Solving Irregular Strip Packing Problems With Free Rotations Using Separation Lines

TL;DR

This paper presents a nonlinear programming approach using separation lines and free polygon rotations to optimize irregular strip packing, minimizing strip length while ensuring non-overlapping constraints.

Contribution

It introduces a novel nonlinear model for irregular strip packing with free rotations and employs IPOPT solver for effective optimization.

Findings

Achieved competitive results on benchmark instances.

Demonstrated effectiveness of separation lines in non-overlapping constraints.

Compared favorably with existing methods in literature.

Abstract

Solving nesting problems or irregular strip packing problems is to position polygons in a fixed width and unlimited length strip, obeying polygon integrity containment constraints and non-overlapping constraints, in order to minimize the used length of the strip. To ensure non-overlapping, we used separation lines. A straight line is a separation line if given two polygons, all vertices of one of the polygons are on one side of the line or on the line, and all vertices of the other polygon are on the other side of the line or on the line. Since we are considering free rotations of the polygons and separation lines, the mathematical model of the studied problem is nonlinear. Therefore, we use the nonlinear programming solver IPOPT (an algorithm of interior points type), which is part of COIN-OR. Computational tests were run using established benchmark instances and the results were compared with the ones obtained with other methodologies in the literature that use free rotation.