A global search framework for practical three-dimensional packing with variable carton orientations

This article aims to tackle a practical three-dimensional packing problem, where a number of cartons of diverse sizes are to be packed into a bin with fixed length and width but open height. Each carton is allowed to be packed in any one of the six orientations, and the carton edges are parallel to the bin edges. The allowance of variable carton orientations exponentially increases the solution space and makes the problem very challenging to solve. This study first elaborately devises the packing procedure, which converts an arbitrary sequence of cartons into a compact packing solution and subsequently develops an improved genetic algorithm (IGA) to evolve a set of solutions. Moreover, a novel global search framework (GSF), utilizing the concept of evolutionary gradient, is proposed to further improve the solution quality. Numerical experiments indicate that IGA provides faster and better results and GSF demonstrates its superior performance, especially in solving relative large-size and heterogeneous instances. Applying the proposed algorithms to some benchmarking cases of the three-dimensional strip packing problem also indicates that the algorithms are robust and effective compared to existing methods in the literature.

► A challenging practical 3D problem was tackled, with diverse sizes and variable carton orientations involved. ► Elaborately devised packing procedure makes packing layout very compact. ► The relative positions provided by the packing algorithm make manual operation very convenient and efficient. ► An improved genetic algorithm and a novel global search framework based on evolutionary gradient were developed. ► Volume utilization by the proposed method increases more than 15% against manual packing.