An Approximation Algorithm for the Capacitated Arc Routing Problem

Abstract

In this paper we consider approximation of the Capacitated Arc Routing Problem, which is the problem of serv- icing a set of edges in a graph using a fleet of capacity constrained vehicles. We present a 7  3  2 W approximation algorithm for the problem and prove that this algorithm outperforms the only existing approximation algorithm for the problem. Fur- thermore, we give computational results showing that the new algorithm performs very well in practice. When solving an optimization problem to suboptimality, two goals are followed. The first goal is to obtain a solution that is as close to the optimal as possible, which leads to the construction of problem specific heuristics and meta heuris- tics, where the latter often outperforms the former. The sec- ond goal is to obtain a solution, which is guaranteed to be within a certain factor of the optimal. This goal leads to the construction of approximation algorithms. In this paper we will present an algorithm for the Capaci- tated Arc Routing Problem (CARP) with the triangle ine- quality preserved by the cost matrix, which is an approxima- tion algorithm with at most the same approximation factor as the only existing approximation algorithm for the problem, and which performs very well in practice, in that it is highly competitive to the existing problem-specific heuristics for the problem on the set of 143 benchmark instances. We refer to the algorithm as A-ALG.