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States and Search

States and Search. Core of intelligent behaviour. The simple problem solver. Restricted form of general agent: Figure 3.1 , p.61 function Simple-Problem-Solving-Agent( percept) returns action seq an action sequence, initially empty state some description of the current world state

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States and Search

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  1. States and Search Core of intelligent behaviour

  2. The simple problem solver Restricted form of general agent: Figure 3.1 , p.61 function Simple-Problem-Solving-Agent( percept) returns action seq an action sequence, initially empty state some description of the current world state goal a goal, initially null problem a problem formulation state = Update-State(state, percept) if seq is empty (ie – do search first time only) goal = Formulate-Goal(state) if (state==goal) return nil problem = Formulate-Problem(state, goal) (performance) seq = Search(problem) action First(seq) seq = Rest(seq) return action Creating a solution sequence by graph search D Goforth - COSC 4117, fall 2006

  3. The simple problem solver • works by simulating the problem in internal representation and trying plans till a good one is discovered • works in deterministic, static, single agent environments • plan is made once and never changed • works if plan is perfect – actions do what plan assumes no corrections to path are required • works efficiently if space is not too large D Goforth - COSC 4117, fall 2006

  4. Representation of Environment – abstractions of real world • states and state space – only relevant information in state representation • actions - successor function costs • and path cost (eg touring problem TSP) • start state • goal state or criterion function of state(s) D Goforth - COSC 4117, fall 2006

  5. Representation of Environment – state space efficiency Faster processing • minimization of number of states • minimization of degree of branching of successor function (actions) Smaller memory allocation • large state spaces are generated/explored, not stored/traversed D Goforth - COSC 4117, fall 2006

  6. Searching state space The fundamental method for creating a plan Is SEARCH D Goforth - COSC 4117, fall 2006

  7. Searching – graph traversals – TREE-SEARCH – p. 70 • start node and all possible actions, then pick another node...: D Goforth - COSC 4117, fall 2006

  8. Design of a search space – the spanning tree over a state space • Node in search space • current state • reference to parent node on path • action from parent to node • path cost from start node (may be just path length) D Goforth - COSC 4117, fall 2006

  9. R L L L L L L L R R L L R L R L R L L R L R L L L L R L L L L R R R R L R R R L R R L R R L R R Ff L R R L L R L R L L R R 3 R R R R L R R R Problem-solving agent – example Node in search space L L R L F 2 State Parent link Action Path length D Goforth - COSC 4117, fall 2006

  10. R L L L L L L L R R L L R L R L R L L R L R L L L L R L L L L R R R R L R R L R R L R R L R R L L R L R L L R R R R R R L R R R Problem-solving agent – example SPANNING TREE Note why some state space edges are not traversed in the spanning tree D Goforth - COSC 4117, fall 2006

  11. General search algorithm – p.72 • EXAMPLE: breadth first search in a binary tree start state (visitedList) fringe (openList) current state D Goforth - COSC 4117, fall 2006

  12. general search algorithm -variation startState initial state of environment adjacentNode, node nodes of search tree: contain state, parent, action, path cost openList collection of Nodes generated, not tested yet (fringe) visitedList collection of Nodes already tested and not the goal action[n] list of actions that can be taken by agent goalStateFound(state) returns boolean evaluate a state as goal precondition(state, action) returns boolean test a state for action apply(node,action) returns node apply action to get next state node makeSequence(node) returns sequence of actions generate plan as sequence of actions

  13. general search algorithm -variation algorithm search (startState, goalStateFound()) returns action sequence openList = new NodeCollection(); // stack or queue or... visitedList = new NodeCollection(); node = new Node(startState, null, null, 0 0); openList.insert(node) while ( notEmpty(openList) ) node = openList.get() if (goalStateFound (node.state) ) // successful search return makeSequence(node) for k = 0..n-1 if (precondition(node.state, action[k])==TRUE) adjacentNode = apply(nextNode,action[k]) if NOT(adjacentNode in openList OR visitedList) openList.insert(adjacentNode) visitedList.insert(node) return null

  14. algorithms of general search • breadth first • depth first • iterative deepening search • uniform cost search D Goforth - COSC 4117, fall 2006

  15. R R R L Ff 3 variations on search algorithm • breadth first search • openList is a queue • depth first search • openList is a stack • (recursive depth first is equivalent) tradeoffs for bfs: shortest path vs resources required State Parent link Action Path length D Goforth - COSC 4117, fall 2006

  16. comparison of bfs and dfs • nodes on openList while search is at level k: • bfs O(nk ) n is branching factor • dfs O(nk) • recursive dfs O(k) • quality of solution path • bfs always finds path with fewest actions • dfs may find a longer path before a shorter one D Goforth - COSC 4117, fall 2006

  17. depth-limited dfs • use depth first search with limited path length eg dfs(startNode,goalStateFound(),3) uses dfs but only goes to level 3 D Goforth - COSC 4117, fall 2006

  18. iterated (depth-limited) dfs • variation on dfs to get best of both • small openList of dfs • finds path with fewest actions like bfs • repeated searching is not a big problem!!! D Goforth - COSC 4117, fall 2006

  19. iterative deepening dfs • search algorithm puts depth-limited dfs in a loop: algorithm search (startState, goalStateFound()) Node node = null depth = 0 while (node == null) depth++ node = dfs(startState,goalStateFound(),depth) return node D Goforth - COSC 4117, fall 2006

  20. uniform cost search • find best path when there is an action cost for each edge: • a path of more edges may be better than a path of fewer edges: • 12+8+9+4+10 (5 edges) is preferred to 35+18 (2 edges) • variation on bfs • openList is a priority queue ordered on path cost from start state D Goforth - COSC 4117, fall 2006

  21. uniform cost search - example openList is a priority queue ordered on path cost from start state . A(0) C(2),B(4),D(8) visited current open A 8 4 2 B C D D Goforth - COSC 4117, fall 2006

  22. . A(0) A(0) C(2) C(2),B(4),D(8) B(4),E(5),D(8) visited current open visited current open A A 8 8 4 4 2 2 B C D B C D 3 E 1 2 A(0),C(2) B(4) E(5),F(7),D(8),G(9) visited current open A 8 4 2 A(0),C(2), B(4) E(5) G(6),F(7),D(8), H(10) B C D visited current open 3 1 5 3 A 8 4 F G E 2 B C D 3 4 3 5 3 1 F G E 5 3 H

  23. variations of the general algorithm • openList structure • time of testing for goal state D Goforth - COSC 4117, fall 2006

  24. (some) problems that complicate search • perceptions are incomplete representation of state • dynamic environment – path of actions is not only cause of state change (eg games) D Goforth - COSC 4117, fall 2006

  25. what kind of problem-reprise • fully / partly observable - is state known? • deterministic / stochastic - effect of action uncertain? • sequential / episodic - plan required/useful? • static / dynamic - state changes between action & perception and/or between perception & action • discrete / continuous - concurrent or sequential actions on state • single- / multi-agent dynamic environment; possible communication, distributed AI D Goforth - COSC 4117, fall 2006

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