Multi-objective Multi-level Filling Evolutionary Algorithm for the 3D Cutting Stock Problem

3D cutting and packing problems have important applications and are of particular relevance to the transportation of cargo in the form of Container Loading Problems (CLP). Many algorithms have been proposed for solving the 2D/3D cutting stock problems but most of them consider single objective optimization. The goal of the problem is to load the boxes that would provide the highest total volume and weight to the container, without exceeding the container limits. These two objectives are conflicting because the volume of a box is usually not proportional to its weight. This work deals with a multi-objective formulation of the CLP. We propose to apply multi-objective evolutionary algorithms in order to obtain a set of non-dominated solutions, from which the final users would choose the one to be definitely carried out. To apply evolutionary approaches we have defined a representation scheme for the candidate solutions, a set of evolutionary operators and a method to generate and evaluate the candidate solutions. The obtained results for generated instances on standard containers demonstrate the importance of the evaluation heuristic to be applied.