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Module_2_rks in Artificial intelligence in Expert System
- 1. MODULE 2 Problem Solving Agents – Searching for solutions- Uninformed Search Strategies – Informed Search Strategies, heuristic functions.
- 2. Artificial intelligence • Intelligence : “Ability to learn, understand, and think”. • The study of the capacity of machines to simulate intelligent human behavior. • AI is the study of how to make computers make things which at the moment people do better. ARTIFICIAL INTELLIGENCE 2
- 3. Problem solving System •Define the problem. •Analyze the problem. •Isolate & represent the task knowledge necessary to solve the problem. •Choose the best problem- solving techniques & apply it to the problem. ARTIFICIAL INTELLIGENCE 3
- 4. Formal description for defining a problem •Representation : •State Space • It contains set of all the possible states of the relevant problem •Initial State •Goal State •Transformation Rules ARTIFICIAL INTELLIGENCE 4
- 5. Production Systems • Production System Consists of • A set of rules : (Pattern) Operation to be performed • One / more Knowledge/ databases • Control strategy –specifies order in which rules will be compared • Rule applier ARTIFICIAL INTELLIGENCE 5
- 6. State-Space Tree •State-Space Tree. A space state tree is a tree that represents all of the possible states of the problem, from the root as an initial state to the leaf as a terminal state. ARTIFICIAL INTELLIGENCE 6
- 17. • Let G= (V,E) be a directed graph with each edge cost cij. • Cij is defined such that cij.>0 for all I and j and cij = ∞ if (i,j) not belongs to E. • A tour of G is a directed simple cycle that includes every vertex in V. • The cost of a tour is the sum of the cost of edges on the tour. The TVs problem is to find a tour of minimum cost. • For example: consider a production environment in wchich several commodities are manufactured by same set of machines. The manufacture proceeds in cycles. In each production cycle, n different commodities are produced. When the machines are changed from production of commodity I to commodity j, a change over cost cij is incurred. ARTIFICIAL INTELLIGENCE 17
- 26. Chess board- problem • Defining the problem as a state space search: • Start the problem of play chess. • 1st we have to specify the starting position of chess board, the rules that define the legal moves, and the board positions that represent a win for one side or the other. • Problem description: • Consider a chess board 8x8 array where each position contains a symbol standing for the appropriate piece in the official chess opening position ARTIFICIAL INTELLIGENCE 26
- 27. Chess board- problem • Goal state: • The goal of any board in which the opponent does not have a legal move and his or her king is under attack. • Legal move from initial state to final state. • If we write legal moves of roughly 10120 possible board positions. ARTIFICIAL INTELLIGENCE 27
- 30. Chess game ARTIFICIAL INTELLIGENCE 30 Transformation Rules: white pawn at square(file e, rank 2) AND square(file e, rank 3) is empty AND square(file e, rank 4) is empty Initial state: Current board position Goal state: opponent does not have a legal move and his /her king is under attack. Move pawn from square(file e, rank 2) to square(file e, rank 4)
- 32. 4 or 8 queen’s problem • A classic combinatorial problem is to place eight queens on a 8x8 chess board so that no two attack, that is no two of them are on the same row, column, or diagonal. • Solution: To model this problem • Assume that each queen in different column; • Assign a variable Ri (i=1 to N) to the queen in the ith column indicating the position of queen in the row. • Apply “no-threatening” constraints between each couple Ri and Rj of the queens and evaluate the algorithm. ARTIFICIAL INTELLIGENCE 32
- 62. • Time Complexity: Time Complexity of BFS algorithm can be obtained by the number of nodes traversed in BFS until the shallowest Node. Where the d= depth of shallowest solution and b is a node at every state. • T (b) = 1+b2+b3+.......+ bd= O (bd) • Space Complexity: Space complexity of BFS algorithm is given by the Memory size of frontier which is O(bd). • Completeness: BFS is complete, which means if the shallowest goal node is at some finite depth, then BFS will find a solution. • Optimality: BFS is optimal if path cost is a non-decreasing function of the depth of the node ARTIFICIAL INTELLIGENCE 62
- 64. • Completeness: DFS search algorithm is complete within finite state space as it will expand every node within a limited search tree. • Time Complexity: Time complexity of DFS will be equivalent to the node traversed by the algorithm. It is given by: • T(n)= 1+ n2+ n3 +.........+ nm=O(nm) • Where, m= maximum depth of any node and this can be much larger than d (Shallowest solution depth) • Space Complexity: DFS algorithm needs to store only single path from the root node, hence space complexity of DFS is equivalent to the size of the fringe set, which is O(dm). • Optimal: DFS search algorithm is non-optimal, as it may generate a large number of steps or high cost to reach to the goal node. ARTIFICIAL INTELLIGENCE 64
- 66. • Completeness: • Uniform-cost search is complete, such as if there is a solution, UCS will find it. • Time Complexity: • Let C* is Cost of the optimal solution, and ε is each step to get closer to the goal node. Then the number of steps is = C*/ε. Here we have taken +1, as we start from state 0 and end to C*/ε. • Hence, the worst-case time complexity of Uniform-cost search isO(b1 + [C*/ε])/. • Space Complexity: • The same logic is for space complexity so, the worst-case space complexity of Uniform-cost search is O(b1 + [C*/ε]). • Optimal: • Uniform-cost search is always optimal as it only selects a path with the lowest path cost. ARTIFICIAL INTELLIGENCE 66
- 68. • Completeness: • This algorithm is complete is if the branching factor is finite. • Time Complexity: • Let's suppose b is the branching factor and depth is d then the worst-case time complexity is O(bd). • Space Complexity: • The space complexity of IDDFS will be O(bd). • Optimal: • IDDFS algorithm is optimal if path cost is a non- decreasing function of the depth of the node. ARTIFICIAL INTELLIGENCE 68
- 70. • Completeness: Bidirectional Search is complete if we use BFS in both searches. • Time Complexity: Time complexity of bidirectional search using BFS is O(bd). • Space Complexity: Space complexity of bidirectional search is O(bd). • Optimal: Bidirectional search is Optimal ARTIFICIAL INTELLIGENCE 70
- 73. • Time Complexity: The worst case time complexity of Greedy best first search is O(bm). • Space Complexity: The worst case space complexity of Greedy best first search is O(bm). Where, m is the maximum depth of the search space. • Complete: Greedy best-first search is also incomplete, even if the given state space is finite. • Optimal: Greedy best first search algorithm is not optimal. ARTIFICIAL INTELLIGENCE 73
- 85. • Time Complexity: The worst case time complexity of Greedy best first search is O(bm). • Space Complexity: The worst case space complexity of Greedy best first search is O(bm). Where, m is the maximum depth of the search space. • Complete: Greedy best-first search is also incomplete, even if the given state space is finite. • Optimal: Greedy best first search algorithm is not optimal. ARTIFICIAL INTELLIGENCE 85