Improved branch-cut-and-price for capacitated vehicle routing

The best performing exact algorithms for the capacitated vehicle routing problem developed in the last 10 years are based in the combination of cut and column generation. Some authors only used cuts expressed over the variables of the original formulation, in order to keep the pricing subproblem rel...

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Bibliographic Details
Published in:Mathematical programming computation Vol. 9; no. 1; pp. 61 - 100
Main Authors: Pecin, Diego, Pessoa, Artur, Poggi, Marcus, Uchoa, Eduardo
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2017
Springer Nature B.V
Subjects:
Algorithms
Customers
Enumeration
Full Length Paper
Heuristic methods
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Optimization
Pricing
Route planning
Routing
Theory of Computation
Vehicle routing
Integer programming
Column generation
Cut separation
90C10 Integer programming
90C39 Dynamic programming
branch-and-cut
90C57 Polyhedral combinatorics
branch-and-bound
Algorithmic engineering
ISSN:1867-2949, 1867-2957
Online Access:Get full text
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Summary:The best performing exact algorithms for the capacitated vehicle routing problem developed in the last 10 years are based in the combination of cut and column generation. Some authors only used cuts expressed over the variables of the original formulation, in order to keep the pricing subproblem relatively easy. Other authors could reduce the duality gaps by also using a restricted number of cuts over the master LP variables, stopping when the pricing becomes prohibitively hard. A particularly effective family of such cuts are the subset row cuts. This work introduces a technique for greatly reducing the impact on the pricing of these cuts, thus allowing much more cuts to be added. The newly proposed branch-cut-and-price algorithm also incorporates and combines for the first time (often in an improved way) several elements found in previous works, like route enumeration and strong branching. All the instances used for benchmarking exact algorithms, with up to 199 customers, were solved to optimality. Moreover, some larger instances with up to 360 customers, only considered before by heuristic methods, were solved too.
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ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-016-0108-8