A fast hybrid optimization algorithm based on TS and PSO 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. Tabu search (TS) has strong global search ability but the convergence accuracy is low. particle swarm optimization (PSO) is quick in convergence, but likely to be premature at the initial stage. Considering both the advantages and disadvantages, a fast hybrid optimization algorithm based on improved TS and PSO for this problem is proposed, which employ the novel intensification search and diversification search balance strategy of TS and the refined search of PSO as a whole to plan large-scale space global search according to the fitness change, and to quicken convergence speed, avoid repeated search work, 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 revised algorithm is feasible and efficient.