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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-020-01523-z