A biased random key genetic algorithm for 2D and 3D bin packing problems

In this paper we present a novel biased random-key genetic algorithm (BRKGA) for 2D and 3D bin packing problems. The approach uses a maximal-space representation to manage the free spaces in the bins. The proposed algorithm hybridizes a novel placement procedure with a genetic algorithm based on random keys. The BRKGA is used to evolve the order in which the boxes are packed into the bins and the parameters used by the placement procedure. Two new placement heuristics are used to determine the bin and the free maximal space where each box is placed. A novel fitness function that improves significantly the solution quality is also developed. The new approach is extensively tested on 858 problem instances and compared with other approaches published in the literature. The computational experiment results demonstrate that the new approach consistently equals or outperforms the other approaches and the statistical analysis confirms that the approach is significantly better than all the other approaches.