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Exploring Searching Techniques in Artificial Intelligence

Dive into the world of searching techniques and strategies in artificial intelligence to efficiently solve complex problems. Learn about state space search, searching tree representation, strategies, and more. Discover how searching algorithms like BFS and DFS work. Explore the Bridges of Konigsberg and Traveling Salesperson problems. Uncover the importance of node expansion and measuring searching performance. Gain insights into blind and heuristic search methods, including Breadth-First Search and A* Algorithm. Enhance your understanding of searching complexity and strategies for finding optimal solutions in AI.

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Exploring Searching Techniques in Artificial Intelligence

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  1. Chap 4: Searching Techniques Artificial Intelligence 605451 Dr.Hassan Al-Tarawneh TIN 5013: Artificial Intelligence

  2. Motivation Attempt the end, and never stand to doubt, nothing’s so hard, but search will find it out “Robert Herrick” TIN 5013: Artificial Intelligence

  3. What we will cover ? • Ideas in searching • Searching tree representation • Uninformed and informed search • Game playing search TIN 5013: Artificial Intelligence

  4. Problem as a State Space Search • To build as system to solve a particular problem, we need: • Define the problem: must include precise specifications ~ initial solution & final solution. • Analyze the problem: select the most important features that can have an immense impact. • Isolate and represent : convert these important features into knowledge representation. • Problem solving technique(s): choose the best technique and apply it to particular problem. TIN 5013: Artificial Intelligence

  5. The Quest • Typical questions that need to be answered: • Is the problem solver guaranteed to find a solution? • Will the system always terminate or caught in a infinite loop? • If the solution is found, it is optimal? • What is the complexity of searching process? • How the system be able to reduce searching complexity? • How it can effectively utilize the representation paradigm? TIN 5013: Artificial Intelligence

  6. Important Terms • Search space possible conditions and solutions. • Initial state  state where the searching process started. • Goal state  the ultimate aim of searching process. • Problem space  “what to solve” • Searching strategy strategy for controlling the search. • Search tree  tree representation of search space, showing possible solutions from initial state. TIN 5013: Artificial Intelligence

  7. Example: The Bridges of Konigsberg Problem • Classical graph applications. • Introduced by Leonhard Euler. • Problem: Can a person walk around the city crosses each bridge exactly once? TIN 5013: Artificial Intelligence

  8. Example: The Bridges of Konigsberg Problem (cont) A b6 b1 b3 b5 C B b4 b7 b2 D Predicates:Connect (B, C, b5) TIN 5013: Artificial Intelligence

  9. Example: Traveling Salesperson Problem • Suppose a salesperson has five cities to visit and them must return home. Goal  find the shortest path to travel. A B 75 125 125 75 100 50 E 125 C 50 100 D TIN 5013: Artificial Intelligence

  10. Searching for Solution • Search through state space (explicitly using searching tree). • Node expansion :- generating new node related to previous nodes. • Concepts: • State :- conditions in which the node corresponds. • Parent node :- the superior node • Path cost :- the cost, from initial to goal state. • Depth:- number of steps along the path from initial state TIN 5013: Artificial Intelligence

  11. Node expansion TIN 5013: Artificial Intelligence

  12. Node expansion (initial) TIN 5013: Artificial Intelligence

  13. Node expansion (expanding Arad) TIN 5013: Artificial Intelligence

  14. Node expansion (expanding Sibiu) TIN 5013: Artificial Intelligence

  15. Measuring Searching Performance • The output from problem-solving (searching) algorithm is either FAILURE or SOLUTION. • Four ways: • Completeness : is guaranteed to find a solution? • Optimality: does it find optimal solution ? • Time complexity: how long? • Space complexity: how much memory? • Complexity : branching factor (b), depth (d), and max. depth (m) TIN 5013: Artificial Intelligence

  16. Searching Strategies • Blind search  traversing the search space until the goal nodes is found (might be doing exhaustive search). • Techniques : Breadth FirstUniform Cost ,Depth first, Interactive Deepening search. • Guarantees solution. • Heuristic search search process takes place by traversing search space with applied rules (information). • Techniques: Greedy Best First Search, A* Algorithm • There is no guarantee that solution is found. TIN 5013: Artificial Intelligence

