The mixed capacitated arc routing problem with non-overlapping routes

Miguel Constantino,Maria Cândida Mourão,Luís Gouveia,Ana Catarina Nunes

doi:10.1016/j.ejor.2015.01.042

Abstract

Real world applications for vehicle collection or delivery along streets usually lead to arc routing problems, with additional and complicating constraints. In this paper we focus on arc routing with an additional constraint to identify vehicle service routes with a limited number of shared nodes, i.e. vehicle service routes with a limited number of intersections. This constraint leads to solutions that are better shaped for real application purposes. We propose a new problem, the bounded overlapping MCARP (BCARP), which is defined as the mixed capacitated arc routing problem (MCARP) with an additional constraint imposing an upper bound on the number of nodes that are common to different routes. The best feasible upper bound is obtained from a modified MCARP in which the minimization criteria is given by the overlapping of the routes. We show how to compute this bound by solving a simpler problem. To obtain feasible solutions for the bigger instances of the BCARP heuristics are also proposed. Computational results taken from two well known instance sets show that, with only a small increase in total time traveled, the model BCARP produces solutions that are more attractive to implement in practice than those produced by the MCARP model.

Highlights

Capacitated arc routing mathematical models are often used to formulate delivering or collecting problems where the demands are associated with the links of the underlying network.There are many variants of these problems
In the typical capacitated arc routing problem (CARP) the objective is to identify minimum cost routes to be traversed by the vehicles of a given fleet to perform the service in the streets of a network, starting and ending at a depot
In this paper we have introduced the bounded overlapping mixed capacitated arc routing problem (MCARP) (BCARP) problem, which is defined as the MCARP with an upper bound on the number of common nodes to different routes

Summary

Introduction

Capacitated arc routing mathematical models are often used to formulate delivering or collecting problems where the demands are associated with the links of the underlying network. It is quite clear that this solution, despite having connected sets of tasks, still exhibits several undesirable situations such as vehicle routes that overlap and spread (being non compact) in the collection zone This attempt to model the “nice” features of the routes by adding connectivity constraints illustrates what we have mentioned before, namely that it may not be straightforward to measure and describe the “attractiveness” specification of the routes, in a mathematical way. Figure 1: lpra instance – optimal solutions for 3 vehicles Motivated by this unsuccessful experiment, in this paper we propose, study and test a new model that uses a constraint simpler to formulate and that is based on a different way to measure the non-overlapping of the vehicle routes.

Literature review

Models

Solving BCARP instances

A 2-phase Heuristic for the BCARP

Conclusions