A Generic Exact Solver for Vehicle Routing and Related Problems

Abstract

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.

Research trends in combinatorial optimization

“…Future research in exact CO algorithms capable of solving large‐scale real‐life problems will definitely continue over time. Exciting developments are to be expected from new algorithmic branch‐and‐bound and branch‐and‐reduce techniques, but one may also look forward to new algorithmic frameworks, of which the recent branch‐cut‐and‐prize framework for vehicle routing and other related problems are good examples (Pessoa et al., 2020).…”

A machine learning-based branch and price algorithm for a sampled vehicle routing problem

“…Further, it has to be noted that the above reported literature on exact algorithms does not include other variants than VRPTW and CVRP. Pessoa et al (2020) generalize recent development on latter problem types to a generic exact solving procedure for multiple variants of routing problems. For a recent review, the reader is referred to Costa et al (2019)..…”

On the exact solution of vehicle routing problems with backhauls

“…The BCP algorithms were coded in Julia 0.6 interface for the generic VRPSolver (Pessoa et al, 2019a) which makes use of JuMP (Dunning et al, 2017) and LightGraphs packages. The models used in the implementation are given in the Appendix B.…”

“…We present here the VRPSolver models used. This appendix is not self-contained, important concepts used in these models, such as main resources, packing sets, mapping between variables and arcs, and Rounded Capacity Cuts (RCC) separators, should be found in Pessoa et al (2019b). The parameterization of the solver for all problems and formulations is the same: τ soft = 5 sec., τ soft = 10 sec., φ bidir = 1, ω labels = 2 • 10 5 , ω routes = 2 • 10 6 , η max = 20, δ gap = 1.5%, ζ num 1 = 50, ζ estim 1 = 1.0.…”

“…The parameterization of the solver for all problems and formulations is the same: τ soft = 5 sec., τ soft = 10 sec., φ bidir = 1, ω labels = 2 • 10 5 , ω routes = 2 • 10 6 , η max = 20, δ gap = 1.5%, ζ num 1 = 50, ζ estim 1 = 1.0. The meaning of these parameters is also explained in Pessoa et al (2019b).…”