Simulated annealing for weighted polygon packing

TL;DR

This paper introduces a simulated annealing algorithm for the complex problem of optimally packing weighted polygons within a circular container, balancing mass distribution and container size, with promising results compared to existing methods.

Contribution

The paper presents a novel simulated annealing approach for polygon packing that handles polygons with rotation, improving solution quality over existing algorithms.

Findings

Algorithm achieves near-optimal container radii.

Outperforms existing methods in solution quality.

Effective for polygons with rotation in packing problems.

Abstract

In this paper we present a new algorithm for a layout optimization problem: this concerns the placement of weighted polygons inside a circular container, the two objectives being to minimize imbalance of mass and to minimize the radius of the container. This problem carries real practical significance in industrial applications (such as the design of satellites), as well as being of significant theoretical interest. Previous work has dealt with circular or rectangular objects, but here we deal with the more realistic case where objects may be represented as polygons and the polygons are allowed to rotate. We present a solution based on simulated annealing and first test it on instances with known optima. Our results show that the algorithm obtains container radii that are close to optimal. We also compare our method with existing algorithms for the (special) rectangular case. Experimental results show that our approach out-performs these methods in terms of solution quality.