More on basic search methods

1. More on basic search methods 2012/3/13

2. start goal Bidirectional Search • search forward from the initial state • generate successors to the current node • search backward from the goal • generate predecessors to the current node • stop when two searches meet in the middle

3. Bidirectional Search (cont.) • Time? O(bd/2) • Space? O(bd/2) • Issues • Search strategy for each half ? • if all operators are reversible, predecessor(n) = successor(n) • Multiple goal states • construct a new dummy goal state whose immediate predecessors are all the actual goal states • Cost of checking if a node exists • implicit description of some possible large set of goal state • e.g., checkmate

4. Compare Uniformed Search Strategies • b: the branching factor • d: the depth of solution • m: the maximum depth of the search tree • l: the depth limit • superscript: a complete if b is finite; b complete if step cost c optimal if step costs are all identicald if both directions use BFS

5. Compare Uniformed Search Strategies (cont.) • Issue considered in selecting search strategies • size of the search space • depth of the solution • solution density • finite vs. infinite depth • any vs. all solutions • optimality? • predecessors?

6. Avoid Repeated States • Failure to detect repeated states can turn a linear problem into an exponential one! • Algorithms that forget their history are doomed to repeat it • trade-off between space and time

7. Avoid Repeated States (cont.) • Do not return to the previous state • Do not create paths with cycles • Do not generate the same state twice • store state in a hash table • check for repeated states

8. Graph Search • To modify Tree Search Algorithm by adding closed list • closed list: store every expanded node • open list: the fringe of unexpanded nodes function GRAPH-SEARCH (problems, fringe) returns a solution, or failure closed an empty set fringe INSERT(MAKE-NODE(INITIAL-STATE[problem]), fringe) loop do if EMPTY?( fringe) then return failure node REMOVE-FIRST( fringe) if GOAL-TEST[ problem](STATE[node]) then return SOLUTION(node) if STATE[node] is not in closedthen add STATE[node] to closed fringe INSERT-ALL(EXPAND(node, problem), fringe)

9. Search with Partial Information • Sensorless problem (conformant problem) • the agent is in one of possible initial states, and actions lead to one of possible successor states • Contingency problem • the environment is partially observable, or actions are uncertain • adversarial problem • the uncertainty is caused by another agent • Exploration problem • the states and actions of the environment are unknown

10. 8 possible states Sensorless Problem • Vacuum world

11. Summary • Problem formulation usually requires abstracting away real-world details to define a state space that can feasibly be explored • Variety of uninformed search strategies • Iterative deepening search uses only linear space and not much more time than other uninformed algorithms