lec16 - 1.203J, 6.281J, 15.073J, 16.76J, etc. Logistical...

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1.203J, 6.281J, 15.073J, 16.76J, etc. Logistical and Transportation Planning Methods Some Important Heuristics for the TSP We summarize below some of the principal characteristics of a number of the best-known heuristic algorithms for the TSP. The worst-case results cited apply to TSPs which have symmetrical distance matrices that satisfy the triangular inequality, but some of the heuristics can also be used in problems that do not satisfy these conditions. Additional details can be found in the following three outstanding references: Jiinger, Michael, G. Reinelt and G. Rinaldi, "The Traveling Salesman Problem", Chapter 3 in Netzoork Models (Voliitne 7 of Handbooks in Operations Research and Management Science series) M.0, Ball, T.L. Magnanti, C.L. Monma and G. Nemhauser (eds.) Elsevier Science, Amsterdam (1995) pp. 225 -330. Lawler, E.L., J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys (editors) The Traueli~zg Salesir~ntz Problem, John Wiley and Sons, Chichester (1985). Rosenkrantz, D.J., R.E. Stearns and P.M. Lewis, "An Analysis of Several Heuristics fot the Traveling Salesman Problem", SIAM Journal of Compzltilzg, 6 (1977) pp. 563-581. A. Construction Heuristics 1. Nearest Neirrhbor Heuristic: Begin at a random node or at a pre-specified node and build a tour by always moving to the nearest neighbor (among the nodes not yet connected to the tour) of the latest node to join the tour. When all nodes have been connected to the tour, join the last node to the origin to complete the tour. Worst-case performance: Computational Complexity: C( n2).
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2. Insertion Heuristics: All the heuristics in this class, initiate the tour-construction process with a "seed tour" consisting either of a single node with a self-loop or of a loop
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lec16 - 1.203J, 6.281J, 15.073J, 16.76J, etc. Logistical...

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