Bi-level hybrid local search approach for three-dimensional loading problem with balancing constraints

Abstract

This paper presents a bi-level hybrid local search (BHLS) algorithm for the three-dimensional loading problem with balancing constraints (3DLP-B), where several rectangular boxes with even densities but different sizes are loaded into a single cubic bin to meet the requirements of the space or capacity utilization and the balance of the center of gravity. The proposed algorithm hybridizes a novel framed-layout procedure in which the concept of the core block and its generation strategy are introduced. Once the block-loading sequence has been determined, we can load one block at a time by the designed construction heuristic. Then, the double-search is introduced; its external search procedure generates a list of compact packing patterns while its internal search procedure is used to search the core-block frames and their best distribution locations. The approach is extensively tested on weakly to strongly heterogeneous benchmark data. The results show that it has better performance in improving space utilization rate and balanced condition of the placement than existed techniques: the overall averages from 79.85% to 86.45% were obtained for the balanced cases and relatively high space-usage rate of 89.44% was achieved for the unbalanced ones.