uninformed search ece457 applied artificial intelligence spring 2007 lecture #2

Uninformed Search

ECE457 Applied Artificial IntelligenceSpring 2007 Lecture #2

ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 2

Outline Problem-solving by searching Uninformed search techniques

Russell & Norvig, chapter 3

ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 3

Problem-solving by searching An agent needs to perform actions

to get from its current state to a goal.

This process is called searching. Central in many AI systems

Theorem proving, VLSI layout, game playing, navigation, scheduling, etc.

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Requirements for searching Define the problem

Represent the search space by states Define the actions the agent can

perform and their cost Define a goal

What is the agent searching for? Define the solution

The goal itself? The path (i.e. sequence of actions) to

get to the goal?

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Assumptions Goal-based agent Environment

Fully observable Deterministic Sequential Static Discrete Single agent

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Formulating problems A well-defined problem has:

An initial state A set of actions A goal test A concept of cost

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Example: 8-puzzle Initial state Action

Move blank left, right, up or down, provided it does not get out of the game

Goal test Are the tiles in the “goal

state” order? Cost

Each move costs 1 Path cost is the sum of

moves

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Example: 8-puzzle

left down

leftright

down downleftup

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Search TreeParent

Child

Edge (action)

Node (state)

Expanding a node

Root

Leaf

Fringe

Branching factor (b)

Maximum depth (m)

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Properties of Search Algos. Completeness

Is the algorithm guaranteed to find a goal node, if one exists?

Optimality Is the algorithm guaranteed to find the best

goal node, i.e. the one with the cheapest path cost?

Time complexity How many nodes are generated?

Space complexity What’s the maximum number of nodes

stored in memory?

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Types of Search Uninformed Search

Only has the information provided by the problem formulation (initial state, set of actions, goal test, cost)

Informed Search Has additional information that allows

it to judge the promise of an action, i.e. the estimated cost from a state to a goal

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Breath-First Search

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Breath-First Search Complete, if b is finite Optimal, if path cost is equal to depth

Guaranteed to return the shallowest goal (depth d)

Number of generated nodes:1+b+b²+b³+…+bd+(bd+1-b) = O(bd+1)

Time complexity = O(bd+1) Space complexity = O(bd+1)

ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 14

Uniform-Cost Search Expansion of Breath-First Search Explore the cheapest node first (in

terms of path cost) Condition: No zero-cost or

negative-cost edges. Minimum cost is є

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Uniform-Cost Search Complete given a finite tree Optimal Time complexity = O(bC*/є) ≥

O(bd+1) Space complexity = O(bC*/є) ≥

O(bd+1)

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Depth-First Search

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Depth-First Search Complete, if m is finite Not optimal Time complexity = O(bm) Space complexity = bm+1 =

O(bm) Can be reduced to O(m)

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Depth-Limited Search Depth-First Search with depth limit

l Avoids problems of Depth-First

Search when trees are unbounded Depth-First Search is Depth-

Limited Search with l =

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Depth-Limited Search Complete, if l > d Not optimal Time complexity = O(bl) Space complexity = O(bl)

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Iterative Deepening Search Depth-First Search with increasing

depth limit l Repeat depth-limited search over and

over, with l = l + 1 Avoids problems of Depth-First

Search when trees are unbounded

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Iterative Deepening Search Complete , if b is finite Optimal, if path cost is equal to

depth Guaranteed to return the shallowest

goal Time complexity = O(bd) Space complexity = O(bd) Nodes on levels above d are

generated multiple times

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Repeated States

left down

leftright

down downleftup

Example: 8-puzzle

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Repeated States Unavoidable in problems where:

Actions are reversible Multiple paths to the same state are

possible Can greatly increase the number of

nodes in a tree Or even make a finite tree infinite!

Maintain a closed list of visited states Detect repeated states Increase space complexity

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Summary / Example Going from Arad to Bucharest

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Summary / Example Initial state

Being in Arad Action

Move to a neighbouring city, if a road exists.

Goal test Are we in Bucharest?

Cost Move cost = distance between cities Path cost = distance travelled since

Arad

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Summary / Example Breath-First Search

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Summary / Example Uniform-Cost Search

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Summary / Example Depth-First Search

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Summary / Example Depth-Limited Search, l = 4

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Summary / Example Iterative Deepening Search