A simple and effective evolutionary algorithm for the vehicle routing problem

The NP-hard Vehicle Routing Problem (VRP) is defined on an undirected network G = (V,E) with a node set V = {0, 1, . . . , n} and an edge set E. Node 0 is a depot with identical vehicles of capacity Q. Each client node i > 0 has a non-negative demand qi and each edge [i, j] has a non-negative cost cij = cji. The VRP consists of determining a set of vehicle trips of minimum total cost, such that each trip starts and ends at the depot, each client is visited exactly once, the total demand handled by any vehicle does not exceed Q, and the cost of any trip does not exceed a given upper limit L. In this paper, the number of vehicles is a decision variable and the costs are real numbers.