Empirical-type simulated annealing for solving the capacitated vehicle routing problem

The Capacitated Vehicle Routing Problem (CVRP) is a well-known combinatorial optimisation problem used to design an optimal route for a fleet of capacitated vehicles based at a single depot, to serve a set of customers. Over the few past years, the interest in solving real-world applications of the CVRP, especially in transportation and logistics, has grown tremendously. The Simulated Annealing (SA) algorithm is among the most effective employed techniques for finding the CVRP's global optimums. However, because of its lack of flexibility, the SA algorithm may have some weakness, like its slowness and its wandering near the global minimum in the final stage of the search. For this reason, we define in this paper the Empirical-Type Simulated Annealing (ETSA) as a new dynamic version of the SA for effectively solving the CVRP and any other vehicle routing problem. The method operates incrementally by exploiting the last portion of worse feasible solutions, which are fitted using a parametric density function, to update the SA's Boltzmann acceptance criterion. This leads to a more accurate decision within the searching process, and consequently, optimums are more rapidly reached. A comparison to state-of-the-art approaches has proven that the new algorithm is capable of locating all optimums while improving the convergence of the SA algorithm.