A heuristic particle swarm optimization with quasi-human strategy for weighted circles packing problem

The weighted circles layout problem belongs to the layout optimization problem with performance constraints. Due to its NP-hard property, it is difficult to solve in polynomial time. In this paper, a heuristic particle swarm optimization approach with quasi-human strategy (HQHPSA) is presented for this problem. Its layout scheme is constructed through the proposed heuristic method: that both circular radius and the norm of row vector of the matrix and sub-vector are taken as the probability factors of the roulette selection and the circles are located by arranging round existing circles in peripheral with counterclockwise. The complexity of the proposed heuristic method is only O(n) for one layout scheme. The better layout solution obtained through the proposed heuristic method is taken as the elite particle individual. The PSO with quasi-human strategy is used to optimize the elite particle into the optimal solution. The numerical experiments show that the performance of proposed algorithm is superior to the existing algorithms.