1. Lecture 4 of 42 State Spaces, Graphs, Uninformed (Blind) Search: ID-DFS, Bidirectional, UCS/B&B Discussion: Term Projects 4 of 5 William H. Hsu Department of Computing and Information Sciences, KSU KSOL course page: http://snipurl.com/v9v3 Course web site: http://www.kddresearch.org/Courses/CIS730 Instructor home page: http://www.cis.ksu.edu/~bhsu Reading for Next Class: Sections 3.5 – 3.7, p. 81 – 88; 4.1 – 4.2, p. 94 - 109, Russell & Norvig 2nd ed. Instructions for writing project plans, submitting homework

3. Past Week: Intelligent Agents (Ch. 2), Blind Search (Ch. 3)

4. Basic search frameworks: discrete and continuous

5. Tree search intro: nodes, edges, paths, depth

6. Depth-first search (DFS) vs. breadth-first search (BFS)

7. Completeness and depth-limited search (DLS)

8. Coping with Time and Space Limitations of Uninformed Search

9. Depth-limited and resource-bounded search (anytime, anyspace)

10. Iterative deepening (ID-DFS) and bidirectional search

11. Project Topic 4 of 5: Natural Lang. Proc. (NLP) & Info. Extraction

12. Preview: Intro to Heuristic Search (Section 4.1)

13. What is a heuristic?

14. Relationship to optimization, static evaluation, bias in learning

16. State Space Graph: Vacuum World Based on slide © 2003 S. Russell & P. Norvig. Reused with permission.

17. State Space Example: Vacuum World Sensorless Conditional Based on slide © 2003 S. Russell & P. Norvig. Reused with permission.

18. Graph Search Example: Route Planning Edge weights based on actual driving distance Based on slides © 2003 S. Russell & P. Norvig. Reused with permission.

19. Single-State Problem Formulation © 2003 S. Russell & P. Norvig. Reused with permission.

20. Selecting A State Space © 2003 S. Russell & P. Norvig. Reused with permission.

22. initialize search tree using initial state of problem

23. loop do

24. if there are no candidates for expansion thenreturn failure

25. choose leaf node for expansion according to strategy

26. If node contains a goal state thenreturn corresponding solution

27. else expand node and add resulting nodes to search tree

28. end

29. Note: Downward Function Argument (Funarg) strategy

30. Implementation of General-Search

31. Rest of Chapter 3, Chapter 4, R&N

32. See also:

33. Ginsberg (handout in CIS library today)

34. Rich and Knight

36. Iterative Deepening Search (ID-DFS): Example Based on slides © 2003 S. Russell & P. Norvig. Reused with permission.

37. Iterative Deepening Search (ID-DFS): Properties © 2003 S. Russell & P. Norvig. Reused with permission.

38. Comparison of Search Strategies for Algorithms Thus Far Based on slides © 2003 S. Russell & P. Norvig. Reused with permission.