  17. Blind Search : Breadth First Search (BFS) • Strategy ~ search all the nodes expanded at given depth before any node at next level. • Concept : First In First Out (FIFO) queue. • Complete ?: Yes with finite b (branch). • Complexity: • Space : similar to complexity – keep nodes in every memory • Optimal ? = Yes (if cost =1) TIN 5013: Artificial Intelligence

  18. 1 2 4 3 Blind Search : Breadth First Search TIN 5013: Artificial Intelligence

  19. Blind Search : Depth First Search (DFS) • Strategy ~ search all the nodes expanded in deepest path. • Last In First Out concept. • Complete ?: No • Complexity: • Space : O(bm) – b ; branching factor, m ; max. depth • Optimality ? : No TIN 5013: Artificial Intelligence

  20. 3 4 5 N+1 ……. Blind Search : Depth First Search (DFS) 1 2 TIN 5013: Artificial Intelligence

  21. Blind Search : Iterative Deepening DFS (ID-DFS) • Strategy ~ combines DFS with best depth limits. • Gradually increase the limit; L=0, L=1… and so on. • Complete ?: Yes (if b is finite) • Complexity: • Space : • Optimality ? : yes (if path costs are all identical) TIN 5013: Artificial Intelligence

  22. Blind Search : Iterative Deepening DFS (ID-DFS) TIN 5013: Artificial Intelligence

  23. Summary TIN 5013: Artificial Intelligence

  24. Heuristic Search : h(n)=67 h(n)=34 E A* • Important aspect: formation of heuristic function (h(n)). • Heuristic function  additional knowledge to guide searching strategy (short cut). • Distance: heuristic function can be straight line distance (SLD) D h(n)=9 h(n)=12 B C* h(n)=24 h(n)=0 TIN 5013: Artificial Intelligence

  25. Heuristic Search : Heuristic Function TIN 5013: Artificial Intelligence

  26. Heuristic Search :Greedy-Best Search • Tries to expand the node that is closest to the goal. • Evaluates using only heuristic function : f(n) = h(n) • Possibly lead to the solution very fast. • Problem ? ~ can end up in sub-optimal solutions (doesn’t take notice of the distance it travels). • Complexity and time: • Complete & optimal ? : No (stuck in infinite loop) TIN 5013: Artificial Intelligence

  27. Heuristic Search :Greedy-Best Search 1 2 TIN 5013: Artificial Intelligence

  28. Heuristic Search :Greedy-Best Search 3 TIN 5013: Artificial Intelligence

  29. Heuristic Search : A* Algorithm • Widely known algorithm – (pronounced as “A star” search). • Evaluates nodes by combining g(n) “cost to reach the node” and h(n) “cost to get to the goal” • f(n) = g(n) + h(n), f(n) estimated cost of the cheapest solution. • Complete and optimal ~ since evaluates all paths. • Time ? ~ a bit time consuming • Space ? ~ lot of it! TIN 5013: Artificial Intelligence

  30. S :10 3 2 D A :9 :8 5 1 3 2 E G H G’ :0 :3 :4 :0 Heuristic Search : A* Algorithm Path cost for S-D-G f(S) = g(S) + h(S) = 0 + 10 10f(D) = (0+3) + 9  12f(G) = (0+3+3) + 0  6 Total path cost = f(S)+f(D)+f(G) 28 Path cost for S-A-G’ f(S) = 0 + 10 10f(A) = (0+2) + 8  10f(G’) = (0+2+2) + 0  4 Total path cost = f(S)+f(A)+f(G’) 24 * Path S-A-G is chosen = Lowest cost

  31. Heuristic Search : A* Algorithm

  32. Heuristic Search : A* Algorithm

  33. Heuristic Search : A* Algorithm TIN 5013: Artificial Intelligence

  34. Heuristic Search : A* Algorithm

  35. Heuristic Search : A* Algorithm TIN 5013: Artificial Intelligence

  36. Issues in Heuristic Search • Searching using heuristic function does not solely on directed solution  but the best algorithm to find shortest path towards goal. • Admissible  attempt to find possible shortest path to a goal whenever it exists. • Informedness  question in what sense the heuristic function is better than another. • Monotonicity  question if the best state is discovered by heuristic search, is there any guarantee that the same state won’t be found later at lowest searching cost?

  37. References • Cawsey, A. (1998). The Essence of Artificial Intelligence, Prentice Hall. • Russell, S. and Norvig, P. (2003). Artificial Intelligence: A Modern Approach, Prentice-Hall 2nd Edition.

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