1. Combining and projecting flow models for the (Precedence Constrained) Asymmetric Traveling Salesman Problem
- Author
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Mario Ruthmair, Pierre Pesneau, Daniel Santos, Luis Borges Gouveia, Centro de Investigação Operacional (CIO), Universidade de Lisboa (ULISBOA), Reformulations based algorithms for Combinatorial Optimization (Realopt), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Austrian Institute of Technology [Vienna] (AIT), Universidade de Lisboa = University of Lisbon (ULISBOA), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Institut de Mathématiques de Bordeaux (IMB), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest
- Subjects
Mathematical optimization ,Computer Networks and Communications ,Property (programming) ,0211 other engineering and technologies ,02 engineering and technology ,Disjoint sets ,valid inequalities ,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] ,Space (mathematics) ,cutting plane algorithm ,Travelling salesman problem ,integer linear programming ,0202 electrical engineering, electronic engineering, information engineering ,Integer programming ,Mathematics ,021103 operations research ,[INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO] ,Flow network ,reformulation ,Variable (computer science) ,Flow (mathematics) ,Hardware and Architecture ,traveling salesman ,020201 artificial intelligence & image processing ,Software ,Information Systems ,precedence constraints - Abstract
There are many ways of modeling the Asymmetric Traveling Salesman Problem (ATSP) and the related Precedence Constrained ATSP (PCATSP). In this paper we present new formulations for the two problems that result from combining precedence variable based formulations with network flow based formulations. The motivation for this work is a property of the so-called GDDL inequalities (Gouveia and Pesneau, Networks 48, 77–89, 2006), the “disjoint sub-paths” property, that is explored to create formulations that combine two (or more) disjoint path network flow based formulations. Several sets of projected inequalities, in the space of the arc and precedence variables, and in the spirit of many inequalities presented in Gouveia and Pesneau (Networks 48, 77–89, 2006), are obtained by projecting these network flow based formulations. Computational results are given for the PCATSP and the ATSP to evaluate the quality of the new inequalities. © 2017 Wiley Periodicals, Inc. NETWORKS, 2017
- Published
- 2017