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

Pecin, Diego; Pessoa, Artur Alves; Poggi, Marcus; Uchôa, Eduardo

doi:10.1007/s12532-016-0108-8

Cited by 176 publications

(138 citation statements)

References 25 publications

Supporting

Mentioning

133

Contrasting

Unclassified

Order By: Relevance

“…R1Cs are potentially strong, but each added cut makes the pricing subproblems significantly harder. The limited memory technique [45] is essential for mitigating that negative impact. In our context, a R1C characterized by its multipliers ρ is associated to a memory set A(ρ) ⊆ A. Variables λ p corresponding to paths p passing by arcs a / ∈ A(ρ) may have their coefficients decreased in (4).…”

Section: Limited Memory Rank-1 Cutsmentioning

confidence: 99%

“…Automatic dual price smoothing [51] is employed to stabilize the column generation convergence. Path enumeration is performed using an extension of the algorithm from [5,47]. Multi-phase strong branching [55,47] is used to reduce the search tree size.…”

Section: Computational Experimentsmentioning

confidence: 99%

“…In recent years, big advances in the exact solution of VRPs had been accomplished. A milestone was certainly the Branch-Cut-and-Price (BCP) algorithm of [45,47], that could solve Capacitated VRP (CVRP) instances with up to 360 customers, a large improvement upon the previous record of 150 customers. That algorithm exploits many elements introduced by several authors, combining and enhancing them.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Generic Exact Solver for Vehicle Routing and Related Problems

Pessoa

Sadykov

Uchôa

et al. 2019

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Limited Memory Rank-1 Cutsmentioning

confidence: 99%

Section: Computational Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Generic Exact Solver for Vehicle Routing and Related Problems

Pessoa

Sadykov

Uchôa

et al. 2019

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…One reason is the numerous applications, where VRPs are involved in logistics, supply chain management, distribution systems, freight and passenger transportation systems, car navigation systems, etc. Many types of VRPs have been introduced to address different objectives or constraints, and a large number of solution approaches have been proposed in the literature .…”

Section: Introductionmentioning

confidence: 99%

Vehicle routing problems with road‐network information: State of the art

et al. 2018

View full text Add to dashboard Cite

Vehicle routing problems have drawn researchers’ attention for more than 50 years. Most approaches found in the literature address these problems using the so‐called customer‐based graph, a complete graph representing the road network, where a node is introduced for every point of interest (eg, customers, depot…) and an arc represents the best path between two points. In many situations, this representation induces negative effects on the solution quality or efficiency. A growing number of works in the literature investigate these issues and propose modeling taking account of more detailed information from the road‐network. In this article, we review these works and classify them with respect to the type of negative effects provoked by the customer‐based graph.

show abstract

“…An extended abstract of this work was published in Pecin et al (45) and a full paper was submitted to Operations Research.…”

Section: Contributions To the Cvrpmentioning

confidence: 99%

Exact Algorithms for the Capacitated Vehicle Routing Problem

PECIN¹

View full text Add to dashboard Cite

Pecin, Diego; Poggi, Marcus; Uchoa, Eduardo. Exact Algorithms for the Capacitated Vehicle Routing Problem. Rio de Janeiro, 2014. 116p. DSc Thesis -Departamento de Informática, Pontifícia Universidade Católica do Rio de Janeiro.Vehicle Routing Problems are among the most difficult combinatorial problems to solve to optimality. They were proposed in the late 1950's and since then have been widely studied. This interest arises from their practical importance, as well as the difficulty of providing efficient algorithms to solve them. This thesis is mainly concerned with the exact resolution of the Capacitated Vehicle Routing Problem (CVRP). In this problem, a set of customers, each one associated to a demand, must be serviced by a fleet of vehicles. All vehicles have the same (limited) capacity and initially are located in the same central depot. A solution is a set of routes, starting and ending at the depot, that visit every customer exactly once. The only constraint on a route is that the sum of the demands of its customers does not exceed the vehicle capacity. The objective is to find a solution with minimum total cost. The best performing exact algorithms for the CVRP 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 thesis introduces a technique for greatly reducing this 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, variable fixing 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.

show abstract

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

Cited by 176 publications

References 25 publications

A Generic Exact Solver for Vehicle Routing and Related Problems

A Generic Exact Solver for Vehicle Routing and Related Problems

Vehicle routing problems with road‐network information: State of the art

Exact Algorithms for the Capacitated Vehicle Routing Problem

Contact Info

Product

Resources

About