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

Problem-Solving Agent environment agent ? sensors actuators Search Problems

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

State Space and Successor Function Actions Initial state Goal test Search Problems

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

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

Example: 8-puzzle 1 2 3 4 5 6 7 8 Initial state Goal state Search Problems

Example: 8-puzzle 1 2 3 4 5 6 7 8 Search Problems

Example: 8-puzzle Size of the state space = 9!/2 = 181,440 15-puzzle  .65 x 1012 24-puzzle  .5 x 1025 0.18 sec 6 days 12 billion years 10 millions states/sec Search Problems

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

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

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

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

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

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 Problems

Search of State Space Search Problems

Search of State Space Search Problems

Search State Space Search Problems

Search of State Space Search Problems

Search of State Space Search Problems

Search of State Space  search tree Search Problems

Simple Agent Algorithm Problem-Solving-Agent initial-state  sense/read state goal  select/read goal successor  select/read action models problem  (initial-state, goal, successor) solution  search(problem) perform(solution) Search Problems

Example: 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 Search Problems

Example: 8-queens  648 states with 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 Search Problems

Example: 8-queens  2,067 states 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  2,067 states Search Problems

실제 n-queen 문제 Neural, Genetic 또는 Heuristic 방법으로 잘 해결 최악의 경우에는 처리 불가능 실제 n이 커지면 답이 매우 많으므로 간단한 Heuristics로도 답을 쉽게 찾음 따라서 n이 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 solution을 원하므로 인공지능 기법이 효과적으로 이용될 수 있음 Search Problems

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

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

Example: Robot navigation Search Problems

Example: Robot navigation Search Problems

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

Example: Robot navigation Search Problems

Example: Robot navigation Search Problems

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

Example: Robot navigation Search Problems

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

Example: Assembly Planning Search Problems

Example: Assembly Planning Search Problems

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

Search Problem Formulation Real-world environment  Abstraction Search Problems

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

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

Search Problems

Search Problems

Search Problems

Search Problems

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 Problems

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 Problems

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 Problems

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 Problems

Important Parameters Number of states in state space 8-puzzle  181,440 15-puzzle  .65 x 1012 24-puzzle  .5 x 1025 8-queens  2,057 100-queens  1052 There exist techniques to solve N-queens problems efficiently! Stating a problem as a search problem is not always a good idea! Search Problems

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

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

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

Interactive English tutor Task Environment Observable Deterministic Episodic Static Discrete Agents Crossword puzzle Fully Sequential Single Chess with a clock Strategic Semi Multi Poker Partially Backgammon Stochastic Taxi driving Dynamic Continuous Medical diagnosis Image-analysis Part-picking robot Refinery controller Interactive English tutor Figure 2.6 Examples of task environments and their characteristics. Search Problems

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 Problems

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