Multi-objective optimization of the 3D container stowage planning problem in a barge convoy system

Abstract

Mainly motivated by the massification of flows in inland shipping, where several barges can be assembled in convoys to transport a large number of containers to and from the hinterland, we introduce an original extension of the Container Stowage Planning Problem (CSPP) (which we denote the 3D – barge Convoy Container Stowage Planning Problem (3D –CCSPP)). The requirements for stowing all containers in a barge convoy entail additional constraints related to both the containers and the convoy. In this paper, the 3D –CCSPP is dealt with, on the basis of its relation to the 3D Bin-Packing Problem (3D-BPP), in which the filled objects represent the containers, and the bins indicate the convoy barges. We consider the multi-objective aspect of the problem with three realistic functions to be optimized: shifting movements, the convoy stability and the number of real-used barges. This is a new and effective aspect considering the state of the art of CSPP in inland shipping. We develop a multi-objective mathematical formulation of the 3D-CCSPP and propose a novel adaptation of the multi-objective evolutionary algorithm NSGA-II (Non-Dominated Sorting Genetic Algorithm-II) based on a set of heuristics introduced by the BPP resolution methods. Specific encoding method, generation of the initial population and genetic operators are designed based on the mathematical description of the problem. Extensive experiments are then carried out on a varied set of instances. The computational results demonstrate the effectiveness of the proposed approaches, they are evaluated using CPLEX solver and their performance is verified by a set of measurements which are adapted to the problem in real-world applications in relation to each objective function. Additional studies are carried out in sensitivity analysis to provide decision makers with a better knowledge of the problem. They can then choose, from the set of compromise solutions of the Pareto front, the most promising one for practical implementation based on their experience and preferences.