Chap 4: Searching Techniques Artificial Intelligence Chapter 4 TIN 5013: Artificial Intelligence

TIN 5013: Artificial Intelligence 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

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

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

TIN 5013: Artificial Intelligence 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

TIN 5013: Artificial Intelligence 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

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

Example: The Bridges of Konigsberg Problem (cont) Predicates: Connect (B, C, b5) TIN 5013: Artificial Intelligence

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 E 50 125 C 50 100 D TIN 5013: Artificial Intelligence

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

TIN 5013: Artificial Intelligence Node expansion TIN 5013: Artificial Intelligence

Node expansion (initial) TIN 5013: Artificial Intelligence

Node expansion (expanding Arad) TIN 5013: Artificial Intelligence

Node expansion (expanding Sibiu) TIN 5013: Artificial Intelligence

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

TIN 5013: Artificial Intelligence Searching Strategies Blind search  traversing the search space until the goal nodes is found (might be doing exhaustive search). Techniques : Breadth First Uniform 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

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

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

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

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

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

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

TIN 5013: Artificial Intelligence Summary TIN 5013: Artificial Intelligence

TIN 5013: Artificial Intelligence 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

Heuristic Search : Heuristic Function TIN 5013: Artificial Intelligence

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

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

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

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

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

Heuristic Search : A* Algorithm

Heuristic Search : A* Algorithm

Heuristic Search : A* Algorithm TIN 5013: Artificial Intelligence

Heuristic Search : A* Algorithm

Heuristic Search : A* Algorithm TIN 5013: Artificial Intelligence

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?

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.