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Chapter 3

Problem Solving using Search

Chapter 3

Problem Solving using Search

CSE 473

© CSE AI Faculty

“First, they do an on-line search”

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Example: The 8-puzzleExample: The 8-puzzle

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Example: Route PlanningExample: Route Planning

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Example: N QueensExample: N Queens

4 Queens

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Example: N QueensExample: N Queens

4 Queens

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State-Space Search ProblemsState-Space Search Problems

General problem:

Given a start state, find a path to a goal state

• Can test if a state is a goal

• Given a state, can generate its successor states

Variants:

• Find any path vs. a least-cost path

• Goal is completely specified, task is just to find the path

– Route planning

• Path doesn’t matter, only finding the goal state

– 8 puzzle

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Tree Representation of 8-Puzzle Problem SpaceTree Representation of 8-Puzzle Problem Space

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Space is the big problem for BFS.

Example: b = 10, 10,000 nodes/sec, 1KB/node

d = 2 ŁŁŁŁ 1100 nodes, 0.11 secs, 1MB

d = 4 ŁŁŁŁ 111,100 nodes, 11 secs, 106 MB

d = 8 ŁŁŁŁ 109 nodes, 31 hours, 1 TB

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Increasing path-cost limits instead of depth limits

This is called Iterative lengthening search (exercise 3.11)

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Forwards vs. BackwardsForwards vs. Backwardsstart

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Problem: Find the shortest route

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Bidirectional SearchBidirectional Search

Motivation: bd/2 + bd/2 << bd

Can use breadth-first search or uniform-cost search

Hard for implicit goals e.g., goal = “checkmate” in chess

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Repeated StatesRepeated States

Failure to detect repeated states can turn a linear problem into an exponential one! (e.g., repeated states in 8 puzzle)

Graph search algorithm: Store expanded nodes in a set called closed and only add new nodes to the fringe

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Graph SearchGraph Search

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Can we do better?Can we do better?

All these methods are slow (blind)

Solution àààà use problem-specific knowledge to guide search (“heuristic function”)

àààà “informed search” (next lecture)