e sfacciatamente
adultera, discende da un incesto, e le meretrici sono figlie di
delinquenti o di beoni; prime fra esse Mad. di Pompadour figlia di
ubbriacone e ladro graziato.
L'influenza ereditaria del delitto ha lasciato traccia nella storia
umana; e basterebbe a provarlo la storia dei Cesari.
La storia orientale, scrive de Hammer, ci mostra che nella medesima
generazione l'infanticidio segue dappresso al parricidio e che lo stilo
del nipote vendica sul padre l'assassinio dell'avo. Kosru e Mastantfzer
parricidi sono uccisi dai figliuoli, Hasan II fu ucciso dal figlio
Mohamed che fu avvelenato dal figlio (Hist. des Assass. 1833).
I papi Giovanni XI e XII e Benedetto IX, figli di cortigiane, portarono
sulla cattedra di San Pietro il sacrilegio, lo stupro e l'omicidio. La
lasciva Poppea era figlia di una donna ancor più lasciva; la madre di
Messalina fu accusata d'incesto col fratello.
Pazzia dei parenti.—Come già ci provano queste lugubri genealogie,
e quella della Motgare e dei K..., un certo numero dei parenti dei
criminali è colpito da alienazione mentale. Noi su 314 ne abbiamo
trovato 7 che avevano il padre alienato, 2 epilettici, 3 il fratello, 4 la
madre e 4 gli zii, 1 il cugino oltre 2 padri e 2 zii cretini, ed 1 fratello
ed 1 padre convulsionari e 2 bevitori: su altri 100 rei 5 che avean la
madre, 3 il padre, 6 i fratelli pazzi, 4 i fratelli epiletici; consimile mi

apparve la genealogia di una famiglia ch'ebbi a curare a Pavia e che
di generazione in generazione alternava pazzi e delinquenti e
meretrici.
Bono nella discendenza di un Ala... avvelenatore della moglie ch'era
a sua volta epilettico, trovava:
Moeli trovò 41 volte la pazzia e l'epilessia nei parenti di 67 rei pazzi
ladri, e cioè nel 15% suicidio e delitto nei parenti, 21% pazzia nei
fratelli, 23% pazzia ed epilessia nei parenti (Ueber Irren Verbrecher,
1888).
Il Kock
[132], lasciando in disparte gli incerti, aveva trovato il 46% di
ascendenza morbosa diretta nei suoi criminali.
Il dottor Virgilio, che studiava 266 condannati, affetti però da
malattie croniche, fra cui 10 alienati e 13 epilettici, riscontrò la pazzia
nella proporzione del 12% nei genitori, predominando sempre anche
qui (8,8) il padre. Riscontrava l'epilessia in una frequenza ancora
maggiore, 14,1%, senza contare il 0,8 di collaterali, e senza contare
un sordo-muto ch'era padre ad uno stupratore, 6 padri ed una
madre affetti da eccentricità, ed un padre semi-imbecille.
L'egregio dott. Penta trovò la pazzia nel 16% dei suoi criminali nati.
Ad Elmira su 6800 rei, dal 1886 al 1890, i genitori pazzi ed epilettici
ammontano da 13 a 127.

Marro e Sichart trovarono:
Pazzia dei parenti
(Sichart)(Marro)
% %
Incendiarii 11,028,5
Libidinosi 3,510,2
Ladri 6,414,5
Truffatori 5,510,3
Spergiuri 3,1 —
Omicidi — 17,0
Feritori — 14,0
Gottin, che appiccò il fuoco alla casa del suo benefattore, aveva il
nonno pazzo; Mio, il nonno ed il padre; Giovanni di Agordo,
parricida, i fratelli; Costa e Militello, gli zii ed il nonno; Martinati
aveva una sorella cretina; Vizzocaro il parricida e fratricida, Palmerini
l'assassino, ebbero alienati zio e fratelli; Bussi il padre e la madre;
Alberti l'avo ed il padre; Faella padre pazzo; Guiteau padre, zii e
cugini; Perussi falsario, macrocefalo e già omicida, nacque in un
manicomio da madre suicida e pazza e da padre megalomane;
Verger la madre ed i fratelli suicidi; Goudfroy, che uccise moglie,
madre e fratelli, speculando sull'assicurazione della loro vita, aveva
la nonna materna e lo zio pazzi; Didier parricida, ebbe il padre
pazzo; Luigia Brienz uxoricida, ebbe la madre epilettica,la sorella
pazza; Ceresa, Abbado e Kulmann ebbero parenti alienati.
Per questo rapporto, come per quello dell'alcoolismo, gli alienati
sono quasi alle stesse condizioni dei delinquenti.—Anche la maggiore
frequenza dell'eredità paterna in confronto alla materna è stata
osservata prevalere, negli alienati maschi, dal Golgi, dallo Stewart e
dal Tigges, benché in proporzioni assai minori
[133].
Tuttavia importerà molto al medico legale il notare che la pazzia dei
genitori si ritrova molto meno frequentemente nei delinquenti. E
basterebbe solo a dimostrarlo la proporzione trovata dal Virgilio, che

