Filtered beam search algorithm for the two‐dimensional rectangular packing problem

Abstract In this study, a filtered beam search (FBS) algorithm is proposed to address the two‐dimensional rectangle packing problem, whose objective is to minimize the height of a rectangular sheet of fixed width in which n rectangular items can be packed without overlapping. The corner‐occupying placement (COP) strategy is introduced in the packing process, which packs each rectangle into the sheet so that it occupies a corner position formed by the sheet's edges and the edges of already packed rectangles. Two evaluation criteria, namely, local evaluation and global evaluation, are proposed to evaluate the benefit of a candidate COP and are seamlessly integrated into the FBS framework in order to maintain a better balance between the solution quality and computation time. Extensive testing on four sets of 112 zero‐waste test instances indicated that the proposed method competes favourably with the state‐of‐the‐art reference methods. Furthermore, the proposed method is modified to handle a variant of the rectangle packing problem where item rotations are not allowed. The modified algorithm is competitive, compared with the existing top algorithms, according to computational results on widely used benchmarks.