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chapter04b - Local search algorithms Chapter 4 Sections 34...

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Local search algorithms Chapter 4, Sections 3–4 Chapter 4, Sections 3–4 1
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Outline Hill-climbing Simulated annealing Genetic algorithms (briefly) Local search in continuous spaces (very briefly) Chapter 4, Sections 3–4 2
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Iterative improvement algorithms In many optimization problems, path is irrelevant; the goal state itself is the solution Then state space = set of “complete” configurations; find optimal configuration, e.g., TSP or, find configuration satisfying constraints, e.g., timetable In such cases, can use iterative improvement algorithms; keep a single “current” state, try to improve it Constant space, suitable for online as well as offline search Chapter 4, Sections 3–4 3
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Example: Travelling Salesperson Problem Start with any complete tour, perform pairwise exchanges Variants of this approach get within 1% of optimal very quickly with thou- sands of cities Chapter 4, Sections 3–4 4
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Example: n -queens Put n queens on an n × n board with no two queens on the same row, column, or diagonal Move a queen to reduce number of conflicts h = 5 h = 2 h = 0 Almost always solves n -queens problems almost instantaneously for very large n , e.g., n = 1 million Chapter 4, Sections 3–4 5
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