Chap 3 Solving Problems by Search

1. Chap 3 Solving Problems by Search • AI technique 1) abstract symbol manipulation 2) use of knowledge 3) search • Why search? • logic --> algebraic --> analytic --> geometric --> statistic --> heuristic

2. 3-1. Problem solving agents 3-2. Formulating problems 3-3. Example problems 3-4. Searching by solutions 3-5. Search strategies 3-6. Avoiding repeated states 3-7. Constraint satisfaction problem

3. 3-1. Problem-solving agents • problem-solving agent  goal-based agent • a simple problem-solving agent • pseudo code [fig 3.1, pp. 57] • example: Road to Bucharest [fig 3.3, pp. 62] • perception --> goal --> problem formulation --> solving --> action

4. 3-2. Formulating problems • four types of problems • example: cleaning a room [fig 3.2, pp. 58] • 8 states, 3 actions 1) single state problem 2) multi state problem 3) contingency problem 4) exploration problem

5. 1) single-state problem • environment -- accessible (knows where it is now) • action -- knows the effect • Action sequence can be completely planned. 2) Multiple-state problem • environment -- partially accessible (e.g., no sensor, with map) • action -- knows the effect • Agent must reason about the state (after its action).

6. 3) Contingency problem • Action prediction is not possible. • Most of the real world problem (e.g., walking -- That’s why we open our eyes.) • Sometimes, action before planning is useful. (e.g., interleaving -- action & search game playing ) • Chapter 13. Planning and acting 4) Exploration problem • environment -- completely unknown (no sensor, no map) • Chapter 20. Re-inforcement learning)

7. state-space search problem • benefit, utility -- quality of the goal • cost -- computational expenses • rule application cost -- # of expanded nodes • control strategy cost search space state (of environment + agent ) - initial state - goal state - operator (rule)

8. measuring performance • solution? • good solution? (high benefit?) • little cost? • The real art of the problem solving is in deciding … • what to consider? • what to be left out? • level of abstraction • Reference “How to solve it?”, G. Polya, Princeton Univ Press, 1945, 1957. trade-off

9. 3-3. Example problems • toy problem vs. real-world problem • small • abstract • exact (deterministic) • why toy problem? • abstract version of real problem [examples: birthday party, pp. 746 ~ 748] • to test AI techniques • Hope the toy problems are scalable.

10. 8 - puzzle (or sliding block puzzle) [fig 3.4, pp. 63] • NP-complete • 8 - queen problem [fig 3.5, pp. 64] • 1948 a German chess magazine • 1950 Gauss found 72 out of 92 solutions. • cryptic - arithmetic [pp. 65]

11. vacuum world [fig 3.6, pp. 66] i) complete information about the world ii) incomplete information about the world • missionaries and cannibals • problem 3 missionaries 3 cannibals 1 boat that can hold 1 ~ 2 # of missionaries  # of cannibals • 1’st example of AI research -- Amarel 1968

12. real-world problems 1) route finding e.g., routing in computer network airline planning 2) touring and TSP 3) VLSI layout See [Sec. 25.5, pp. 790] 4) robot navigation • generation of route • continuous space • See [Winston, fig 5.6 ~ 5.10] 5) Internet search engine

13. 3-4. Searching for solutions • search algorithm [pp. 64, Nilsson] Create a search graph, GRAPH GRAPH <--- { s } OPEN <--- { s } CLOSE <--- { } if OPEN = { } , then exit ( fail ) n <--- SELECT ( OPEN ) ; search strategy CLOSED <--- CLOSED  { n } if n = goal , then exit ( success ) CHILDREN <--- EXPAND ( n ) for each m  CHILDREN, modify GRAPH (I.e., CLOSED, OPEN) REORDER (OPEN)

14. 3-5. Search strategies • criteria • completeness -- Find a solution when there is one? • admissibility (optimality) -- Find the best solution? • time complexity • space complexity • un-informed search ( vs. informed search) • blind search • no information about the cost from the current to the goal. • Consider the cost from the start to the current = g(n)

15. 1) Breadth-first search • g(n) = depth(n) • completeness -- yes • admissible -- no • time complexity -- bad [fig 3.12, pp. 75] • space complexity -- worse 2) Uniform cost search • lowest-cost node from OPEN [fig 3.13, pp. 76] • SELECT (OPEN) ==> min { OPEN } wrt g(n) • if g (SUCCESSOR(n))  g(n)) then admissible. (I.e., non-decreasing path cost)

16. 3) Depth-first search • completeness • admissible • time complexity • space complexity

17. 4) Depth-limited search • depth-first • cut-off on the max depth of a path (e.g., diameter of the graph) • time complexity • space complexity • completeness • admissible • problem -- How to determine the cut-off?

18. 5) Iterative deepening search • Try all possible depth limits. [fig 3.16, pp. 79] • Combine the benefits of depth-first and breadth first. (small memory) (completeness) • Some states are expanded multiple times. But the overhead is small. • # of expanded nodes • breadth first • iterative deepening • if b = 5, d = 5, 111,111 vs. 123,456 (11% more)

19. 6) Bi-directional search • search in both directions [fig 3.17, pp. 81] • time complexity • space complexity • problems • generating predecessors from the goal. • multiple goals • implicit goal (example: 바둑) • checking the duplicacy on the other side.

20. 7) Comparison table [fig 3.18, pp 81]

21. 3-6. Avoiding repeated states • theorem operators are States may repeat. reversible. • solution I) Do not return to the parent. 2) Do not create a cycle. 3) Do not create CLOSED.

22. 3-7. Constraint satisfaction search • state • constraints • unary, binary, n-ary • discrete, continuous • technique • relaxation