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Mixed Integer Programming Formulations for the Balanced Traveling Salesman Problem with a Lexicographic Objective

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Metaheuristics for Combinatorial Optimization (MESS 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1332))

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Abstract

This paper presents a Mixed Integer Program to solve the Balanced TSP. It exploits the underlying structure of the instances and is able to find optimal solutions for all the instances provided in the Metaheuristics Summer School competition. We study the efficiency of this new model on several variants of the Balanced TSP. The proposed method was ranked first in the MESS18 Metaheuristic competition among 9 submissions.

Instances and ranking: http://195.201.24.233/mess2018/home.html..

Source code: https://gitlab.com/librallu/balancedtspcode.

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Notes

  1. 1.

    http://195.201.24.233/mess2018/home.html.

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Author information

Authors and Affiliations

  1. Univ. Grenoble Alpes, CNRS, Grenoble INP, G-SCOP, 38000, Grenoble, France

    Luc Libralesso

Authors
  1. Luc Libralesso
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Corresponding author

Correspondence to Luc Libralesso .

Editor information

Editors and Affiliations

  1. Department of Economics and Business, University of Catania, Catania, Italy

    Salvatore Greco

  2. Department of Mathematics and Computer Science, University of Catania, Catania, Italy

    Mario F. Pavone

  3. Laboratoire Cristal, University of Lille and Inria, Lille, France

    El-Ghazali Talbi

  4. Department of Electrical, Electronics, and Information Engineering and CIRI-ICT, University of Bologna, Bologna, Italy

    Daniele Vigo

A Appendix

A Appendix

Fig. 1.
figure 1

btsp 0100 convergence curves

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Fig. 2.
figure 2

btsp 0250 convergence curves

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Fig. 3.
figure 3

btsp 0500 convergence curves

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Fig. 4.
figure 4

btsp 0700 convergence curves

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Fig. 5.
figure 5

btsp 1000 convergence curves

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Table 2. Numerical results on the balanced assignment problem
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Table 3. Numerical results on the balanced spanning-tree problem
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Table 4. Numerical results on the balanced subset problem
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Table 5. Numerical results on the classical TSP problem
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Fig. 6.
figure 6

btsp 1500 convergence curves

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Cite this paper

Libralesso, L. (2021). Mixed Integer Programming Formulations for the Balanced Traveling Salesman Problem with a Lexicographic Objective. In: Greco, S., Pavone, M.F., Talbi, EG., Vigo, D. (eds) Metaheuristics for Combinatorial Optimization. MESS 2018. Advances in Intelligent Systems and Computing, vol 1332. Springer, Cham. https://doi.org/10.1007/978-3-030-68520-1_1

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