A new mixed-integer programming model for irregular strip packing based on vertical slices with a reproducible survey

TL;DR

This paper introduces a novel mixed-integer programming model for irregular strip packing that improves efficiency over existing models by using a new convex decomposition based on vertical slices, supported by a reproducible protocol.

Contribution

The paper presents a new MIP formulation based on vertical slices and convex decomposition, enhancing the solving efficiency for complex nesting problems.

Findings

The new NFP-CM-VS models outperform existing state-of-the-art MIP models.

Experiments demonstrate improved solution efficiency for large and complex instances.

A reproducibility protocol and dataset are provided for exact replication.

Abstract

The irregular strip-packing problem, also known as nesting or marker making, is defined as the automatic computation of a non-overlapping placement of a set of non-convex polygons onto a rectangular strip of fixed width and unbounded length, such that the strip length is minimized. Nesting methods based on heuristics are a mature technology, and currently, the only practical solution to this problem. However, recent performance gains of the Mixed-Integer Programming (MIP) solvers, together with the known limitations of the heuristics methods, have encouraged the exploration of exact optimization models for nesting during the last decade. Despite the research effort, the current family of exact MIP models for nesting cannot efficiently solve both large problem instances and instances containing polygons with complex geometries. In order to improve the efficiency of the current MIP models, this work introduces a new family of continuous MIP models based on a novel formulation of the NoFit-Polygon Covering Model (NFP-CM), called NFP-CM based on Vertical Slices (NFP-CM-VS). Our new family of MIP models is based on a new convex decomposition of the feasible space of relative placements between pieces into vertical slices, together with a new family of valid inequalities, symmetry breakings, and variable eliminations derived from the former convex decomposition. Our experiments show that our new NFP-CM-VS models outperform the current state-of-the-art MIP models. Finally, we provide a detailed reproducibility protocol and dataset based on our Java software library as supplementary material to allow the exact replication of our models, experiments, and results.