Chap 4' Informed Search Methods

1
Chap 4. Informed Search Methods

• 4-1. Best-first search
• 4-2. Heuristic functions
• 4-3. Memory bounded search
• 4-4. Iterative improvement algorithms

2
4-0. Preliminary

• Reference Chapter 4, Winston
• How to put heuristics?
• 1) as program codes
• 2) as rules
• 3) as parameters
• Role of knowledge
• 1) to reduce the search time (by reducing the
  of expanded nodes)
• 2) to help to reduce a problem into a simpler one.

3

• heuristic search -- Newell Ernst (1965)
• Where is the heuristics incorporated in the
  search algorithm?
• n lt--- SELECT (OPEN), or
• OPEN lt--- Re-order (OPEN)
• heuristic power lt----gt of expanded nodes

4

• 1) Heuristic function (evaluation function)
• the ability to forecast the future.
• candidates
• probability that a node is on the best path.
• distance between a node and the goal.
• 2) Hill climbing
• similar to depth-first

5

• 3) Beam search
• similar to breadth-first search.
• Move down only thru the best W nodes at each
  level.
• Other nodes are ignored.
• 4) Greedy method
• Choose the node that is likely to be the closest
  to goal.
• completeness -- no
• admissibility -- no, but tends to find
  solutions quickly.

6
4-1. A-search and A-search

• Best-first actually means seemingly-best-first
  .
• idea
• evaluation function estimated min cost from
  s to n
• estimated min cost from n to g
• algorithm
• n lt---- SELECT (OPEN)
• n lt---- min OPEN wrt eval. fn

7

• (1) A-search
• (2) A-search

8
(1) A-search

• f(n) g(n) h(n)

9
(2) A-search

• Hart, Nilsson, Raphael (1968)
• Def. admissibility
• Def. A
• Thm. A is admissible
• Homework 1 Proove that A is admissible.

10
4-2. Heuristic functions

• heuristic functions for 8-puzzle problem
• 1) of mis-placed tiles
• 2) the sum of the distances of the tiles from
  their goal position
• performance fig 4.8, pp. 103

11

• Comparison of two A algorithms
• Def. (more) informed
• Thm. a relation between informedness and of
  nodes

12

• inventing heuristic functions
• Consider a relaxed problem.
• example shortest path on the map
• example 8 puzzle
• Automatic generation of a relaxed problem?
• ABSOLVER (Prieditis 1993)
• statistical info
• training

13

• Def. monotonic restriction
• Thm. monotonic restriction gt less
  book-keeping

14

• Homework 2 A? algorithm
• OPEN
• FOCAL
• sublist of OPEN
• contains only those nodes which do not deviate
  from the node which has the lowest expected
  evaluation function by a factor greater than 1
  ?.
• A? selects a node from FOCAL with the minimum f
  value.
• Show that A? is ??-admissible, I.e., it always
  find a solution whose cost dos not exceed the
  optimal cost more than a factor of (1 ?).

15
4-3. Memory-bound search

• Memory is more critical than time.
• iterative-deepening search
• ---gt IDA (iterative deepening A)
• A
• ----gt SMA (simplified memory-bounded A)

16

• 1) Iterative deepening A search (IDA)
• iterative deepening
• memory -- depth-first
• completeness -- breadth-first
• depth-first, but use f-value, rather than depth.
• complete, admissible
• algorithm fig 4.10, pp. 107
• space? ? longest path
• ( shortest path to the optimal solution)
• time
• total of expansions 1 2 3 N
• where A expands N nodes.

17

• 2) Simplified memory-bound A search (SMA)
• IDA uses too little memory.
• idea Keep OPEN CLOSE ? Nmax
• algorithm fig 4.12, pp. 110
• example fig 4.11, pp.109
• complete if the available memory is sufficient to
  store the shallowest solution path.
• admissible if the available memory is sufficient
  to store the shallowest optimal solution path.