Solving a load balancing problem with a multi-objective particle swarm optimisation approach: application to aircraft cargo transportation

To make air cargo carrier operations cost-effective, a challenging task consists on making profitable the stowage step of the transported freight. This can be accomplished by maximising the weight of the loaded cargo. Owing to the nature and the urgency of the carried cargo, a priority level can also constitute a relevant potential objective to be maximised. In this paper, we present a two level load balancing problem that consists in loading items into containers which are then stowed in cargo holds of an aircraft. Two objectives are maximised: the total weight and the total priority of loaded cargo. In order to minimise fuel consumption and satisfy stability requirements, a load balancing constraints are expressed in terms of the deviation between the gravity centre after loading and its ideal position. An integer linear programming-based formulation is presented for the problem at hand. The loading process performs a discrete multi-objective particle swarm optimisation approach. In order to show the effectiveness of our algorithm and due to the importance of satisfying the load balancing constraints, a practical case study is addressed. An experimental investigation of our approach shows that the proposed approach performs well.