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中文摘要：
以卫星布局为背景的带平衡约束的圆形Packing问题属NP难问题．该文用给出的改进的散射搜索方法求解．一是给出基于极坐标变换的散射搜索多样性生成策略，二是采取基于极角和极径差异度的参考集更新策略，三是用梯度下降法和Nelder-Mead直接搜索法分别作为散射搜索法中不同阶段所产生新解的改进方法，从而构成改进的散射搜索法，提高了散射搜索法的探索和搜索能力．数值实验结果表明了该改进散射搜索法的可行性和有效性．
英文摘要：
The equilibrium-constrained circles Packing problem with the background of satellite module layout design belongs to NP-hard problem. The authors extend scatter search （SS） to deal with this problem, and propose the improved scatter search. The authors empirically study the coordinate transformation-based diversification method and the reference set update method on the basis of two dissimilarities. The gradient descent algorithm and Nelder-Mead simplex algorithm are adopted to improve the trial solution generated at two different stages in SS, respectively. The improved scatter search can make a tradeoff between exploration and exploitation. Experiment results show the feasibility and effectiveness of the improved scatter search.
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