A Quasiphysical and Dynamic Adjustment Approach for Packing the Orthogonal Unequal Rectangles in a Circle with a Mass Balance: Satellite Payload Packing

Ziqiang Li,Xianfeng Wang,Jiyang Tan,Yishou Wang

doi:10.1155/2014/657170

Ziqiang Li, Xianfeng Wang + Show 2 more

Open Access

https://doi.org/10.1155/2014/657170

Copy DOI

Abstract

Packing orthogonal unequal rectangles in a circle with a mass balance (BCOURP) is a typical combinational optimization problem with the NP-hard nature. This paper proposes an effective quasiphysical and dynamic adjustment approach (QPDAA). Two embedded degree functions between two orthogonal rectangles and between an orthogonal rectangle and the container are defined, respectively, and the extruded potential energy function and extruded resultant force formula are constructed based on them. By an elimination of the extruded resultant force, the dynamic rectangle adjustment, and an iteration of the translation, the potential energy and static imbalance of the system can be quickly decreased to minima. The continuity and monotony of two embedded degree functions are proved to ensure the compactness of the optimal solution. Numerical experiments show that the proposed QPDAA is superior to existing approaches in performance.

Highlights

For the 2D rectangle container, the packing approaches mainly include graph theories [4,5,6,7], branch-and-bound methods [8,9,10], dynamic planning [11], heuristics [12,13,14,15], artificial intelligent [16], evolutionary approaches [17], and hybrid approaches [18,19,20]
The layout design problem of the satellite module described in [32] is an important packing problem, which can be transformed into the problem of packing 2D orthogonal unequal rectangles within a circular container with the mass balance (BCOURP)
Taking the layout design of a satellite module as the application background, we have proposed the quasiphysical and dynamic adjustment approach (QPDAA) for the BCOURP problem in this paper

Summary

Introduction

For the 2D rectangle container, the packing approaches mainly include graph theories [4,5,6,7], branch-and-bound methods [8,9,10], dynamic planning [11], heuristics [12,13,14,15], artificial intelligent [16], evolutionary approaches [17], and hybrid approaches [18,19,20]. In 2007, Xu et al [34] defined embedded degree functions between two rectangles and between the rectangle and circular container and presented a compaction algorithm with the particle swarm local search (CA-PSLS). Their idea is that a feasible solution with a smaller envelope radius obtained through the gradient method is taken as an elite individual and the optimal solution is obtained by the PSO iteration. By combining the heuristic method with the stochastic algorithm, their respective advantages can be exerted to the utmost Based on this mechanism, CA-PSLS and GAHA are consecutively proposed to solve this problem.

Problem Statement and Mathematical Model

Compact and Feasible Solution Strategy

Dynamic Adjustment Strategy

The Proposed Algorithm

Experiments and Analysis

Conclusions