Efficient Solution of Capacitated Arc Routing Problems with a Limited Computational Budget

Abstract

Capacitated Arc Routing Problem (CARP) is a well known combinatorial problem that requires the identification of the minimum total distance travelled by a set of vehicles to service a given set of roads subject to the vehicle’s capacity constraints. While a number of optimization algorithms have been proposed over the years to solve CARP problems, all of them require a large number of function evaluations prior to its convergence. Application of such algorithms are thus limited for practical applications as many of such applications require an acceptable solution within a limited time frame, e.g., dynamic versions of the problem. This paper is a pre-cursor to such applications, and the aim of this study is to develop an algorithm that can solve such problems with a limited computational budget of 50,000 function evaluations. The algorithm is embedded with a similarity based parent selection scheme inspired by the principles of multiple sequence alignment, hybrid crossovers, i.e., a combination of similarity preservation schemes, path scanning heuristics and random key crossovers. The performance of the algorithm is compared with a recent Memetic algorithm, i.e., Decomposition-Based Memetic Algorithm proposed in 2010 across three sets of commonly used benchmarks (gdb, val, egl). The results clearly indicate the superiority of performance across both small and large instances.