Two-Stage Multi-Swarm Particle Swarm Optimizer for Unconstrained and Constrained Global Optimization

This paper presents a new two-stage multi-swarm particle swarm optimizer (TMPSO), which employs the multi-swarm method and takes two-stage different search strategies in the whole iteration process. This new optimizer includes two versions: unconstrained TMPSO (uTMPSO) and constrained TMPSO (cTMPSO) for unconstrained and constrained global optimizations respectively. For the uTMPSO version, TMPSO makes a certain number of sub-swarms in the first stage to iterate to increase the probability to find the global optimum. Further in the second stage, all the sub-swarms are merged into one large swarm to further refine the global best particle. In both these two stages, each sub-swarm of the first stage and the merged swarm of the second stage all employ a local three-stage multi-point particle swarm optimization (MpPSO) algorithm, which is enlightened by human decision-making and cusp catastrophe theory to enhance the local search ability. To solve constrained optimization problems, the uTMPSO is further upgraded to handle the constraints by using trial and error method to form the cTMPSO version, in which constraints violations are checked on each new created particle in the above uTMPSO procedures, and the violating ones are enforced to execute “retreat” operations, return into the feasible region and recreate new positions, which replaces the traditional penalty function method. This proposed uTMPSO is tested on two unconstrained optimization test functions benchmark set with 25 and 28 functions (including multimodal hybrid composition functions) respectively, and compared with other twelve particle swarm optimization variants. The test results show that uTMPSO has better performance and outperforms most compared algorithms. The cTMPSO is also tested on eight benchmark constrained optimization functions and five engineering application problems.