An open-source heuristic to reboot 2D nesting research

TL;DR

The paper tackles the NP-hard problem of 2D irregular strip packing ($2DISPP$) by reframing it as a sequence of feasibility problems and solving with an open-source heuristic, sparrow. It builds on a Collision Detection Engine to separate geometry from optimization, introducing a continuous collision-penalty framework that combines an overlap proxy, decaying penetration depth, and shape-based penalties. A Guided Local Search with adaptive sampling and a two-phase exploration/compression strategy yields state-of-the-art solution densities on academic benchmarks and reveals a reproducibility gap in prior work. The authors also provide ten real-world benchmark instances and an open-source implementation to enable reproducible progress and practical deployment, arguing that openness accelerates innovation in 2D nesting. Overall, sparrow demonstrates both high performance and a cultural shift toward open, reproducible research in operations research and related fields.

Abstract

2D nesting problems rank among the most challenging cutting and packing problems. Yet, despite their practical relevance, research over the past decade has seen remarkably little progress. One reasonable explanation could be that nesting problems are already solved to near optimality, leaving little room for improvement. However, as our paper demonstrates, we are not at the limit after all. This paper presents $\texttt{sparrow}$, an open-source heuristic approach to solving 2D irregular strip packing problems, along with ten new real-world instances for benchmarking. Our approach decomposes the optimization problem into a sequence of feasibility problems, where collisions between items are gradually resolved. $\texttt{sparrow}$ consistently outperforms the state of the art - in some cases by an unexpectedly wide margin. We are therefore convinced that the aforementioned stagnation is better explained by both a high barrier to entry and a widespread lack of reproducibility. By releasing $\texttt{sparrow}$'s source code, we directly address both issues. At the same time, we are confident there remains significant room for further algorithmic improvement. The ultimate aim of this paper is not only to take a single step forward, but to reboot the research culture in the domain and enable continued, reproducible progress.

Figures (12)

• Figure 1: The 2D irregular strip packing problem.
• Figure 2: Example of an infeasible and feasible configuration of a set of items within containers of equal dimensions.
• Figure 3: Two shapes in different configurations, with their respective poles drawn. In (c), the penetration depth ($\delta$) between the largest pair of poles is marked in red.
• Figure 4: Visualization of the overlap proxy for the same pair of items from Figure \ref{['fig:poles']}. : feasible, : \ref{['alg:overlap_area_proxy']}.
• Figure 5: Comparing the standard ($\delta$) and decaying ($\delta'$) penetration depth functions.