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Pareto-Based Hybrid Algorithms for the Bicriteria Asymmetric Travelling Salesman Problem

  • Yulia V. KovalenkoEmail author
  • Aleksey O. Zakharov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)

Abstract

We consider the bicriteria asymmetric travelling salesman problem (bi-ATSP): Given a complete directed graph where each arc is associated to a couple of positive weights, the aim is to find the Pareto set, consisting of all non-dominated Hamiltonian circuits. We propose new hybrid algorithms for the bi-ATSP using the adjacency-based representation of solutions and the operators that use the Pareto relation. Our algorithms are based on local search and evolutionary methods. The local search combines principles of the well-known Pareto Local Search procedures and Variable Neighborhood Search approach, realizing the search in width and depth. A genetic algorithm with NSGA-II scheme is applied to improve and extend a set of Pareto local optima by means of evolutionary processes. The experimental evaluation shows applicability of the algorithms to various structures of the bi-ATSP instances generated randomly and constructed from benchmark asymmetric instances with single objective.

Keywords

The Pareto set Genetic algorithm Local search Computational experiment 

Notes

Acknowledgement

The research reported in Sects. 2 and 3 is supported by RFBR grant 19-47-540005, and the research reported in Sect. 4 is supported by the Ministry of Science and Higher Education of the Russian Federation, government program of Sobolev Institute of Mathematics SB RAS, project N 0250-2019-0001 (Yu. Kovalenko). The research reported in Sect. 5 is supported by RFBR grant 17-07-00371 (A. Zakharov).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Saint Petersburg State UniversitySt. PetersburgRussia

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