MergeDJD: A Fast Constructive Algorithm with Piece Merging for the Two-Dimensional Irregular Bin Packing Problem

TL;DR

MergeDJD is a new constructive algorithm for 2D irregular bin packing that improves upon DJD by merging pieces into larger shapes, achieving better results efficiently.

Contribution

It introduces a novel piece merging preprocessing step and an enhanced placement strategy, significantly improving packing efficiency over existing heuristics.

Findings

Outperforms DJD on 1,083 of 1,089 benchmark instances.

Achieves new best solutions on 515 instances.

Maintains short runtimes despite improved performance.

Abstract

The two-dimensional irregular bin packing problem (2DIBPP) aims to pack a given set of irregular polygons, referred to as pieces, into fixed-size rectangular bins without overlap, while maximizing bin utilization. Although numerous metaheuristic algorithms have been proposed for the 2DIBPP, many industrial applications favor simpler constructive heuristics due to their deterministic behavior and low computational overhead. Among such methods, the DJD algorithm proposed by L'opez-Camacho et al. is one of the most competitive constructive heuristics for the 2DIBPP. However, DJD is less effective for cutting instances, in which many pieces can be seamlessly combined into larger polygons. To address the issue, we propose MergeDJD, a novel constructive algorithm that integrates and extends the DJD framework. MergeDJD first preprocesses the instance by iteratively identifying groups of pieces that can be combined into larger and more regular piece. It then employs an improved version of DJD, in which the placement strategy is enhanced to better handle non-convex and combined shapes, to pack all resulting pieces into bins. Computational experiments on 1,089 well-known benchmark instances show that MergeDJD consistently outperforms DJD on 1,083 instances while maintaining short runtimes. Notably, MergeDJD attains new best known values on 515 instances. Ablation studies further confirm the effectiveness of the proposed components. To facilitate reproducibility and future research, we have open-sourced the complete implementation and provided interfaces for visualizing packing results.