An Improved Scatter Search for Circles Packing Problem with the Equilibrium Constraint

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.