Solving the Undirected Capacitated Arc Routing Problem with a memory based Method

In the capacitated arc routing problem (CARP) there is a network of streets, and on a subset of streets we have to make services (e.g. winter gritting, litter collection, school bus scheduling). A fleet of identical vehicles of limited capacity provides services; the fleet is based at a depot and each trip starts and ends at the depot. Each street can be traversed any number of times, with a known cost. The CARP consists of determining a set of vehicle trips of minimum total cost, such that each required street is serviced by one single trip, and the total demand processed by a trip fits vehicle capacity. The CARP is NP-hard. Exact methods for the CARP (like the branch and bound method) have only been able to solve relatively small instances to optimality. For larger instances different heuristic algorithms have been proposed. Commonly used heuristics are the constructive heuristics e.g. the Path-scanning, Ulusoy's tour splitting algorithm. The metaheuristics are also important: e.g. taboo search, evolutionary algorithm (EA) and variable neighbourhood search. In this paper we show a new EA for the undirected CARP. This EA is a hybrid steadystate algorithm. It works without recombination operator and it uses a memory based technique, the extended virtual loser (EVL) [1] for mutation. To modulate these methods for the CARP: we adapted the EVL for the CARP, we used a restart strategy in the EVL, we used two special versions of the mutation operator and we used five special stochastic 2-opt local search algorithms to improve the solutions. The published evolutionary algorithms (e.g. [3], [4]) solve the CARP problems by using problem specific, sophisticated operators. We will show that our approach is a simpler one.