non passava il 12%, mentre su 3115 alienati il Tigges trovò il 28%, e
lo Stewart il 49 ed il Golgi il 53%.
Zillman trovò che nei paesi ove domina endemico il cretinismo è
frequente l'ozio, la tendenza ai litigi e ai delitti atroci, che son più
numerosi di 5 volte tanto nelle donne che negli uomini (Ueber die
Cretinimus in Salzburg, 1868).
Che se vogliamo considerare l'influenza ereditaria anche dell'epilessia
e di altre nevrosi, noi troviamo che il Golgi giungerebbe al 78%.
Epilessia nei parenti.—Il Knecht trova 60 epilettici tra i parenti di 400
criminali. Brancaleone Ribaudo su 559 soldati delinquenti trova
l'epilessia dei genitori nel 10,1%. Il Penta su 184 rei nati, nel 9,2%.
Clarcke trova nel 46% dei parenti di epilettici delinquenti l'epilessia
con sicurezza constatata; mentre negli epilettici non delinquenti il
rapporto è solo del 21%.
Dejerine negli epilettici delinquenti trova che l'epilessia dei parenti si
può riconoscere nel 74,6%: pei non rei nel 34,6% l'epilessia dei
parenti e nel 16,5% le psicosi.
Marro e Sichart trovarono:
Epilessia
(Sichart) (Marro)
% %
Ladri 2,1 3,3
Truffatori 2,0 1,3
Incendiarii 1,8 —
Libidinosi 1,2 —
Spergiuri — —
Omicidi — 7,0
Totale 6,7% (Vedi per altre prove il vol. II, parte I).
Eredità di alcoolismo.—Penta trovò (v. s.) l'alcoolismo nel 27% e nel
33% dei genitori grandi criminali, io nel 20%. Ad Elmira su 6500 rei i

genitori beoni erano da 37,5 a 38,4%.
L'alcoolismo, secondo un calcolo fatto in 50 famiglie alcooliste da
Legrain
[134] con 157 discendenti, diede per eredità:
54% di alienati
62% di alcoolisti
61% di epilettici
29% di convulsionari
14% pazzi morali (o rei-nati)
6,5% meningitici.
Egli osservò che nell'alcoolismo ereditario, il primo carattere è la
precocità; vi trovò degli alcoolisti perfino di 4 anni; l'altro carattere è
di essere di una suscettibilità speciale per l'alcool; mentre un padre
per 7 anni beone pure non sragiona ancora, il figlio dopo due giorni
di orgia ha già il delirio; e la sua ebbrezza è già una specie di delirio;
il padre può non avere il delirio, il figlio sempre, perché ha già il
delirio in potenza.—Un altro carattere è il bisogno di alcoolici sempre
più forti; son caratteri frequentissimi nei criminali.
In Sassonia
[135]
il10,5%dei rei è nato da ubbriachi
In Baden il 19,5%dei rei è nato da ubbriachi
In Wurtemberg il19,8%dei rei è nato da ubbriachi
In Alsazia il 22,0%dei rei è nato da ubbriachi
In Prussia il 22,1%dei rei è nato da ubbriachi
In Baviera il 34,6%dei rei è nato da ubbriachi (Baer,1882).
Sichart e Marro trovarono;
Parenti alcoolisti
(Sichart)(Marro)
% %
Ladri 14,346,6
Truffatori 13,332,4
Incendiarii 13,342,8
Falso giuramento 11,1 —
Libidinosi 14,243,5

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