Adaptive Ant Colony Optimization With Node Clustering for the Multidepot Vehicle Routing Problem

This article deals with the novel metaheuristic algorithm based on the Ant Colony Optimization (ACO) principle. It implements several novel mechanisms that improve its overall performance, lower the optimization time, and reduce the negative behavior which is typically connected with ACO-based algorithms (such as prematurely falling into local optima, or the impact of setting of control parameters on the convergence for different problem configurations). The most significant novel techniques, implemented for the first time to solve the Multi-Depot Vehicle Routing Problem (MDVRP), are as follows: (a) node clustering where transition vertices are organized into a set of candidate lists called clusters; (b) adaptive pheromone evaporation which is adapted during optimization according to the diversity of the population of ant solutions (measured by information entropy). Moreover, a new termination condition, based also on the population diversity, is formulated. The effectiveness of the proposed algorithm for the MDVRP is evaluated via a set of experiments on 23 well-known benchmark instances. Performance is compared with several state-of-the-art metaheuristic methods; the results show that the proposed algorithm outperforms these methods in most cases. Furthermore, the novel mechanisms are analyzed and discussed from points of view of performance, optimization time, and convergence. The findings achieved in this article bring new contributions to the very popular ACO-based algorithms; they can be applied to solve not only the MDVRP, but also, if adapted, to related complex NP-hard problems.