An evolutionary algorithm for solving Capacitated Vehicle Routing Problems by using local information

The Capacitated Vehicle Routing Problem (CVRP) is a widely investigated NP-hard problem, which aims to determine the routes for a fleet of vehicles to serve a group of customers with minimum travel cost. In this paper, a fast evolutionary algorithm is proposed to solve CVRPs. To this end, a relevance matrix storing the probability that two customers are served successively by the same vehicle is calculated according to the local information of customer location and elite individuals in population. Based on the relevance matrix, an evolutionary algorithm called RMEA is proposed, where the relevance matrix is used to guide the crossover operation and accelerate the convergence of algorithm. Moreover, a relevance matrix based diversity preservation strategy is designed to increase the population diversity and solution quality. In the experiments, the proposed RMEA is compared to eight state-of-the-art heuristic methods tailored for CVRPs. Experimental results on three CVRP benchmarks demonstrate that the proposed RMEA is superior over eight compared algorithms and shows fast convergence speed. •A fast evolutionary algorithm is proposed to solve CVRPs, where a relevance matrix is designed to accelerate the convergence of evolutionary algorithm in solving CVRPs.•A relevance matrix based crossover operator and diversity preservation strategy are developed to help the population evolving.•According to the experimental results on three common CVRP benchmarks, the proposed algorithm finds better solutions than six state-of-the-art algorithms tailored for CVRPs and shows fast speed of convergence.