CS.462Artificial Intelligence

SOMCHAI THANGSATHITYANGKUL

Lecture 02 : Search

Searching for Solutions• The state space model provides a formal definition of a

problem and what constitutes a solution to a problem.• State space is the set of all states reachable from the

initial state by any sequence of operators/actions.• Operators -- generate new states from existing states• A solution is• a state (called a goal state) whose attributes have

certain properties and maybe• a sequence of operators that will change the initial

state to a goal state• A solution is found by searching through the state

space until a (goal) state with “specific” properties is found

Artificial Intelligence Chapter 12

What is a Solution in this type of Search?

• A solution to a search problem is a sequence of operators that generate a path from the initial state to a goal state.

• An optimal solution is a minimal cost solution.

• Solution cost versus search cost -- which one to optimize?

Artificial Intelligence Chapter 13

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A directed graph in state space

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Three coins problem

Given three coins arrange as in the picture,

which is the initial

state I.

These are goal state G.

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Three coins problem

Operation : Flipping the coin one at a time Let A represent flipping the first coin Let B represent flipping the middle

coin Let C represent flipping the last coin

• The search problem: find a path from a sta te in I to a state in G.

• Draw the state space Graph

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Three coins problem

State space graph

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Three coins problem

Let put some rule into the problemRule : Use exactly 3 flips.This means that 1flip cannot reach the goal

and2 flips also cannot reach the goal.For example: state I : HHTc HHH not goalState I : HHT B HTT A TTT not goal

Let draw the state space

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Three coins problem

State space tree

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Search

• Many AI problems can be formu lated as search.

• Iterative deepening is good wh en you don’t know much.

First Method of Search• Uninformed Search

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Depth First Search (DFS)• Search• Put start state in the agenda• Loop

Get a state from the agenda If goal, then return Expand state (put children in agenda) Avoiding loops Don’t add a node to the agenda if it’s already

in the agenda Don’t expand a node (or add it to the agenda)

if it has already been expanded.

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DFS

Graph:

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DFSAgenda:

– Expansion: put children at top of stack– Get new nodes from top of stack

Expand node Nodes list

s

{s}

{As ,Bs ,Cs }

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Try this

Find a path from node A to the goal nod B. Use

DFS method.A

B

ZO

S F

C

PR

T L M D

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Breadth First Search (BFS)

• Search• Put start state in the agenda• Loop

Get a state from the agenda If goal, then return Expand state (put children in agenda) Avoiding loops Don’t add a node to the agenda if it’s

already in the agenda Don’t expand a node (or add it to the

agenda) if it has already been expanded.

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BFS

Graph:

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BFSAgenda:

– Expansion: put children at end of queue– Get new nodes from the front of queue

Expand node Nodes list

s

{s}

{As ,Bs ,Cs }

18

Try thisFind a path from node A to the goal

nod B. UseBFS method.

AB

ZO

S F

C

PR

T L M D