A hybrid algorithm combining path scanning and biased random sampling for the Arc Routing Problem

The Arc Routing Problem is a kind of NP-hard routing problems where the demand is located in some of the arcs connecting nodes and should be completely served fulfilling certain constraints. This paper presents a hybrid algorithm which combines a classical heuristic with biased random sampling, to solve the Capacitated Arc Routing Problem (CARP). This new algorithm is compared with the classical Path scanning heuristic, reaching results which outperform it. As discussed in the paper, the methodology presented is flexible, can be easily parallelised and it does not require any complex fine-tuning process. Some preliminary tests show the potential of the proposed approach as well as its limitationsPostprint (published version

The Time-Dependent Multiple-Vehicle Prize-Collecting Arc Routing Problem

In this paper, we introduce a multi vehicle version of the Time-Dependent Prize-Collecting Arc Routing Problem (TD-MPARP). It is inspired by a situation where a transport manager has to choose between a number of full truck load pick-ups and deliveries to be performed by a fleet of vehicles. Real-life traffic situations where the travel times change with the time of day are taken into account. Two metaheuristic algorithms, one based on Variable Neighborhood Search and one based on Tabu Search, are proposed and tested for a set of benchmark problems, generated from real road networks and travel time information. Both algorithms are capable of finding good solutions, though the Tabu Search approach generally shows better performance for large instances whereas the VNS is superior for small instances. We discuss the structural differences of the implementation of the algorithms which explain these results

A matheuristic for the Team Orienteering Arc Routing Problem

In the Team OrienteeringArc Routing Problem (TOARP) the potential customers are located on the arcs of a directed graph and are to be chosen on the basis of an associated profit. A limited fleet of vehicles is available to serve the chosen customers. Each vehicle has to satisfy a maximum route duration constraint. The goal is to maximize the profit of the served customers. We propose a matheuristic for the TOARP and test it on a set of benchmark instances for which the optimal solution or an upper bound is known. The matheuristic finds the optimal solutions on all, except one, instances of one of the four classes of tested instances (with up to 27 vertices and 296 arcs). The average error on all instances fo rwhich the optimal solution is available is 0.67 percent.Angel Corberan, Isaac Plana and Jose M. Sanchis wish to thank the Ministerio de Economia y Competitividad (project MTM2012-36163-C06-02) of Spain and the Generalitat Valenciana (project GVPROMETEO2013-049) for their support.Archetti, C.; Corberan, A.; Plana, I.; Sanchís Llopis, JM.; Speranza, MG. (2015). A matheuristic for the Team Orienteering Arc Routing Problem. European Journal of Operational Research. 245(2):392-401. https://doi.org/10.1016/j.ejor.2015.03.022S392401245