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-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.

A Reduced Variable Neighborhood Search Approach to the Heterogeneous Vector Bin Packing Problem

“…The set of 6 small 2D-HetVBPP instances (with up to 20 items) and the 50 large 2D-HetVBPP instances (with up to 1000 items) was prepared and used to test the efficiency of the algorithm. The specialized version of the algorithm solved some new instances (compared to results in [2], [6], [10], [19], [27], [36]) of the bench-mark set 2CBP [8] and the set of instances with larger demands [19]. More precisely, _ on 400 instances of the data set 2CBP [8], our solution approach solved 356 for 360 s and 365 for 1440 s of running time, _ 400 instances of the data set from [19], with 61 unsolved instances with the known upper and lower bounds, we provided 10 new optimal solutions and 4 new upper bounds.…”

“…However, when it comes to the 50 larger instances from the classes: 1, 4, 5, 9 and 10, our RVNS was more successful in obtaining 31 solutions, compared to 20 solutions from [19], as displayed in Figure 3. On the set of 40 instances with 200 items belonging to classes: 1, 4, 5, and 9, our RVNS solved 22 instances for 360 s and 29 for the time limit of 1440 s, which is less then 35 solutions obtained in [27]. However, having in mind that our RVNS is pri-marily designed for solving 2D-Het VBPP, it is overall comparable with the most successful solution methods of 2D-Hom VBPP on 2CBP .…”

“…Having in mind the total number of solved instances from the set 2CBP, the best results were achieved by Heßler et al [19] where 370 of 400 instances were solved; the unsolved 30 instances include 200 items and belong to classes: 1, 4, 5, 9, and 10. On the other hand, Pessoa et al [27] solved 35 of 40 instances from this set, considering only the first four classes: 1, 4, 5 and 9. In the work of Aringhieri et al [2] and Turky et al [36], authors treated all 200 instances from the following 5 classes: 1, 6, 7, 9, and 10, solving 133 and 119 instances, respectively.…”

“…Aringhieri et al [2] developed the two heuristics: greedy and neighborhood search algorithm for the same problem. Sophisticated branch-cut-and-price algorithms were proposed by Pessoa et al [27] for solving vehicle routing, assignment and bin packing problems, including the 2DHom-VBPP. In the early work of Spieksma [33] a branch-and-bound algorithm for 2DHom-VBPP was described, but it provided optimal solutions only for small-size instances.…”

A fast $$(2 + \frac{2}{7})$$-approximation algorithm for capacitated cycle covering

“…While there has been much progress regarding computational results (see e.g. [18,19,22]), from the viewpoint of approximation algorithms only small progress has been made. The simple optimal tour partitioning algorithm by Altinkemer and Gavish [1], which achieves an approximation ratio of 3.5, has not been substantially improved in the past 30 years.…”