Problem Solving Strategies Pg Sem 1.pptx

Problem solving strategies

1. Problem Solving

2. A general model of problem solving Ernst and Newell (1969) developed a computer simulation called general problem solver (GPS) as a model for exploring the nature of human problem solving. Their intent was to show that an artificial intelligence (AI) program based on certain general methods could, in fact solve a wide range of problems. Psychological research has tested whether GPS provides a good simulation of human problem solving. The steps involves representation of problem, problem space and solution path.

3. Representation of problem The way a problem is defined and structured. GPS fast translates the description of a problem into an internal representation or model of a problem description. The translator interprets is sentence and attempts to identify the initial state, the goal state, and the operators. Initial state : The starting point or condition. Goal state : The desired outcome or solution. Operators : Actions or transformations that can be applied to move from the initial state to the goal state.

4. Problem space After the representation of problem, the problem space that must be searched using methods or techniques of problem solving. Universe of all possible states that can be reached while solving a problem (from the initial state to the goal state). Algorithm and heuristics Solution path A path must be found that takes GPS from the initial statement to the goal state.
A representation of this solution path is generated in the final stage. A solution path is a sequence of operators that can be applied to the initial state to reach the goal state. It represents the route taken to solve the problem.

5. Strategies for problem solving Algorithms An algorithm is a systematic set of step-by-step operations that covers the entire problem space and guarantees a solution if one exists. Algorithms are sequences of operations that may be repeated over and over again and that, in theory, guarantee the solution to a problem (Hunt, 1975; Sternberg, 2000). Eg : A recipe for cooking a particular dish, Instructions for how to solve a Rubik’s cube. Advantages They provide a consistent approach to solving problems, reducing errors caused by guesswork or intuition.
Algorithms can solve complex problems by breaking them down into smaller, manageable steps.
Once learned, algorithms can make problem-solving more efficient and structured.

6. Disadvantages Algorithms are efficient for well-defined problems (where the complete problem space is visible), but much less so for ill-defined problems, where it is not clear how the problem space looks like. We humans are not good at applying algorithms, because our reasoning is slow and we rapidly get bored of repetitive tasks. Algorithms also require careful planning and time consuming. As a result, we are always on the look-out for simple solutions, shortcuts. Rather than systematically covering the entire problem space, we look for action sequences that rapidly diminish the distance between the problem and the solution.

7. Heuristics Rule of thumb that is cognitively undemanding and often produces approximately accurate answers; compare algorithm.
They are based on hunches, intuitions, which themselves are based on experiences and solutions that have worked in the past. Types of heuristics 1. Representativeness Heuristic: Judging a situation based on how similar it is to a familiar prototype or stereotype. Eg : Assuming a person who wears glasses is intelligent. 2. Availability Heuristic: Making judgments based on information that is readily available in memory.Eg : After hearing news about airplane crashes, someone might overestimate the danger of flying. 3. Anchoring and Adjustment Heuristic: Starting with a reference point (anchor) and then adjusting it to reach a final decision. Eg : A student sees a textbook listed for a high price. Even if they find a cheaper version later, they may still feel like they're getting a good deal because the initial high price anchors their perception of the textbook's value.

8. Advantages They don’t require extensive information processing.
Heuristics allow for quick decision-making, particularly useful in situations where time is limited or information is incomplete.
They reduce the mental effort required to process complex information, making them useful in everyday life.
Heuristics help in identifying patterns and applying previous knowledge to new situations. Disadvantages Heuristics can lead to cognitive biases like overconfidence, stereotyping, or incorrect assumptions, which may result in poor decisions.
Can cause a misapplication of rules
Useful in familiar situations, they may fail when applied to novel or complex problems that require detailed analysis.
From time to time they fail and we get stuck or even come to a wrong solution

9. Search strategy A search strategy is defined by picking the order of node expansion. Cognitive processes used to explore different paths or options to reach a goal. These strategies involve systematically examining various possibilities and making decisions about which ones to pursue. Key dimensions of search strategies Completeness: refers to whether the search strategy will always find a solution, assuming one exists. For psychological problem solving, it’s about whether a given approach will reliably generate a potential answer. Does the strategy guarantee finding a solution if one exists? T ime complexity: involves how long it takes to find a solution, determined by how many mental or computational “steps” are required. How many nodes (or potential solutions) does the strategy generate? Space complexity: how much mental or cognitive “capacity” is used at any given time, such as the number of possibilities one must keep track of while solving a problem. What is the maximum number of nodes that need to be stored in memory at any given time? Optimality: refers to whether the search strategy always results in the best or most efficient solution. Does the strategy always find the best (least-cost) solution?

10. Types of search strategies Uninformed search strategies : Uninformed search strategies use only the information available in the problem definition. Simply, Uninformed search strategies rely solely on the information provided in the problem definition and do not use any domain-specific knowledge. Informed (heuristic) search : Strategies use additional knowledge (heuristics) to estimate the cost or benefit of different options and guide the search toward more promising solutions. These strategies use domain-specific knowledge to make the search process more efficient.
A heuristic is a function that estimates the cost or distance from the current state to the goal. Heuristics help the search be more efficient by focusing on paths that are likely to lead to a solution faster.

