Multi-Criteria 3-Dimension Bin Packing Problem

In this paper a multi-criteria approach to the 3-dimensions bin packing problem is considered. The chosen maximization criteria are the number and the total volume of the boxes loaded into the container. Existing solution representation and decoding method are applied to the problem. Next, two metaheuristic algorithms, namely simulated annealing and genetic algorithm are developed using the TOPSIS method for solution evaluation. Both algorithms are then used to obtain approximations of the Pareto front for a set of benchmarks from the literature. Despite the fact that both criteria work in favor of each other, we managed to obtain multiple solutions in many cases, proving that lesser number of boxes can lead to better utilization of the container volume and vice versa. We also observed, that the genetic algorithms performs slightly better in our test both in the terms of hyper-volume indicator and number of non-dominated solutions.