Single Agent Search

PSU CS441/541 Lecture 3
October 9, 2000

• Consider Ginsberg 2.2.4 Examples
  • Game Playing
    • chess
    • backgammon
  • Pathfinding
    • missionaries and cannibals
    • Towers of Hanoi
    • 15 puzzle
    • Rubik's Cube
  • Satisfiying/Satisficing
    • cryptarithmetic
    • n-queens
    • mutilated checkerboard
• What Is The Common Ground?
  • We could build giant database and look up answer
  • No database in the world big enough
  • Even if there was, lookup always too slow
  • Problems are (problem is) NP-hard
    • problem description
    • NP
    • NP-hardness
    • NP-completeness
    • reductions
    • P = NP?
• Blind Search
  • Build database lazily (on-demand)
    • solves first problem
    • might attack second
  • Tree-structure database
    • initial state at root
    • solutions at leaves
    • move toward more knowledge
  • Blind search algorithms
    • breadth-first search for pathfinding
      • node represents location
      • select least recently examined node until
        • out of nodes
        • reach goal
      • move away from node in direction not previously visited
      • not space-efficient: cannot discard nodes
      • produces shortest paths: optimal
      • depth-first search?
    • depth-first search for SAT
      • node represents partial assignment
      • extend partial assignments until
        • contradiction
        • total assignment (solution)
      • ``obvious'' approach
      • runs forever (except small or easy instances)
      • space-efficient
    • making DFS more like BFS
      • iterative deepening
      • iterative broadening
    • nonsystematic methods
    • undirected and directed graphs: open and closed lists
    • dynamic backtracking
• Heuristic Search
  • DFS gets lost: add problem-specific ``hints''
  • Goal distance estimates in pathfinding search
  • How to use the goal distance heuristic
    • Hill climbing: local search
    • Best-first search
  • A*: a ``provably optimal'' pathfinding search algorithm
    • admissable heuristics
    • monotonic heuristics
    • algorithm
    • extension to graphs
    • IDA*
• Nogoods
  • DFS for SAT does not use memory effectively
  • Keep nogoods around: partial assignments that fail
  • Resolve nogoods to shorter nogoods
  • Prune search using nogoods
  • What nogoods to keep?
    • short nogoods: does not work
    • "relevant" nogoods: RELSAT
• Local Search
  • Completeness of search
  • Hill climbing: problems
    • local maxima
    • plateaus
    • ridges
  • Noise
    • natural noise
    • introducing noise
    • convergence
    • restarts
    • simulated annealing
  • Systematic hill climbing: iterated randomness
    • dynamic backtracking
    • PDB
  • WSAT: local search for Boolean SAT
    • idea: start with total assignment and ``flip''
    • problem: can get stuck
    • solution: noise flips
    • algorithm
      1. Start with (random?) total assignment
      2. Repeatedly flip a coin and on
         • Heads: pick ``best'' variable in unsat clause, flip it
         • Tails: pick random variable, flip it
      3. If a solution is ever found, stop
    • ``walks'' through total assignment space