V. H. Nguyen, T. Q. T. Vo

We consider several equitable versions of the Traveling Salesman Problem where the equity is based on the cost of the edges taken by the tour. One of these versions is the balanced traveling salesman problem defined by Larusic and Punnen (COR, vol. 38, pp 868-875 2010) where the objective is to minimize the difference between the maximum cost and the minimum cost of the edges in the tour. We also consider the OWA (ordered weighted averaging) TSP which favors tours with similar costs on the edges while assuring a degree of efficiency on the total cost. We propose MIP formulations for those problems where the equity constraints are formulated as linear constraints. Moreover, no additional integer variable is needed with respect to the IP formulation of the original TSP. We also present numerical experiments where, to our knowledge, optimal solutions for several instances of the balanced TSP are proved for the first time.

Keywords: Traveling salesman problem, Equity, Ordered weighted averaging, Mixed integer linear programming


TB3 TSP and its variants
June 10, 2021  11:15 AM
3 - TC Koopmans

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