A hybrid ant colony system approach for the capacitated vehicle routing problem

Abstract

In this paper we propose a hybrid approach for solving the capacitated vehicle routing problem (CVRP). We combine an Ant Colony System (ACS) with a Savings algorithm and, then, we improve solutions by a local search heuristic. The CVRP is a class of well-known NP-hard combinatorial optimization problem, which can be formally defined as a complete graph G=(V,E) where V={0, ...,n} is a set of vertices and E is a set of arcs [4]. The vertex {0} represents the depot and the other vertices represent customers. The cost of travel between vertices i and j is denoted dij and represents the distance or the travel time. We assume that costs are symmetric(i.e. dij = d ji), and an unlimited fleet of identical vehicles, each of capacity Q>0, is available. Each customer i has a demand qi, with 0