A Hyper-Heuristic Approach to solve the Multi-Objective Container Loading Problem

The Container Loading Problem (CLP) belongs to an area of active research and has numerous applications in the real world, particularly in container transportation and distribution industries. When solving the CLP, normally, the goal is to distribute a set of rectangular pieces (boxes) in one large rectangular object (container) so as to maximize the total volume of packed boxes. However, a rather common aspect in the scope of this problem is the weight limit of the containers, since they normally can’t exceed a certain weight for their transportation. In our case of study, the goal is to load the items (boxes) that would provide the highest total volume and weight to the container. These two objectives are conflicting because the volume of the box is usually not proportional to its weight. This way, the problem can be stated as a multi-objective optimization problem, trying to optimize the pieces layout inside the container so that the volume is maximized at the same time that the weight, without exceeding the weight limits. The formulation of the here addressed problem is as follows. We have a container with known width W , length L, height H , maximum weight Pmax, and a set of N rectangular boxes. These boxes belong to one of the sets of boxes types D = {T1 . . . Tm}. Associated with each Ti type exists a weight pi < Pmax and a volume vi. The aim is to find: