Search Problems Russell and Norvig: Chapter 3, Sections 3.1 – 3.3

Search Problems2 Problem-Solving Agent environment agent ? sensors actuators

Search Problems3 Problem-Solving Agent environment agent ? sensors actuators Actions Initial state Goal test

Search Problems4 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

Search Problems5 State Space and Successor Function Actions Initial state Goal test state space successor function

Search Problems6 Initial State Actions Initial state Goal test state space successor function

Search Problems7 Goal Test Actions Initial state Goal test state space successor function

Search Problems8 Example: 8-puzzle Initial state Goal state

Search Problems9 Example: 8-puzzle

Search Problems10 Example: 8-puzzle Size of the state space = 9!/2 = 181, puzzle .65 x puzzle .5 x millions states/sec 0.18 sec 6 days 12 billion years

Search Problems11 Search Problem State space Initial state Successor function Goal test Path cost

Search Problems12 Search Problem State space each state is an abstract representation of the environment the state space is discrete Initial state Successor function Goal test Path cost

Search Problems13 Search Problem State space Initial state: usually the current state sometimes one or several hypothetical states (“what if …”) Successor function Goal test Path cost

Search Problems14 Search Problem State space Initial state Successor function: [state  subset of states] an abstract representation of the possible actions Goal test Path cost

Search Problems15 Search Problem State space Initial state Successor function Goal test: usually a condition sometimes the description of a state Path cost

Search Problems16 Search Problem 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

Search Problems17 Search of State Space

Search Problems18 Search of State Space

Search Problems19 Search State Space

Search Problems20 Search of State Space

Search Problems21 Search of State Space

Search Problems22 Search of State Space  search tree

Search Problems23 Simple Agent Algorithm Problem-Solving-Agent 1. initial-state  sense/read state 2. goal  select/read goal 3. successor  select/read action models 4. problem  (initial-state, goal, successor) 5. solution  search(problem) 6. perform(solution)

Search Problems24 Example: 8-queens Place 8 queens in a chessboard so that no two queens are in the same row, column, or diagonal. A solutionNot a solution

Search Problems25 Example: 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  64 8 states with 8 queens

Search Problems26 Example: 8-queens Formulation #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

Search Problems27 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

Search Problems28 Example: Robot navigation What is the state space ?

Search Problems29 Example: Robot navigation Cost of one horizontal/vertical step = 1 Cost of one diagonal step =  2

Search Problems30 Example: Robot navigation

Search Problems31 Example: Robot navigation

Search Problems32 Example: Robot navigation Cost of one step = ???

Search Problems33 Example: Robot navigation

Search Problems34 Example: Robot navigation

Search Problems35 Example: Robot navigation Cost of one step: length of segment

Search Problems36 Example: Robot navigation

Search Problems37 Example: Assembly Planning Initial state Goal state Successor function: Merge two subassemblies Complex function: it must find if a collision-free merging motion exists

Search Problems38 Example: Assembly Planning

Search Problems39 Example: Assembly Planning

Search Problems40 Assumptions in Basic Search The environment is static The environment is discretizable The environment is observable The actions are deterministic  open-loop solution

Search Problems41 Search Problem Formulation Real-world environment  Abstraction

Search Problems42 Search Problem Formulation Real-world environment  Abstraction Validity:  Can the solution be executed?

Search Problems43 Search Problem Formulation Real-world environment  Abstraction Validity:  Can the solution be executed?  Does the state space contain the solution?

Search Problems44

Search Problems45

Search Problems46

Search Problems47

Search Problems48 Search Problem Formulation Real-world environment  Abstraction Validity:  Can the solution be executed?  Does the state space contain the solution? Usefulness  Is the abstract problem easier than the real- world problem?

Search Problems49 Search Problem Formulation Real-world environment  Abstraction Validity:  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

Search Problems50 Search 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

Search Problems51 Problem 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

Search Problems52 Important Parameters Number of states in state space 8-puzzle  181, puzzle .65 x puzzle .5 x queens  2, queens  There exist techniques to solve N-queens problems efficiently! Stating a problem as a search problem is not always a good idea!

Search Problems53 Important Parameters Number of states in state space Size of memory needed to store a state

Search Problems54 Important Parameters Number of states in state space Size of memory needed to store a state Running time of the successor function

Search Problems55 Applications Route finding: airline travel, telephone/computer networks Pipe routing, VLSI routing Pharmaceutical drug design Robot motion planning Video games

Search Problems56 Task EnvironmentObservableDeterministicEpisodicStaticDiscreteAgents Crossword puzzleFullyDeterministicSequentialStaticDiscreteSingle Chess with a clockFullyStrategicSequentialSemiDiscreteMulti PokerPartiallyStrategicSequentialStaticDiscreteMulti BackgammonFullyStochasticSequentialStaticDiscreteMulti Taxi drivingPartiallyStochasticSequentialDynamicContinuousMulti Medical diagnosisPartiallyStochasticSequentialDynamicContinuousSingle Image-analysisFullyDeterministicEpisodicSemiContinuousSingle Part-picking robotPartiallyStochasticEpisodicDynamicContinuousSingle Refinery controllerPartiallyStochasticSequentialDynamicContinuousSingle Interactive English tutorPartiallyStochasticSequentialDynamicDiscreteMulti Figure 2.6 Examples of task environments and their characteristics.

Search Problems57 Summary 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

Search Problems58 Future Classes Search strategies Blind strategies Heuristic strategies Extensions Uncertainty in state sensing Uncertainty action model On-line problem solving