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Computing the variance of tour costs over the solution space of the TSP in polynomial time

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  • Paul Sutcliffe
  • Andrew Solomon
  • Jenny Edwards

Abstract

We give an O(n 2 ) time algorithm to find the population variance of tour costs over the solution space of the n city symmetric Traveling Salesman Problem (TSP). The algorithm has application in both the stochastic case, where the problem is specified in terms of edge costs which are pairwise independently distributed random variables with known mean and variance, and the numeric edge cost case. We apply this result to provide empirical evidence that, in a range of real world problem sets, the optimal tour cost correlates with a simple function of the mean and variance of tour costs. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Paul Sutcliffe & Andrew Solomon & Jenny Edwards, 2012. "Computing the variance of tour costs over the solution space of the TSP in polynomial time," Computational Optimization and Applications, Springer, vol. 53(3), pages 711-728, December.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:3:p:711-728
    DOI: 10.1007/s10589-012-9472-0
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    References listed on IDEAS

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    1. Richard M. Karp, 1977. "Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 209-224, August.
    2. Alan Frieze, 2004. "On Random Symmetric Travelling Salesman Problems," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 878-890, November.
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