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

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

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.

Keywords

  • Balanced TSP
  • MIP
  • Metaheuristics

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  • DOI: 10.1007/978-3-030-68520-1_1
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Correspondence to Luc Libralesso .

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A Appendix

A Appendix

Fig. 1.
figure 1

btsp 0100 convergence curves

Fig. 2.
figure 2

btsp 0250 convergence curves

Fig. 3.
figure 3

btsp 0500 convergence curves

Fig. 4.
figure 4

btsp 0700 convergence curves

Fig. 5.
figure 5

btsp 1000 convergence curves

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

btsp 1500 convergence curves

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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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