40. Search “from both ends”

41. Caveat: what does it mean to “search backwards from solution”?

42. Analysis

43. Solution depth (in levels from root, i.e., edge depth): d

44. Analysis

45. bi nodes generated at level i

46. At least this many nodes to test

47. Total: I bi = 1 + b + b2 + … + bd/2= (bd/2)

48. Worst-Case Space Complexity:(bd/2)

49. Properties

50. Convergence: suppose b, l finite and l  d

51. Complete: guaranteed to find a solution

52. Optimal: guaranteed to find minimum-depth solution

54. No heuristics: only g(n) used

55. Breadth-first search (BFS) and variants: uniform-cost, bidirectional

56. Depth-first search (DFS) and variants: depth-limited, iterative deepening

57. Heuristic Search

58. Based on h(n) – estimated cost of path to goal (“remaining path cost”)

59. h – heuristic function

60. g: node  R; h: node  R; f: node  R

61. Using h

62. h only: greedy (akamyopic) informed search

63. f = g + h: (some) hill-climbing, A/A*

64. Uniform-Cost (Branch and Bound) Search

65. Originates from operations research (OR)

66. Special case of heuristic search: treat as h(n) = 0

68. Definition: h(n) = estimated cost of cheapest path from state at node n to a goal state

69. Requirements for h

70. In general, any magnitude (ordered measure, admits comparison)

71. h(n) = 0 iffn is goal

72. For A/A*, iterative improvement: want

73. h to have same type as g

74. Return type to admit addition

75. Problem-specific (domain-specific)

76. Typical Heuristics

78. Heuriskein – to find (to discover)

79. Heureka (“I have found it”) – attributed to Archimedes

80. Usage of Term

81. Mathematical logic in problem solving

82. Polyà [1957]

83. Methods for discovering, inventing problem-solving techniques

84. Mathematical proof derivation techniques

85. Psychology: “rules of thumb” used by humans in problem-solving

86. Pervasive through history of AI

87. e.g., Stanford Heuristic Programming Project

88. One origin of rule-based (expert) systems

89. General Concept of Heuristic (A Modern View)

90. Standard (rule, quantitative measure) used to reduce search

91. “As opposed to exhaustive blind search”

93. Applying Knowledge

94. In problem representation (state space specification)

95. At Insert(), akaQueueing-Fn()

96. Determines node to expand next

97. Knowledge representation (KR)

98. Expressing knowledge symbolically/numerically

99. Objective

100. Initial state

101. State space (operators, successor function)

103. Justification: using only g doesn’t direct search toward goal

104. Nodes ordered

105. Node with best evaluation function (e.g., h) expanded first

106. Best-first: any algorithm with this property (NB: not just using h alone)

107. Note on “Best”

108. Refers to “apparent best node”

109. based on eval function

110. applied to current frontier

112. inputs: problem, specification of problem (structure or class) Eval-Fn, an evaluation function

113. Queueing-Fn  function that orders nodes by Eval-Fn

114. Compare: Sort with comparator function <

115. Functional abstraction

116. returnGeneral-Search (problem, Queueing-Fn)

117. Implementation

118. Recall: priority queue specification

119. Eval-Fn: node  R

120. Queueing-Fn Sort-By: node list  node list

121. Rest of design follows General-Search

122. Issues

123. General family of greedy (akamyopic, i.e., nearsighted) algorithms

125. Heuristics for General-Search Function of Problem-Solving-Agent

126. Informed (heuristic) search: heuristic definition, development process

127. Best-First Search

128. Greedy

129. A/A*

130. Admissibility property

131. Developing good heuristics

132. Humans

133. Intelligent systems (automatic derivation): case studies and principles

134. Constraint Satisfaction Heuristics

135. This Week: More Search Basics

136. Memory bounded, iterative improvement (gradient, Monte Carlo search)

139. Search Types: Uninformed (“Blind”) vs. Informed (“Heuristic”)

140. Basic Search Algorithms

141. British Museum (depth-firstakaDFS)

142. Breadth-Firstaka BFS

143. Depth-Limited Search (DLS)

144. Refinements

145. Iterative-deepening DFS (ID-DFS)

146. Bidirectional (as adaptation of BFS or ID-DFS)

147. Cost, c(n1, n2) and Cumulative Path Cost, g(n)

148. Online (Path) Cost, g(goal) vs. Offline (Search) Cost

149. Heuristic: Estimate of Remaining Path Cost, h(n)

151. This Week: Search, Chapters 3 - 4

152. State spaces

153. Graph search examples

154. Basic search frameworks: discrete and continuous

155. Uninformed (“Blind”) vs. Informed (“Heuristic”) Search

156. h(n) and g(n) defined: no h in blind search; online cost = g(goal)

157. Properties: completeness, time and space complexity, offline cost

158. Uniform-cost search (B&B) as generalization of BFS: g(n) only

159. Relation to Intelligent Systems Concepts

160. Knowledge representation: evaluation functions, macros

161. Planning, reasoning, learning

162. Coming Week: Heuristic Search, Chapter 4

163. Later: Goal-Directed Reasoning, Planning (Chapter 11)