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

2026-02-28

AI Summary

This work addresses the low packing efficiency of traditional constructive heuristics for the two-dimensional irregular bin packing problem in scenarios involving nestable pieces. To overcome this limitation, the authors propose MergeDJD, a novel algorithm that integrates geometry-based piece merging as a preprocessing step with an enhanced Djang and Finke (DJD) constructive heuristic. During preprocessing, seamlessly nestable irregular pieces are merged into larger, more regular composite items, and a placement strategy tailored to non-convex and merged shapes is introduced. Evaluated on 1,089 benchmark instances, MergeDJD outperforms the original DJD on 1,083 instances, achieves new best-known results on 515 of them, and maintains low computational overhead.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Data Mining & Knowledge Management: Data Compression
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Web Mining and Content Analysis: Bridging structured and unstructured data

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.

Problem

• two-dimensional irregular bin packing problem
• constructive heuristic
• piece merging
• bin utilization
• irregular polygons

Innovation

• piece merging
• constructive heuristic
• irregular bin packing
• DJD algorithm
• non-convex shapes