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Automation and Remote Control

, Volume 79, Issue 7, pp 1296–1310 | Cite as

Probabilistic Prediction of the Complexity of Traveling Salesman Problems Based on Approximating the Complexity Distribution from Experimental Data

  • V. A. Goloveshkin
  • G. N. Zhukova
  • M. V. Ulyanov
  • M. I. Fomichev
Optimization, System Analysis, and Operations Research
  • 13 Downloads

Abstract

We show the results of a statistical study of the complexity of the asymmetric traveling salesman problem (ATSP) obtained by processing a specially generated pool of matrices. We show that the normal distribution can serve as an approximation to the distribution of the logarithm of complexity for a fixed problem dimension. We construct a family of probability distributions that represent satisfactory approximations of the complexity distribution with a dimension of the cost matrix from 20 to 49. Our main objective is to make probabilistic predictions of the complexity of individual problems for larger values of the dimension of the cost matrix. We propose a representation of the complexity distribution that makes it possible to predict the complexity. We formulate the unification hypothesis and show directions for further study, in particular proposals on the task of clustering “complex” and “simple” ATSP problems and proposals on the task of directly predicting the complexity of a specific problem instance based on the initial cost matrix.

Keywords

traveling salesman problem complexity of an individual traveling salesman problem approximations of probability distributions quantile skewness quantile kurtosis probabilistic prediction 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • V. A. Goloveshkin
    • 1
    • 2
  • G. N. Zhukova
    • 3
  • M. V. Ulyanov
    • 4
    • 5
  • M. I. Fomichev
    • 3
  1. 1.Moscow Technological UniversityMoscowRussia
  2. 2.Institute of Applied MechanicsRussian Academy of SciencesMoscowRussia
  3. 3.National Research University Higher School of EconomicsMoscowRussia
  4. 4.Institute of Control SciencesRussian Academy of SciencesMoscowRussia
  5. 5.Lomonosov State UniversityMoscowRussia

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