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The Multiple Steiner TSP with order constraints: complexity and optimization algorithms

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Gabrel2020.pdf (835.4Kb)
Date
2020
Dewey
Programmation, logiciels, organisation des données
Sujet
Steiner TSP; Order constraints; Integer linear programming; Branch-and-Price algorithm; Branch-and-Cut algorithm
Journal issue
Soft Computing
Publication date
2020
DOI
http://dx.doi.org/10.1007/s00500-020-05043-y
URI
https://basepub.dauphine.fr/handle/123456789/20901
Collections
  • LAMSADE : Publications
Metadata
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Author
Gabrel, Virginie
Mahjoub, Ali Ridha
Taktak, Raouia
Uchoa, Eduardo
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider a variant of the Travelling Salesman Problem (TSP), the Multiple Steiner TSP with Order constraints (MSTSPO). Consider a weighted undirected graph and a set of salesmen, and each salesman is associated with a set of compulsory vertices to visit, called terminals. The MSTSPO consists in finding a minimum-cost subgraph containing for each salesman a tour going in a specified order through its terminals. Along with its importance from a theoretical point of view, the problem is also challenging in practice since it has applications in telecommunication networks. We show that the problem is NP-hard even for a single salesman and propose integer programming formulations. We then devise both Branch-and-Cut and Branch-and-Price algorithms to solve the problem. The extensive computational results are presented, showing the efficiency of our algorithms.

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