Maria Cândida Mourão

Heuristic method for a mixed capacitated arc routing problem: A refuse collection application

Abstract The capacitated arc routing problem (CARP) is known to be NP-hard. The aim of this paper is to present a new heuristic method to generate feasible solutions to an extended CARP on mixed graphs, inspired by the household refuse collection problem in Lisbon. Computational experience was done to compare the method with some well-known existing heuristics, generalised for a different extended CARP by Lacomme et al. [Fast algorithm for general arc routing problems, Presented at IFORS 2002 Conference, Edinburgh, UK], namely, the Path-Scanning, the Augment-Merge and the Ulusoy’s algorithms. The results reveal a good performance of the proposed heuristic method. Generally providing a good use of the vehicles capacity, the resulting sets of feasible trips may also be considered good. The test instances involve more than 300 randomly generated test problems with dimensions of up to 400 nodes and 1220 links.

Heuristic methods for the sectoring arc routing problem

The sectoring arc routing problem (SARP) is introduced to model activities associated with the streets of large urban areas, like municipal waste collection. The aim is to partition the street network into a given number of sectors and to build a set of vehicle trips in each sector, to minimize the total duration of the trips. Two two-phase heuristics and one best insertion method are proposed. In the two-phase methods, phase 1 constructs the sectors using two possible heuristics, while phase 2 solves a mixed capacitated arc routing problem (MCARP) to compute the trips in each sector. The best insertion method determines sectors and trips simultaneously. In addition to solution cost, some evaluation criteria such as imbalance, diameter and dispersion measures are used to compare algorithms. Numerical results on large instances with up to 401 nodes and 1056 links (arcs or edges) are reported and analysed.

Lower bounds for the mixed capacitated arc routing problem

Capacitated arc routing problems (CARP) arise in distribution or collecting problems where activities are performed by vehicles, with limited capacity, and are continuously distributed along some pre-defined links of a network. The CARP is defined either as an undirected problem or as a directed problem depending on whether the required links are undirected or directed. The mixed capacitated arc routing problem (MCARP) models a more realistic scenario since it considers directed as well as undirected required links in the associated network. We present a compact flow based model for the MCARP. Due to its large number of variables and constraints, we have created an aggregated version of the original model. Although this model is no longer valid, we show that it provides the same linear programming bound than the original model. Different sets of valid inequalities are also derived. The quality of the models is tested on benchmark instances with quite promising results.

The mixed capacitated arc routing problem with non-overlapping routes

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.

Local search heuristics for sectoring routing in a household waste collection context

This paper addresses the problem of residential waste collection, as a real life application of a sectoring-arc routing problem (SARP). Tactical decisions comprise the partition of the service territory into a number of sectors so that each sector can be covered by a set of vehicle trips. In addition, operational decisions involving the design of the vehicle trips that minimize total routing time are to be made. Apart from supporting good vehicle trips, sectors should also be planned such that the workload time imbalance as well as the number of connected components are minimized. These later try to promote service areas (sectors) geographically concentrated and grouped into delimited regions. We propose two local search methods: a hill climbing and a tabu search based heuristic. A constructive heuristic for obtaining an initial solution is also suggested. By means of a normalized weighted sum of criteria for evaluating solutions, the local search heuristics were tailored to improve the features of the initial solution. The algorithms are tested on random instances and also on real life based instances. The results show that the proposed local search methods are an efficient way of obtaining good quality solutions to implement in practice. Results also highlight that the proposed function for evaluating solutions during the search phase plays an essential role.

A Routing and Waste Collection Case-Study

Waste collection systems are among the main concerns of municipalities due to the resources involved. In this paper we present a hybrid heuristic to find the vehicle routes that should be performed to collect the household waste along the streets of a network. The solution method hybridizes the resolution of ILP based models with some simple heuristic ideas to assign services (collecting streets) to the vehicles. The Seixal case study, in the Lisbon Metropolitan Area, is tackled and some encouraging results are reported.