An Exact Approach for the Precedence Constrained Generalized Traveling Salesman Problem
hal.structure.identifier | Kedge Business School [Kedge BS] | |
hal.structure.identifier | Formulations étendues et méthodes de décomposition pour des problèmes génériques d'optimisation [EDGE] | |
dc.contributor.author | KHACHAI, Daniil | |
hal.structure.identifier | Kedge Business School [Kedge BS] | |
dc.contributor.author | BATTAÏA, Olga | |
hal.structure.identifier | Ivannikov Institute for System Programming of the RAS | |
dc.contributor.author | KHACHAY, Michael | |
hal.structure.identifier | Reformulations based algorithms for Combinatorial Optimization [Realopt] | |
hal.structure.identifier | Formulations étendues et méthodes de décomposition pour des problèmes génériques d'optimisation [EDGE] | |
dc.contributor.author | SADYKOV, Ruslan | |
dc.date.accessioned | 2024-04-04T02:36:59Z | |
dc.date.available | 2024-04-04T02:36:59Z | |
dc.date.created | 2022-11-20 | |
dc.date.issued | 2022-11-20 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190768 | |
dc.description.abstractEn | The Precedence Constrained Generalized Traveling Salesman Problem (PCGTSP) is an extension of two well-known combinatorial optimization problems --- the Generalized Traveling Salesman Problem (GTSP) and the Precedence Constrained Asymmetric Traveling Salesman Problem (PCATSP), whose path version is known as the Sequential Ordering Problem (SOP). Similarly to the classic GTSP, the goal of the PCGTSP, for a given input digraph and partition of its node set into clusters, is to find a minimum cost cyclic route (tour) visiting each cluster in a single node. In addition, as in the PCATSP, feasible tours are restricted to visit the clusters with respect to the given partial order. Unlike the GTSP and SOP, to the best of our knowledge, the PCGTSP still remain to be weakly studied both in terms of polyhedral theory and algorithms. In this paper, for the first time for the PCGTSP, we propose several families of valid inequalities, establish dimension of the PCGTS polytope and prove sufficient conditions ensuring that the extended Balas' $\pi$- and $\sigma$-inequalities become facet-inducing. Relying on these theoretical results and evolving the state-of-the-art algorithmic approaches for the PCATSP and SOP, we introduce a family of MILP-models (formulations) and several variants of the branch-and-cut algorithm for the PCGTSP. We prove their high performance in a competitive numerical evaluation against the public benchmark library PCGTSPLIB, a known adaptation of the classic SOPLIB to the problem in question. | |
dc.language.iso | en | |
dc.title.en | An Exact Approach for the Precedence Constrained Generalized Traveling Salesman Problem | |
dc.type | Document de travail - Pré-publication | |
dc.type | Prepublication/Preprint | |
dc.subject.hal | Informatique [cs]/Recherche opérationnelle [cs.RO] | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
hal.identifier | hal-03906983 | |
hal.version | 1 | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-03906983v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2022-11-20&rft.au=KHACHAI,%20Daniil&BATTA%C3%8FA,%20Olga&KHACHAY,%20Michael&SADYKOV,%20Ruslan&rft.genre=preprint&unknown |
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