A generic exact solver for vehicle routing and related problems

Major advances were recently obtained in the exact solution of vehicle routing problems (VRPs). Sophisticated branch-cut-and-price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those...

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Published in:	Mathematical programming Vol. 183; no. 1-2; pp. 483 - 523
Main Authors:	Pessoa, Artur, Sadykov, Ruslan, Uchoa, Eduardo, Vanderbeck, François
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2020 Springer Nature B.V Springer Verlag
Subjects:	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Computer Science Enumeration Exact solutions Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Operations Research Route planning Theoretical Vehicle routing Integer programming logistics and supply chain management Column generation etc. for problems pertaining to operations research and mathematical programming 90C11 Mixed integer programming 90B06 Transportation source code 90-04 Software Routing 90C06 Large-scale problems in mathematical programming
ISSN:	0025-5610, 1436-4646
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Abstract	Major advances were recently obtained in the exact solution of vehicle routing problems (VRPs). Sophisticated branch-cut-and-price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This work proposes a BCP solver for a generic model that encompasses a wide class of VRPs. It incorporates the key elements found in the best existing VRP algorithms: ng-path relaxation, rank-1 cuts with limited memory, path enumeration, and rounded capacity cuts; all generalized through the new concepts of “packing set” and “elementarity set”. The concepts are also used to derive a branching rule based on accumulated resource consumption and to generalize the Ryan and Foster branching rule. Extensive experiments on several variants show that the generic solver has an excellent overall performance, in many problems being better than the best specific algorithms. Even some non-VRPs, like bin packing, vector packing and generalized assignment, can be modeled and effectively solved.
AbstractList	Major advances were recently obtained in the exact solution of Vehicle Routing Problems (VRPs). Sophisticated Branch-Cut-and-Price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However , adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This work proposes a BCP solver for a generic model that encompasses a wide class of VRPs. It incorporates the key elements found in the best recent VRP algorithms: ng-path relaxation, rank-1 cuts with limited memory, and route enumeration; all generalized through the new concept of "packing set". This concept is also used to derive a new branch rule based on accumulated resource consumption and to generalize the Ryan and Foster branch rule. Extensive experiments on several variants show that the generic solver has an excellent overall performance, in many problems being better than the best existing specific algorithms. Even some non-VRPs, like bin packing, vector packing and generalized assignment, can be modeled and effectively solved. Major advances were recently obtained in the exact solution of vehicle routing problems (VRPs). Sophisticated branch-cut-and-price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This work proposes a BCP solver for a generic model that encompasses a wide class of VRPs. It incorporates the key elements found in the best existing VRP algorithms: ng-path relaxation, rank-1 cuts with limited memory, path enumeration, and rounded capacity cuts; all generalized through the new concepts of “packing set” and “elementarity set”. The concepts are also used to derive a branching rule based on accumulated resource consumption and to generalize the Ryan and Foster branching rule. Extensive experiments on several variants show that the generic solver has an excellent overall performance, in many problems being better than the best specific algorithms. Even some non-VRPs, like bin packing, vector packing and generalized assignment, can be modeled and effectively solved.
Author	Vanderbeck, François Pessoa, Artur Uchoa, Eduardo Sadykov, Ruslan
Author_xml	– sequence: 1 givenname: Artur surname: Pessoa fullname: Pessoa, Artur organization: Universidade Federal Fluminense – sequence: 2 givenname: Ruslan surname: Sadykov fullname: Sadykov, Ruslan organization: INRIA Bordeaux — Sud-Ouest – sequence: 3 givenname: Eduardo orcidid: 0000-0002-8687-2613 surname: Uchoa fullname: Uchoa, Eduardo email: uchoa@producao.uff.br organization: Universidade Federal Fluminense – sequence: 4 givenname: François surname: Vanderbeck fullname: Vanderbeck, François organization: Atoptima
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Snippet	Major advances were recently obtained in the exact solution of vehicle routing problems (VRPs). Sophisticated branch-cut-and-price (BCP) algorithms for some of... Major advances were recently obtained in the exact solution of Vehicle Routing Problems (VRPs). Sophisticated Branch-Cut-and-Price (BCP) algorithms for some of...
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SubjectTerms	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Computer Science Enumeration Exact solutions Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Operations Research Route planning Theoretical Vehicle routing
Title	A generic exact solver for vehicle routing and related problems
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