A matheuristic algorithm for the mixed capacitated general routing problem

Abstract

We study the general routing problem defined on a mixed graph and subject to capacity constraints. Such a problem aims to find the set of routes of minimum overall cost servicing a subset of required elements like vertices, arcs, and edges, without exceeding the capacity of a fleet of homogeneous vehicles based at the same depot. The problem is a generalization of a large variety of node and arc routing problems. It belongs to the family of NP‐hard combinatorial problems. Instances with a small number of vehicles and required elements can be effectively solved by means of exact methods. Heuristic approaches are helpful to obtain feasible solutions for medium to large size instances. In this article, we present a matheuristic approach to the problem, in which a set of neighborhood structures is iteratively searched and a branch‐and‐cut algorithm is used to improve the quality of the solutions found during the search. The search is iterated within a defined global number of steps, in which the solution space is explored. We demonstrate the effectiveness of this approach through an extensive computational study on several benchmark instances. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 64(4), 262–281 2014

The mixed capacitated general routing problem with time‐dependent demands

“…Equation 7implies that each vehicle has at most one task at each step. Equation 8presents the connectivity constraint, (9) implies that the first step starts from the depot. Equation 10links the passage by node i at step s with the service of node i at step s. Also Equation 11links the passage on link (i, j) at step s with the service of the required link (i,j) at step s by the same vehicle.…”

Node, Edge, Arc Routing and Turn Penalties: Multiple Problems—One Neighborhood Extension

“…Early research on this problem concerned constructive heuristics. Later, several metaheuristics have been introduced: a giant-tour-based hybrid GA (Prins and Bouchenoua 2005), a simulated annealing (Kokubugata et al 2007), the Spider solver based on ILS and VNS (Hasle et al 2012), a large neighborhood search and integer programming hybrid (Bosco et al 2014), and an adaptive ILS (Dell'Amico et al 2016). This last method generates high-quality results for a wide range of instances.…”

An updated annotated bibliography on arc routing problems

“…Good behavior of the metaheuristic is reported also on isolated CVRP and CARP instances ( gdb , val , egl , bmcv ). The matheuristic of involves a large number of neighborhood structures and draws upon the branch‐and‐cut algorithm developed by Bosco et al for improving the substructures of a solution obtained by considering two routes at a time. The effectiveness of the heuristic is demonstrated through an extensive computational study.…”

“…Good behavior of the metaheuristic is reported also on isolated CVRP and CARP instances (gdb, val, egl, bmcv). The matheuristic of [43] involves a large number of neighborhood structures and draws upon the branch-and-cut algorithm developed 25,43,44,75,115] Turn penalties; Forbidden turns [47] Min(cost; makespan) makespan= (most -least) costly route [137] Min(cost; imbalance) 4 alternatives for the imbalance [103] MCGRPSD Min(cost)…”

“…To close this gap from the upper bound perspective, Dell'Amico et al propose an adaptive iterated local search, and Bosco et al develop the first matheuristic for the MCGRP. The hybrid metaheuristic of is a new iterated local search including an adaptive large neighborhood search combined with further intensification.…”