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 d ij and represents the distance or the travel time. We assume that costs are symmetric(i.e. d ij = d ji ), and an unlimited fleet of identical vehicles, each of capacity Q>0, is available. Each customer i has a demand q i , with 0<q i ≤ Q. Each customer must be served by a single vehicle and no vehicle can serve a set of customers whose demand exceeds its capacity. The task is to find a set of vehicle routes of minimum cost, where each vehicle used leaves from and returns to the depot. In the following, we explain our algorithm then, we give results and conclusions.