Particle Swarm Algorithm for Weighted Rectangle Placement Yi-Chun Xu Institute of Intelligent Vision and Image Information and School of Electrical Engineering and Information Technology China Three Gorges University China xuyichun@tom.com Ren-Bin Xiao School of Electrical Engineering and Information Technology China Three Gorges University China rbxiao@163.com Martyn Amos Department of Computing and Mathematics Manchester Metropolitan University United Kingdom M.Amos@mmu.ac.uk Abstract In this paper we present a new algorithm for a layout optimization problem: this concerns the placement of rect- angular, weighted objects 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 almost exclu- sively with purely circular objects, but here we deal with the much more realistic case where objects are rectangular. We present a particle swarm-based solution and compare it with the best published algorithm for this problem. Exper- imental results show that our approach out-performs this existing method in terms of both solution quality and execu- tion time. 1. Introduction The Layout Optimization Problem (LOP) concerns the physical placement of instruments or pieces of equipment in a spacecraft or satellite. Because these objects have mass, the system is subject to additional constraints (beyond sim- ple Cartesian packing) that affect our solution. The two main constraints that we handle in this paper are (1) the space occupied by a given collection of objects (envelop- ment), and (2) the non-equilibrium (i.e. imbalance) of the system. The rest of the paper is organized as follows: In Section 2 we first present a detailed description of the prob- lem, and describe previous related research. In Section 3 we discuss in detail how to measure and thus optimize ob- ject overlap. In Section 4 we describe the initial compaction algorithm, and in Section 5 we describe our own particle swarm local search method. We then give the results of numerical experiments in Section 6, which confirm that our method out-performs the previous best known algorithm for this problem. We conclude with a discussion of future work. 2. Definition of the problem The LOP was proposed by Feng et al. [2] in 1999, and has significant implications for the cost and performance of devices such as satellites and spacecraft. It concerns the two dimensional physical placement of a collection of objects (instruments or other pieces of equipment) within a space- craft/satellite “cabinet”, or container. Previous work on this