The Steiner Traveling Salesman Problem and its extensions

Jessica Rodríguez-Pereira; Elena Fernández; Gilbert Laporte; Enrique Benavent; Antonio Martínez-Sykora

doi:10.1016/j.ejor.2019.04.047

The Steiner Traveling Salesman Problem and its extensions

Jessica Rodríguez-Pereira, Elena Fernández, Gilbert Laporte, Enrique Benavent, Antonio Martínez-Sykora

Research output: Contribution to journal › Article › peer-review

2 Citations (SciVal)

Abstract

This paper considers the Steiner Traveling Salesman Problem, an extension of the classical Traveling Salesman Problem on an incomplete graph where not all vertices have demand. Some extensions including several depots or location decisions are introduced, modeled and solved. A compact integer linear programming formulation is proposed for each problem, where the routes are represented with two-index decision variables, and parity conditions are modeled using cocircuit inequalities. Exact branch-and-cut algorithms are developed for all formulations. Computational results obtained confirm the good performance of the algorithms. Instances with up to 500 vertices are solved optimally.

Original language	English
Pages (from-to)	615-628
Number of pages	14
Journal	European Journal of Operational Research
Volume	278
Issue number	2
DOIs	https://doi.org/10.1016/j.ejor.2019.04.047
Publication status	Published - 16 Oct 2019

Keywords

Branch-and-cut
Integer linear programming
Steiner Traveling Salesman Problem
Valid inequalities

ASJC Scopus subject areas

Computer Science(all)
Modelling and Simulation
Management Science and Operations Research
Information Systems and Management

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10.1016/j.ejor.2019.04.047

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title = "The Steiner Traveling Salesman Problem and its extensions",

abstract = "This paper considers the Steiner Traveling Salesman Problem, an extension of the classical Traveling Salesman Problem on an incomplete graph where not all vertices have demand. Some extensions including several depots or location decisions are introduced, modeled and solved. A compact integer linear programming formulation is proposed for each problem, where the routes are represented with two-index decision variables, and parity conditions are modeled using cocircuit inequalities. Exact branch-and-cut algorithms are developed for all formulations. Computational results obtained confirm the good performance of the algorithms. Instances with up to 500 vertices are solved optimally.",

keywords = "Branch-and-cut, Integer linear programming, Steiner Traveling Salesman Problem, Valid inequalities",

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AU - Fernández, Elena

AU - Laporte, Gilbert

AU - Benavent, Enrique

AU - Martínez-Sykora, Antonio

PY - 2019/10/16

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N2 - This paper considers the Steiner Traveling Salesman Problem, an extension of the classical Traveling Salesman Problem on an incomplete graph where not all vertices have demand. Some extensions including several depots or location decisions are introduced, modeled and solved. A compact integer linear programming formulation is proposed for each problem, where the routes are represented with two-index decision variables, and parity conditions are modeled using cocircuit inequalities. Exact branch-and-cut algorithms are developed for all formulations. Computational results obtained confirm the good performance of the algorithms. Instances with up to 500 vertices are solved optimally.

AB - This paper considers the Steiner Traveling Salesman Problem, an extension of the classical Traveling Salesman Problem on an incomplete graph where not all vertices have demand. Some extensions including several depots or location decisions are introduced, modeled and solved. A compact integer linear programming formulation is proposed for each problem, where the routes are represented with two-index decision variables, and parity conditions are modeled using cocircuit inequalities. Exact branch-and-cut algorithms are developed for all formulations. Computational results obtained confirm the good performance of the algorithms. Instances with up to 500 vertices are solved optimally.

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KW - Integer linear programming

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KW - Valid inequalities

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The Steiner Traveling Salesman Problem and its extensions

Abstract

Keywords

ASJC Scopus subject areas

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