Problem Solving Agents Blind and Informed Searches

Problem Solving Agent

Problem Types Well defined Non well defined Initial state Operator(Successor and predecessor Functions) Goal Test Path cost function Non well defined Missing at least on criteria

Example 1: TSM In Romania On holiday in Romania; currently in Arad. Formulate goal: be in Bucharest Formulate problem: states: various cities actions: drive between cities Find solution: sequence of cities, e.g., Arad, Sibiu, Fagaras, Bucharest Goal Test> Are we in Bucharest. Cost Function> Sum of road lengths to the destination

TSM In Romania

Example 2: 8-Puzzel

Example 2: 8-Puzzel states??: integer locations of tiles (ignore intermediate positions) actions??: move blank left, right, up, down (ignore unjamming etc.) transition model??: effect of the actions goal test??: = goal state (given) path cost??: 1 per move [Note: optimal solution of n-Puzzle family is NP-hard]

Example Problems Toy problems Real-world problems vacuum cleaner agent 8-puzzle 8-queens Crypt arithmetic missionaries cannibals Real-world problems route finding traveling salesperson VLSI layout robot navigation assembly sequencing

Search Know the fundamental search strategies and algorithms uninformed search breadth-first, depth-first, uniform-cost, iterative deepening, bidirectional informed search best-first (greedy, A*), heuristics, memory-bounded Evaluate the suitability of a search strategy for a problem completeness, optimality, time & space complexity

Searching for Solutions Traversal of some search space from the initial state to a goal state legal sequence of actions as defined by operators The search can be performed on On a search tree derived from expanding the current state using the possible operators Tree-Search algorithm A graph representing the state space Graph-Search algorithm

Searching for Solutions

Uninformed search strategies Uninformed strategies use only the information available in the problem definition Breadth-first search Uniform-cost search Depth-first search Depth-limited search Iterative deepening search Bidirectional Search

BFS Expand shallowest unexpanded node (shortest path in the frontier)

Evaluation b: branching factor d: depth of the shallowest goal node m: depth of stop l: current depth N: Total number of genretaed Nodes

Evaluation Complete?? Yes (if b is finite) Optimal?? Yes (if cost = 1 per step); not optimal in general Time?? b^d Number of nodes generated: 1 + b + b^2 + … + b^d Space?? b^d Space is the big problem; can easily generate nodes at 100MB/sec so 24hrs = 8640GB.

Uniform-cost search Expand first least-cost path (Equivalent to breadth-first if step costs all equal) Implementation: fringe = priority queue ordered by path cost, lowest first

Depth First Search

DFS Depth first search is another way of traversing graphs, which is closely related to preorder traversal of a tree. Recall that preorder traversal simply visits each node before its children. It is most easy to program as a recursive routine. Complete?? No Optimal?? No Time?? b^d Space?? b*d

Depth limited search A version of DFS in which l is defined by an expert There is a chance of converging to local optima Complete?? Yes(if l>d) Optimal?? Yes Time?? b^l Space?? b*l

Iterative Deeping Search(IDS) This search strategy always expands one node to the deepest level of the tree. Only when a dead-end is encountered does the search backup and expand nodes at shallower levels. N=(d+1)1+(d)b+(d-1)b2+...+(3)bd-2+(2)bd-1+bd

IDS Evaluation Complete?? Yes Optimal?? Yes Time?? b^d Space?? b.d

Bidirectional search Idea: Run two simultaneous searches. One Forward from initial state One Backward from goal state Until two fingers met

Summary