lec15 - Networks Lecture 2 Amedeo R Odoni Outline Generic...

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Networks: Lecture 2 Amedeo R. Odoni November 20, 2006 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 Reference: Sections 6.4.5-6.4.13 + Handouts
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Node Covering (TSP, VRP, et al) Huge literature, endless applications Traveling Salesman Problem (TSP) is the prototypical “hard” problem Some applications: _ Routing of all kinds _ Job shop scheduling _ Vehicle routing problem (VRP) _ Dial-a-ride problem (DARP) _ Electronics industry _ Biotechnology _ Air traffic control _ Genomics 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
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Heuristics: Euclidean TSP 8 9 1 3 2 7 10 4 5 6 The Nearest Neighbor Heuristic 7 6 5 2 8 3 9 1 10 4
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Performance: Nearest Neighbor L ( NEARNEIGHBOR ) 1 1 L ( TSP ) 2 log 2 n + 2 Poor performance in practice (+20%) Can be improved through refinements (e.g., “likely subgraph”) Insertion Heuristics ?
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