1. Problem Solving by Searching Copyright, 1996 © Dale Carnegie & Associates, Inc. Chapter 3

2. Fall 2002 Huan Liu for CSE471/5982 Problem-Solving Agents This is a kind of goal-based agents that decide what to do by finding sequences of actions that lead to desirable states. zFormulating problems zExample problems zSearching for solutions

3. Fall 2002 Huan Liu for CSE471/5983 A simple problem-solving agent zGoal formulation - limiting the objectives yA goal is a set of world states in which the goal is satisfied. zProblem formulation - deciding what actions and states to consider zSearch - looking for the best sequence of actions

4. Fall 2002 Huan Liu for CSE471/5984 A simple agent zSolutions - the results of search, so they are sequences of actions that lead to the goal zExecution - acting upon the world Formulate -> Search -> Execute An algorithm in Fig 3.1 (book)

5. Fall 2002 Huan Liu for CSE471/5985 Formulating Problems zKnowledge and problem types (Fig 3.2pdf) yThree possible actions (left, right, suck) yGoal states {7, 8} ySingle-state problem yMultiple-state problem yContingency problem (if) yExploration problem (experiment and discover) zSearch in a model vs. search in the world

6. Fall 2002 Huan Liu for CSE471/5986 Well-defined problems and solutions zProblem - a collection of information that the agent will use to decide what to do. States and actions are the basic elements of a problem zA world of states: initial state I, operator O (or successor) zState space - the set of all states reachable from I by any sequences of O

7. Fall 2002 Huan Liu for CSE471/5987 Problems and Solutions zExample: a simple Romania road map (Fig 3.3) zPath - connecting sets of states zPath cost zGoal test From single-state problems to multiple-state problems zState set space (Fig 3.7) ysee Fig 3.6 for a state space

8. Fall 2002 Huan Liu for CSE471/5988 Measuring problem-solving performance zReach the goal zSearch cost zTotal cost = path cost + search cost Choosing states and actions zThe real art of problem solving is in what goes into the description of the states and operators and what does not zAbstraction - removing detail from a representation

9. Fall 2002 Huan Liu for CSE471/5989 Example Problems zToy problems: concise and exact, used to illustrate or exercise various problem- solving methods - ideal cases zReal-world problems: more difficult and we want solutions, but there might be many different descriptions

10. Fall 2002 Huan Liu for CSE471/59810 Toy problem (1) zThe 8-puzzle yStates yOperators yGoal test yPath cost

11. Fall 2002 Huan Liu for CSE471/59811 Toy problem (2) zThe 8-queens yStates yOperators yGoal test yPath cost

12. Fall 2002 Huan Liu for CSE471/59812 Toy problem (3) zCryptarithmetic yStates yOperators yGoal test yPath cost

13. Fall 2002 Huan Liu for CSE471/59813 Toy problem (4) zThe vacuum world yStates yOperators yGoal test yPath cost zSingle-state vs. Multiple-state

14. Fall 2002 Huan Liu for CSE471/59814 Real-world problems zRoute finding zTouring and traveling salesperson problem zVLSI layout zRobot navigation zAssembly sequencing

15. Fall 2002 Huan Liu for CSE471/59815 Search zGenerating action sequences yExpanding the current state by... yGenerating a new set of states Let’s look at a situation we come to ECG … xPHX -> ASU -> ECG zA state map

16. Fall 2002 Huan Liu for CSE471/59816 What is search? zThe essence of search is to consider one at a time. z“Which one first?” -> Search Strategies zSearch tree - a representation of a state map yroot, nodes, fringe (leaf nodes) zHow to implement the fringe - a queue

17. Fall 2002 Huan Liu for CSE471/59817 Search Evaluation zEvaluating search strategies (Criteria) yCompleteness yTime complexity ySpace complexity yOptimality zBlind search (uninformed) zHeuristic search (informed)

18. Fall 2002 Huan Liu for CSE471/59818 Search Strategies zBreadth-first search yHow to implement it ybranching factor - a killing cost yFig 3.12 The main concerns ythe memory requirements yexponential complexity Uniform cost search

19. Fall 2002 Huan Liu for CSE471/59819 Search Strategies (2) zDepth-first search yHow to implement it The main concerns yWrong branch yDeep branch The cures yDepth-limited search yIterative deepening search

20. Fall 2002 Huan Liu for CSE471/59820 Search Strategies (3) zBidirectional search yThe two directions: Start, Goal (Fig 3.17) The main concerns yHow to search backwards yMultiple goal states yEfficient checking to avoid redundant search in the other tree

21. Fall 2002 Huan Liu for CSE471/59821 Search Strategies (4) zWhich one to use when yWe need to know the strategies in terms of the four criteria yWe need to know the problem

22. Fall 2002 Huan Liu for CSE471/59822 Summary zProblem solving is goal-based zA problem is of 4 parts yinitial state, operator, goal test, path cost zA single general search algorithm can solve any problem, but … zFour criteria: completeness, optimality, time complexity, space complexity zVarious search strategies