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Combining and projecting flow models for the (precedence constrained) asymmetric traveling salesman problem
Author(s) -
Gouveia Luis,
Pesneau Pierre,
Ruthmair Mario,
Santos Daniel
Publication year - 2018
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.21765
Subject(s) - travelling salesman problem , disjoint sets , flow network , path (computing) , flow (mathematics) , mathematics , variable (mathematics) , mathematical optimization , computer science , combinatorics , mathematical analysis , geometry , programming language
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, Vol. 71(4), 451–465 2018