A fast heuristic particle swarm optimization algorithm for circles packing problem with the equilibrium constraints

The packing problem with the behavioral constraints is difficult to solve due to its NP-hard nature. Particle swarm optimization (PSO) is quick in convergence, but likely to be premature at the initial stage. Considering its characteristics, a fast heuristic PSO algorithm for this problem is proposed, which employ the heuristic method to get the initial approximate position of global optimum by randomly arranging round existing circles in peripheral with counter-clockwise movement, and the refined search of improved PSO as a whole to plan large-scale space global search according to the fitness change, and to quicken convergence speed, avoid premature problem, economize computational expenses, and obtain global optimum. The proposed algorithm is tested and compared it with other published methods on constrained layout examples, demonstrated that the algorithm is superior to the exiting algorithms in performance.