A branch-and-price algorithm for the Minimum Latency Problem

Bulhões, Teobaldo; Sadykov, Ruslan; Uchôa, Eduardo

doi:10.1016/j.cor.2018.01.016

Cited by 44 publications

(36 citation statements)

References 34 publications

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“…We have implemented a dynamic extension of ng-sets [74,22], which is useful for some problems. Given a fractional solutionλ obtained after column generation convergence, we augment ng-sets based on "elementarity set cycles" in paths p ∈ P k such thatλ p > 0.…”

Section: Column and Cut Generationmentioning

confidence: 99%

A generic exact solver for vehicle routing and related problems

et al. 2020

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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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Section: Column and Cut Generationmentioning

confidence: 99%

A generic exact solver for vehicle routing and related problems

et al. 2020

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“…An ng-path may use two arcs belonging to the same packing set B, but only if the subpath between those two arcs passes by an arc a such that B / ∈ N G(a). The ng-sets may be determined a priori or dynamically, like in [54] and [17].…”

Section: Ng-pathsmentioning

confidence: 99%

A Generic Exact Solver for Vehicle Routing and Related Problems

Pessoa

Sadykov

Uchôa

et al. 2019

Lecture Notes in Computer Science

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Major advances were recently obtained in the exact solution of Vehicle Routing Problems (VRPs). Sophisticated Branch-Cutand-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.

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“…To overcome this issue, several authors have focused their attention on strengthening the bounds by partially imposing path elementarity. Two main frameworks can be found in the literature to deal with the issue of partially addressing the elementarity constraints in an efficient manner: decremental state‐space relaxation (DSSR, Boland et al., 2006; Righini and Salani, 2006); and cycle elimination (Desrochers et al., 1992; Irnich and Villeneuve, 2006; Baldacci et al., 2011; Bulhões et al., 2018).…”

Section: Introductionmentioning

confidence: 99%

“…More recently, Bulhões et al. (2018) proposed the arc ‐ ng ‐SPPRC, an extension of the classical ng ‐SPPRC, in which the neighborhoods are associated with arcs instead of nodes. Arc‐based neighborhoods allow better management of the undesirable cycles, although, when embedded into a DSSR framework, they usually induce many more iterations compared to a traditional node‐based ng ‐SPPRC.…”

Section: Introductionmentioning

confidence: 99%

“…In this article, we extend the set‐based dominance criterion of Bulhões et al. (2018) by making it selective. Unlike the original approach of using additional data structures to keep track of the nondominated labels (Desaulniers et al., 2019), the proposed mechanism requires minimal modifications of the labeling algorithm and is therefore easy to implement.…”

Section: Introductionmentioning

confidence: 99%

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Selective arc‐ng pricing for vehicle routing

Costa

Contardo

Desaulniers

et al. 2020

Int Trans Operational Res

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Column generation algorithms for solving vehicle routing problems often rely on a relaxed pricing subproblem where routes may be nonelementary and which is solved by a labeling algorithm. This pricing algorithm is said to be selective if it can discard nonelementary paths that may be Pareto‐optimal but guarantees finding at least one (not necessarily elementary) path of negative reduced cost when there exists at least one elementary path of negative reduced cost. In this paper, we propose a selective pricing mechanism for a recently introduced variant of the ng‐route relaxation, in which the neighborhoods are associated with arcs instead of nodes. We extend a state‐of‐the‐art set‐based dominance criterion for this problem and show, by means of an exhaustive computational campaign, that the resulting mechanism is effective at reducing the number of nondominated labels as compared to the original pricing algorithm for the same problem. As a result, typically shorter computing times are required to compute similar lower bounds when the proposed mechanism is embedded within a column generation solver.

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A branch-and-price algorithm for the Minimum Latency Problem

Cited by 44 publications

References 34 publications

A generic exact solver for vehicle routing and related problems

A generic exact solver for vehicle routing and related problems

A Generic Exact Solver for Vehicle Routing and Related Problems

Selective arc‐ng pricing for vehicle routing

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