Combinatorial neighborhood topology bumble bees mating optimization for the vehicle routing problem with stochastic demands

The bumble bees mating optimization (BBMO) algorithm is a relatively new swarm intelligence algorithm that simulates the mating behavior that a swarm of bumble bees performs. In this paper, this nature inspired algorithm is used in a hybrid scheme with other metaheuristic algorithms for successfully solving the vehicle routing problem with stochastic demands (VRPSD). More precisely, the proposed algorithm for the solution of the VRPSD, the combinatorial neighborhood topology bumble bees mating optimization, combines a BBMO algorithm, the variable neighborhood search algorithm and a path relinking procedure. The algorithm is evaluated on a set of benchmark instances (40 instances) from the literature and 16 new best solutions are found. The algorithm is compared with a number of algorithms from the literature (two versions of a particle swarm optimization algorithm, the classic one and the combinatorial expanding neighborhood topology particle swarm optimization algorithm, a differential evolution algorithm, a genetic algorithm and a honey bees mating optimization) and with the initial version of the BBMO algorithm.