Russell and Norvig, Chapter 4: Informed Search Methods

4.1 Best-First Search
- evaluation function = desirability of expanding a node
- best-first search always selects a node for expansion having the
  highest evaluation function
- greedy search
  - minimize estimated cost to reach goal
  - estimate provided by heuristic function
  - e.g., straight-line distance in route finding
- A* search
  - minimize total path cost (path so far + estimate to goal)
    - f(n) = g(n) + h(n)
  - if estimate to goal never overestimates, heuristic is admissible
    and search is optimal and complete
  - e.g., straight-line distance
  - no other optimal algorithm is guaranteed to expand fewer nodes
    than A*
  - still exponential
  - still keeps all nodes in memory (see Sec 4.3)

4.2 Heuristic Functions
- h2 is better than h1 if h2 >= h1 always (h2 dominates h1)
- invent heuristics by relaxing problem constraints
- heuristic evaluation should be efficient
- constraint-satisfaction problems
  - selecting a variable
    - most-constrained variable (fewest possible values)
    - most-constraining variable (involved in most constraints)
  - selecting a value
    - least-constraining value (rules out fewest values of other variables)

4.3 Memory-Bounded Search
- Iterative Deepening A* (IDA*) [Fig4.10]
  - depth-first search through all nodes whose f <= flimit
  - new flimit is the minimum f of nodes expanded beyond flimit
  - number of IDA* iterations proportional to number of different f values
  - could used fixed flimit increment, but not admissible (e-admissible)
- Simplified Memory-bounded A* (SMA*) [Fig4.12]
  - removes high-f-value nodes from queue as memory constraints dictate
  - f values of removed nodes retained in ancestors
  - removed nodes regenerated only if all other paths are worse
  - optimal and complete if shallowest, optimal solution fits in memory
    - otherwise, returns best solution reachable
  - example [Fig4.11]

4.4 Iterative Improvement Algorithms
- start with complete configuration and modify until solution
  - e.g., 8 queens
- hill-climbing search (gradient descent) [Fig4.14]
  - move to best successor, discarding path information
  - local maxima, plateaus (random walk)
  - ridges (steep sides and gentle slope to peak)
    - oscillate side-to-side with little progress
  - random-restart hill climbing
- simulated annealing [Fig4.15]
  - hill-climbing with some probability of making poor moves
    - move selected randomly
    - probability related to quality of move
    - improving move always taken
  - poor moves more likely at high temperatures, but search "freezes"
    as temperature decreases (P = e^(dE/T))
    - dE = value(nextstate) - value(currentstate)
    - T = temperature
  - slow enough temperature-decrease-schedule yields optimal solution
- constraint satisfaction problems
  - choose a value for each variable, then use heuristic repair
    - e.g., choose values with minimum conflicts with other variables