The Multiple Steiner TSP with order constraints: complexity and optimization algorithms
Gabrel, Virginie; Mahjoub, Ali Ridha; Taktak, Raouia; Uchoa, Eduardo (2020), The Multiple Steiner TSP with order constraints: complexity and optimization algorithms, Soft Computing. 10.1007/s00500-020-05043-y
TypeArticle accepté pour publication ou publié
Journal nameSoft Computing
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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.
Subjects / KeywordsSteiner TSP; Order constraints; Integer linear programming; Branch-and-Price algorithm; Branch-and-Cut algorithm
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