A hybrid approach for the vehicle routing problem with three-dimensional loading constraints

This paper addresses a recently practical combinatorial problem named Three-Dimensional Loading Capacitated Vehicle Routing Problem, which combines three-dimensional loading problem and vehicle routing problem in distribution logistics. The problem requires a combinatorial optimization of a feasible loading and successive routing of vehicles to satisfy customer demands, where all vehicles must start and finish at a central depot. The goal of this combinatorial problem is to minimize the total transportation cost while serving customers. Despite its clearly practical significance in the real world distribution management, for its high combinatorial complexity, published papers on this problem in literature are very limited.We present a hybrid approach which combines Honey Bee Mating Optimization and six loading heuristics, one for vehicle routing and the other for three-dimensional loading, to solve the integrated problem. We computationally evaluate this hybrid approach on all publicly available test instances, and obtain new best solutions for several scenarios.