A Beam Search Based Parallel Algorithm for the Two-Dimensional Strip Packing Problem

TL;DR

The paper tackles the two-dimensional strip packing problem with a fixed width container $W$ by introducing BSPA, a parallel beam-search-based algorithm that reformulates the problem as a 2D rectangular packing problem (2DRP) and uses three beam searches across block generation, minimum container filling, and multiple container filling. It decomposes the method into a spatial overlapping representation, block generation (simple and complex blocks), and a greedy beam-search scoring mechanism controlled by a tuning parameter $b$, enabling scalable parallel search over container lengths $L_i$ in $(S/W,L_{max}]$. Experimental results on standard datasets demonstrate BSPA can achieve small gaps to the minimum fill length under both OF and RF constraints, and that performance scales with parallelism; the authors provide public access to code and data for reproducibility. Overall, BSPA offers a practical, tuneable approach to 2D strip packing with demonstrated potential for industrial material cutting applications.

Abstract

This paper introduces BSPA, a parallel algorithm that leverages beam search to address the two-dimensional strip packing problem. The study begins with a comprehensive review of existing approaches and methodologies, followed by a detailed presentation of the BSPA algorithm. Experimental results demonstrate the effectiveness of the proposed method. To facilitate further research, both the code and datasets are publicly available.

Figures (4)

• Figure 1: Partial Representation.
• Figure 2: Overlapping Representation.
• Figure 3: Gap Value Variation with Parameter $b$.
• Figure 4: Runtime Variation with Parameter $p$.