Problem solving as Search (summary)

Transcription

1 Problem solving as Search (summary) References Russell and Norvig, Artificial Intelligence: A modern approach, 2nd ed. Prentice Hall, 2003 (chapter 3) Nilsson, Artificial intelligence: A New synthesis. McGraw Hill, 2001

2 A sample problem: 8-puzzle States: cell position (ignore intermediate positions) Actions: Up, Down, Left, Right (ignore unjamming cells) Goal test: a specific state (given) Path cost: 1 per move Remember that optimal solution of n-puzzle family is NP hard!

3 Search strategies Strategy how the order of node expansion is chosen Dimensions completeness - if there is a solution, will it be found? time complexity related with the number of nodes generated / expanded space complexity related with the max number of nodes held in memory optimality will it find a least-cost solution?

4 Search strategies Time and space complexity are measured in terms of: b - maximum branching factor of the search tree d - depth of the least-cost solution m - max depth of the state space (may be infinite)

5 Search strategies or blind uninformed non-adversary search informed adversary or heuristic

6 Non-adversary search Search strategies or blind uninformed non-adversary search informed adversary or heuristic

7 Uninformed vs. Informed Search We can assume that non-adversary search has an associate search tree Each node in the search tree including goals embeds a state and has an associate cost In principle, we can assume that the cost f(x) of a node x results from adding two components: g(x) h(x) Non-adversary search i.e. the cost already spent to get the current node i.e. the least cost to be spent to get the goal Under these assumptions, we can state that blind search considers only g(x), whereas heuristic search tries to estimate h(x)

8 Non-adversary search Tree search algorithms Idea: offline, i.e. simulated, exploration of the space state by generating ( expanding ) successors of states already explored

9 Non-adversary search Tree search algorithms A strategy must provide, at least, the following operation: tree-search :: strategy x problem solution A problem must provide the following operations: initial-state :: problem state goal-test :: problem x state boolean eval-step :: problem x state x action float eval-heuristics :: problem x state float eval-heuristics-p :: problem boolean successors :: problem x state 2 state-info where state-info action x state x g-step x h-val

10 Implementation: states and nodes Non-adversary search A state is a (representation of) a world configuration A node is a data structure which embeds a state Additional information contained in a node is related with the search: parent, children, depth, path cost = g(x)

11 Implementation: states and nodes Non-adversary search The EXPAND function uses SUCCESSORS (to create the next states) and creates the corresponding nodes, filling their fields

12 Non-adversary search Implementation: general tree search defun TREE-SEARCH (problem, fringe) returns solution state INITIAL-STATE(problem) fringe.insert(make-node(state)) loop do if EMPTY?(fringe) then return *FAILURE* node fringe.remove() if problem.goal-test?(state(node)) then return SOLUTION(node) for each child in problem.expand(node) do fringe.insert(child)

13 Non-adversary search Implementation: general tree search defun EXPAND(problem, node) returns successors successors {} --- set of NODES, initially empty for each action, state in problem.successors(state(node)) do child new NODE, child.parent node child.action action, child.state state step-cost problem.step-cost(state(node), action, state) child.cost COST(node) + step-cost child.depth DEPTH(node) + 1 successors.add(child) return successors

14 Search strategies or blind uninformed non-adversary search informed adversary or heuristic

15 Non-adversary search Tree search algorithms No heuristics helps the search Main strategies: - Breadth-first (queue) - Depth-first (stack) - Uniform-cost (ordered queue --> g) - Iterative deepening (e.g. with depth-search)

16 Non-adversary search Search strategies or blind uninformed non-adversary search informed adversary or heuristic

17 Non-adversary search Tree search algorithms Using heuristics to drive the search towards the goal Main strategies: - Greedy (ordered queue --> h) - A-star (ordered queue --> g+h) Others (not described in the course): - IDA* (= iterative deepening with A-star) - SMA* (= bounded memory A*)

18 Non-adversary search Search strategies or blind search non-adversary adversary uninformed CSP informed or heuristic

19 Non-adversary search CSP search Special kind of problems in which a correct assignment must be given to a set of variables, according to the given constraints Hard or soft constraints

20 Non-adversary search Tree search algorithms Main uninformed strategy: - Backtracking General purpose heuristics: - most-constrained variables (i.e., vars with the fewest legal values) - most-constraining variables (i.e., vars that affect the highest number of other variables) - least-constraining value (i.e., vars that affect as less as possible the values of other variables)

21 Adversary search Search strategies or blind uninformed non-adversary search informed adversary or heuristic

22 Adversary search Tree search algorithms Basic strategy: - Minimax (det. / non det.) Pruning: - alpha-beta pruning (det. / non det.)