11. Means-ends analysis Means-ends analysis is a problem solving strategy that arose from the work on problem solving of Newell and Simon (1972).
It is a strategy in which the problem solver divides the problem into a number of sub problems, or smaller problems. Each of these sub problems is solved by detecting the difference between the original state and the goal state and then reducing the difference between these two states. The name means ends analysis fits the process, because it involves figuring out the “ends” you want and then figuring out what “means” you will use to reach those ends.
Every day we all solve problems by using means ends analysis ( Eg : cleaning a room).
Means ends analysis involves sub goals to eliminate the difference between the current state and the condition for applying desired operator.

12. This strategy repeatedly compares states and seeks operators, establishing sub goals and finding ways to reach the sub goals, all on the way to finding a path to the final goal. Eg : Tower of Hanoi

13. Hill climbing a simple heuristic used by problem solvers in which they focus on making moves that will apparently put them closer to the goal or problem solution. Hill climbing involves a focus on short-term goals (rather than the final goal aimed for). The elements of the situation are listed and changes tried out. The element that leads to the largest improvement is selected. Someone using this heuristic is like a climber who wants to reach the highest mountain peak in the area. He/she uses the strategy of always moving upwards. This strategy may work, but it is possible the climber will find himself/herself trapped on a hill separated by several valleys from the highest mountain. Simply, hill climbing is a problem-solving strategy where a person makes decisions by taking small steps toward a solution, choosing the option that seems to move them closer to the goal at each step. It’s like climbing a hill, where you continually take steps upward without necessarily seeing the entire path to the top. However, people may get stuck at some points where they can’t improve their situation further by making small steps, even though they haven’t reached the best possible solution.

14. The hill-climbing heuristic is a simpler strategy than means-ends analysis and is mostly used when the problem solver has no clear understanding of the structure of a problem. As a result, it more often fails to lead to problem solution than a means-ends analysis (Robertson, 2001). Eg : A student solving a maze might choose paths that seem to lead closer to the exit at each turn. If they hit a dead-end, they might backtrack but will always try the path that seems to get them closer to the goal, even if it might lead them into a trap. They are not considering the entire maze but are focused on immediate progress. Analogical transfer The technique of using the solution to a similar problem to guide solution of a new problem is called analogical problem solving. The starting point for much of the research on analogical problem solving has been to first determine how well people can transfer their experience from solving one problem to solving another, similar problem. This transfer from one problem to another is called analogical transfer. Analogical transfer is the transfer of knowledge from one situation to another by finding a set of one-to-one correspondences between aspects of one body of information and aspects of another .

15. Analogical transfer is one method we have of coming up with creative solutions to some of life’s problems.
To study analogical transfer, participants who are trying to solve a target problem (the new or unfamiliar problem) are presented with a problem or a story, called the source problem or source story(a similar or previously solved problem), and by comparing the two, they can transfer the knowledge from the source to the target.
Simply, it illustrates a way to solve the target problem. Eg : Russian marriage problems, The mutilated checkerboard problem. Steps of Analogical Problem Solving Noticing : Seeing that there is a possible analogy between problems. Most difficult, especially in the real world Mapping : Connecting elements of the source problem to elements of the target problem. Applying : Using the analogy to generate the solution

16. Improving Analogical Transfer Two types of features (best when similar) * Structural Features (structural features remain the same across different problems even if the surface details differ). * Surface Features (these are the superficial details or characteristics of a problem that make it appear unique but are often less important in terms of the solution). Analogical Encoding : Strategy for training people to be able to notice and apply analogies. It involves two steps, compare different source problems first, then solve Target. working backward The problem solver starts at the end and tries to work backward from there. With the backward search heuristic, the problem solver starts at the goal state. Sometimes it is useful to start at the goal state of a problem and attempt to work backward to the initial state. In solving a paper-pencil maze, it may be easier to see the correct path by starting at the end.

17. Working backwards can be a very useful heuristic, particularly for problems that contain a uniquely specified goal state.
For example, a backward search would be ideal for a maze with many paths out of the beginning point yet only one path leading form the goal. Back tracking Back tracking is a general algorithmic technique that considers searching every possible combination in order to solve an optimization problem. Back tracking is also known as depth-first search or branch and bound. The term “backtrack” was coined by American mathematician D. H. Lehmer in the 1950s. By inserting more knowledge of the problem, the search tree can be pruned to avoid considering cases that don't look promising. While backtracking is useful for hard problems to which we do not know more efficient solutions, it is a poor solution for the everyday problems that other techniques are much better at solving.

