Particle swarm Multi_optimizer for locating all local solutions

In order to overcome the disadvantage that only one solution can be found in particle swarm optimization (PSO), a novel niche particle swarm multi_optimizer (multi_PSOer) which combines two strategies is devised in this paper. Firstly, guaranteed convergence PSO (GCPSO) is adopted to guarantee the algorithm can converge on a local point. Secondly, niche technique is used to ensure the algorithm is a global search algorithm. Different hills are looked as different niches. Particles are divided into different sub_swarms according to the same_hill function. The function can judge whether particles are in the same hill through monitoring the change of particlespsila tangent. If the tangent values change from negative into positive, they are in different niches, otherwise they are in the same niche. Particle flies following the best one in the same hill with itself. Therefore each peak can be found in this way. It is necessary to know neither the niche radius nor other parameters at all. Numerical experiments show that the multi_PSOer may, efficiently and reliably, obtain all local and global optima for multimodal optimization problems.