search problems russell and norvig: chapter 3, sections 3.1 – 3.3

Search ProblemsSearch Problems

Russell and Norvig: Chapter 3, Sections 3.1 – 3.3

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Problem-Solving Problem-Solving AgentAgent

environmentagent

?

sensors

actuators

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Problem-Solving AgentProblem-Solving Agent

environmentagent

?

sensors

actuators• Actions • Initial state• Goal test

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문제를 어떻게 탐색 문제로

단순한 탐색 길 찾기 추적하기

규칙 문제를 탐색으로 If 비교조건 then 행동 또는 결론 우선순위 없는 수많은 규칙에서 적합한 것 찾기

고차원적 문제 Meta-knowledge 에서 찾기

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State Space and Successor State Space and Successor FunctionFunction

• Actions • Initial state• Goal test

state space

successor function

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Initial StateInitial State


state space

successor function

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Goal TestGoal Test


state space

successor function

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Example: 8-puzzleExample: 8-puzzle

1

2

3 4

5 6

7

8 1 2 3

4 5 6

7 8

Initial state Goal state

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1

2

3 4

5 6

7

8

1

2

3 4

5 6

7

8

1

2

3 4

5 6

78

1

2

3 4

5 6

7

8

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Size of the state space = 9!/2 = 181,440

15-puzzle .65 x 1012

24-puzzle .5 x 1025

10 millions states/sec

0.18 sec

6 days

12 billion years

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Search ProblemSearch Problem

State space Initial state Successor function Goal test Path cost

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State space each state is an abstract

representation of the environment the state space is discrete

Initial state Successor function Goal test Path cost

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State space Initial state: usually the current state sometimes one or several

hypothetical states (“what if …”)

Successor function Goal test Path cost

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State space Initial state Successor function: [state subset of states] an abstract representation of the

possible actions

Goal test Path cost

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State space Initial state Successor function Goal test: usually a condition sometimes the description of a state

Path cost

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State space Initial state Successor function Goal test Path cost: [path positive number] usually, path cost = sum of step costs e.g., number of moves of the empty tile

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Search of State SpaceSearch of State Space

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Search State SpaceSearch State Space

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search tree

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Simple Agent AlgorithmSimple Agent Algorithm

Problem-Solving-Agent1. initial-state sense/read state2. goal select/read goal3. successor select/read action models4. problem (initial-state, goal,

successor)5. solution search(problem)6. perform(solution)

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Example: 8-queensExample: 8-queens

Place 8 queens in a chessboard so that no two queens are in the same row, column, or diagonal.

A solution Not a solution

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Example: 8-queensExample: 8-queens

Formulation #1:• States: any arrangement of 0 to 8 queens on the board• Initial state: 0 queens on the board• Successor function: add a queen in any square• Goal test: 8 queens on the board, none attacked

648 states with 8 queens

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Example: 8-queensExample: 8-queensFormulation #2:• States: any arrangement of k = 0 to 8 queens in the k leftmost columns with none attacked• Initial state: 0 queens on the board• Successor function: add a queen to any square in the leftmost empty column such that it is not attacked by any other queen• Goal test: 8 queens on the board

2,067 states

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실제 n-queen 문제

Neural, Genetic 또는 Heuristic 방법으로 잘 해결 최악의 경우에는 처리 불가능 실제 n 이 커지면 답이 매우 많으므로 간단한

Heuristics 로도 답을 쉽게 찾음 따라서 n 이 커도 답을 잘 찾는다고 해서 인공지능

접근방법이 문제를 해결한다는 증거는 아님 그러나 많은 실제 문제는 알고리즘에서 이야기하는

최악의 경우로는 잘 가지 않음 더구나 대부분 우리가 원하는 답은 최적이 아니라 실제

활용해서 도움이 되는 , feasible solution 을 원하므로 인공지능 기법이 효과적으로 이용될 수 있음

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Example: Robot Example: Robot navigationnavigation

What is the state space?

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Cost of one horizontal/vertical step = 1Cost of one diagonal step = 2

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Cost of one step = ???

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Cost of one step: length of segment

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Example: Assembly Example: Assembly PlanningPlanning

Initial state

Goal state

Successor function:• Merge two subassemblies

Complex function:it must find if a collision-freemerging motion exists

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Assumptions in Basic Assumptions in Basic SearchSearch

The environment is staticThe environment is discretizableThe environment is observableThe actions are deterministic

open-loop solution

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Search Problem Search Problem FormulationFormulation

Real-world environment Abstraction

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Real-world environment Abstraction Validity:

Can the solution be executed?

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Can the solution be executed? Does the state space contain the

solution?

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Can the solution be executed? Does the state space contain the

solution? Usefulness

Is the abstract problem easier than the real-world problem?

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Can the solution be executed? Does the state space contain the solution?

Usefulness Is the abstract problem easier than the real-

world problem?

Without abstraction an agent would be swamped by the real world

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Search Problem VariantsSearch Problem Variants

One or several initial states One or several goal states The solution is the path or a goal node In the 8-puzzle problem, it is the path

to a goal node In the 8-queen problem, it is a goal

node

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Problem VariantsProblem Variants

One or several initial states One or several goal states The solution is the path or a goal node Any, or the best, or all solutions

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Important ParametersImportant Parameters

Number of states in state space

8-puzzle 181,44015-puzzle .65 x 1012 24-puzzle .5 x 1025

8-queens 2,057100-queens 1052

There exist techniques to solveN-queens problems efficiently!

Stating a problem as a search problem is not always a good idea!

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Number of states in state space Size of memory needed to store a state

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Number of states in state space Size of memory needed to store a state Running time of the successor function

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ApplicationsApplications

Route finding: airline travel, telephone/computer networks Pipe routing, VLSI routing Pharmaceutical drug design Robot motion planning Video games

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Task Environment Observable Deterministic Episodic Static Discrete Agents

Crossword puzzle Fully Deterministic Sequential Static Discrete Single

Chess with a clock Fully Strategic Sequential Semi Discrete Multi

Poker Partially Strategic Sequential Static Discrete Multi

Backgammon Fully Stochastic Sequential Static Discrete Multi

Taxi driving Partially Stochastic Sequential Dynamic Continuous Multi

Medical diagnosis Partially Stochastic Sequential Dynamic Continuous Single

Image-analysis Fully Deterministic Episodic Semi Continuous Single

Part-picking robot Partially Stochastic Episodic Dynamic Continuous Single

Refinery controller Partially Stochastic Sequential Dynamic Continuous Single

Interactive English tutor Partially Stochastic Sequential Dynamic Discrete Multi

Figure 2.6 Examples of task environments and their characteristics.

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SummarySummary

Problem-solving agent State space, successor function, search Examples: 8-puzzle, 8-queens, route finding, robot navigation, assembly planning Assumptions of basic search Important parameters

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Future ClassesFuture Classes

Search strategies Blind strategies Heuristic strategies

Extensions Uncertainty in state sensing Uncertainty action model On-line problem solving

search problems russell and norvig: chapter 3, sections 3.1 – 3.3

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