18. Two main mechanisms in BT Backtracking:
• To recover from dead-ends • To go back
Consistency checking:
• To expand consistent paths • To move forward Backtracking Methodology 1. View picking a solution as a sequence of choices
2. For each choice, consider every option recursively
3. Return the best solution found
Backtracking can be applied only for problems which admit the concept of a “partial candidate solution” and a relatively quick test of whether it can possibly be completed to a valid solution.
Backtracking is an important tool for solving constraint satisfaction problems, such as crosswords, verbal arithmetic, Sudoku, and many other puzzles. It is often the most convenient technique for parsing, for the knapsack problem and other combinatorial optimization problems.

19. It is also the basis of the so-called logic programming languages such as Icon, Planner and Prolog . Schema based models A schema is an organized structure “consisting of certain elements and relations” specific to a situation (Mayer, 1999).
Schemata are the appropriate mechanism for the problem solver to “capture both the patterns of relationships as well as their linkages to operations” (Marshall, 1995). Schema-Based Problem Solving Model involves applying four procedural steps • Schema knowledge/Problem Schema Identification : First step is to read and understand the problem to determine which problem type (or schema) it belongs to. It helps in recognizing patterns or structures similar to problems the solver has encountered before. Eg : The student first reads the problem and identifies the problem schema. • Elaboration knowledge/Representation : In this step, the solver represents the problem by organizing and diagramming the key information. This can involve drawing diagrams, charts, or any other visual aid that helps break down and display the problem clearly. Eg : the student represents the problem by diagramming the key infor­mation.

20. • Strategic Knowledge/Planning : The solver plans how to solve the problem by selecting the appropriate operations and writing the corresponding equation or approach. This involves deciding on a strategy based on the problem schema and the representation of the information. Eg : the student plans how to solve the problem by selecting the appropriate operation and writing out the math equation.
• Executive Knowledge/Solution : Finally, the student executes the plan by performing the necessary calculations or steps to arrive at the solution. After solving, the student can verify the solution for accuracy and completeness. Eg : the student solves the problem. Multiple trace theory (memory) Multiple Trace Theory (MTT) builds on the distinction between semantic memory and episodic memory and addresses perceived shortcomings of the standard model with respect to the dependency of the hippocampus. Multiple Trace Theory argues that the hippocampus is always involved in the retrieval and storage of episodic memories. It is thought that semantic memories, including basic information encoded during the storage of episodic memories, can be established in structures apart from the hippocampal system such as the neo-cortex in the process of consolidation.

21. Hence, while proper hippocampal functioning is necessary for the retention and retrieval of episodic memories, it is less necessary during the encoding and use of semantic memories.
As memories age there are long-term interactions between the hippocampus and neo-cortex and this leads to the establishment of aspects of memory within structures aside from the hippocampus.
MTT thus states that both episodic and semantic memories rely on the hippocampus and the latter becomes somewhat independent of the hippocampus during consolidation.
An important distinction between MTT and the standard model is that the standard model proposes that all memories become independent of the hippocampus after several years.
However, Nadel and Moscovitch have shown that the hippocampus was involved in memory recall for all remote autobiographical memories no matter of their age.

22. Criticisms of multiple trace theory Haist , Gore, and Mao, sought to examine the temporal nature of consolidation within the hippocampus to test the multiple trace theory against the standard view.
* The hippocampus does not substantially contribute to the recollection of remote memories after a period of a few years.
* Advances in the fMRI have allowed them to improve their distinction between the hippocampus and the entorhinal cortex which is more enduring in its activation from remote memory retrieval.
* The use of memories during testing which cannot be confirmed as accurate.
* Finally, they state that the initial interview in the scanner acted as an encoding event as such differences between recent and remote memories would be obscured.

23. Multiple Choice Questions 1. Which problem-solving strategy involves following a specific set of rules or steps to guarantee a solution? A) Heuristics B) Algorithms C) Hill Climbing D) Working Backward 2. A heuristic is best described as: A) A method that guarantees a solution
B) A mental shortcut that may not guarantee a correct solution
C) A way to examine every possible solution to find the best one
D) A solution process that always involves trial and error 3. Which strategy involves reverting to previous steps after hitting an obstacle and trying an alternative approach? A) Backtracking B) Means-End Analysis C) Hill Climbing D) Algorithm

24. 4. Analogical transfer in problem solving involves: A) Repeating a solution that worked for a different problem B) Applying a strategy used in one domain to another similar problem C) Working from the goal state to the current state D) Systematically exploring every possible solution 5. Which problem-solving strategy works best when you have a clear vision of the goal but are unsure of the steps needed to achieve it? A) Backtracking B) Heuristics C) Working Backward D) Algorithms

25. Fill in the blanks 6. In problem-solving, __________ involves comparing the current state to the goal state and then taking steps to reduce the difference. 7. A __________ is a cognitive framework or blueprint that helps individuals organize and interpret information. 8. The ability to apply schemas from one problem to a new, similar problem is called __________ transfer. 9. The __________ method involves choosing the option that seems to lead most directly to the goal, without necessarily considering all possibilities. 10. GPS is proposed by ___________&______________.

26. THANK YOU PREPARED BY JALVAJANNA K