nlec2 - Networks: Lecture 2 Amedeo R. Odoni November 17,...

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Unformatted text preview: Networks: Lecture 2 Amedeo R. Odoni November 17, 2004 Outline • Generic heuristics for the TSP • Euclidean TSP: tour construction, tour improvement, hybrids • Worst-case performance • Probabilistic analysis and asymptotic result for Euclidean TSP [ Separate handout ] • Extensions Solving the TSP • Best existing exact algorithms can solve optimally problems with up to 15,000 points (as of 2001) • Numerous heuristic approaches for good solutions to MUCH larger problems • For practical purposes, heuristics are very powerful. A classification: _ Tour construction _ Tour improvement _ Hybrid • Analysis of heuristics: _ Worst case _ Empirical _ Asymptotic _ Probabilistic Heuristics: Euclidean TSP 8 9 10 7 6 1 5 4 3 2 The Nearest Neighbor Heuristic 8 9 10 7 6 1 5 4 3 2 Performance: Nearest Neighbor • Poor performance in practice (+20%) • Can be improved through refinements (e.g., “likely subgraph”) ⎡ ⎤ 2 1 log 2 1 ) ( ) ( 2 + ≤ n TSP L OR NEARNEIGHB L Insertion Heuristics Nearest insertion Farthest insertion Cheapest insertion Random insertion ? Worst-case Performance: Insertion Heuristics ⎡ ⎤ 1 log ) ( ) ( 2 + ≤ n TSP L INSERT RANDOM L ) ( ) ( TSP L INSERT FAR L 2 ) ( ) ( < TSP...
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This note was uploaded on 11/08/2011 for the course AERO 16.72 taught by Professor Hansman during the Fall '06 term at MIT.

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nlec2 - Networks: Lecture 2 Amedeo R. Odoni November 17,...

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