A hybrid ant colony optimization-variable neighborhood descent approach for the cumulative capacitated vehicle routing problem

In this paper, we present two swarm intelligence algorithms for the solution of the Cumulative Capacitated Vehicle Routing Problem. In particular, two hybrid algorithms of the Ant Colony Optimization family have been implemented, the Ant Colony System-Variable Neighborhood Decent and the Max-Min Ant System-Variable Neighborhood Decent. In this novel implementation, the ant-solution population, in both algorithms, is generated by applying local search operators on a single solution generated by the ant transition rules. This method of generating the population is compared to the traditional ACO population generation method. Their effectiveness is tested against well known benchmark instances in the literature and the results are compared to other approaches. The Ant Colony System-Variable Neighborhood Decent provided the best results among the two implemented versions and was able to find a new best known solution for two instances. Overall, on the 112 instances tested, best known solutions were reached in 92 of them. From the 20 instances in which the best known solution was not reached, 19 are instances with over 220 customers. The average gap from the best known solution in those instances is 0.35% and the maximum gap is 0.98%.

Automated summary

Two swarm intelligence algorithms for the Cumulative Capacitated Vehicle Routing Problem were implemented, with one of them achieving new best known solutions for two instances and reaching best known solutions in 92 out of 112 tested instances. The effectiveness of the algorithms was compared to other approaches in the literature.