Research On Particle Swarm Optimization Algorithm For Multimodal Multi-objective Optimization Problems

Optimization problems exist widely in scientific research and engineering practice.It is theoretical significance and application value for researchers to research on many complex optimization problems.The traditional methods which solve realistic optimization problems by establishing mathematical models or functional expressions encounter bottlenecks.Therefore,intelligent algorithms inspired by nature takes a different approach to break through the situation.Swarm intelligence has used to work out multimodal optimization problems and multi-objective optimization problems over the past two decades.With the further development,some special multi-objective problems which contain two or more different decision vectors corresponding to the same function value have drawn attentions of researchers in recent years,and the problem is denoted as multimodal multi-objective optimization problem.Most of multi-objective optimization algorithms pay attention on objective space rather than decision space during the process of searching Pareto-optimal solutions.In order to search for more Pareto-optimal solutions in the decision space,this paper employs niche technology based on multi-modal optimization problems and non-dominated sort method in view of multi-objective optimization problems to conduct a research on particle swarm optimization algorithm.It proposes a novel particle swarm optimization algorithm based on multiple populations and ring topology to deal with multimodal multi-objective optimization problems,which called MMO_CLRPSO.Experimental results show the superiority of our algorithm.The main work and innovation can be summarized as follow:(1)In order to improve global search ability in multimodal multi-objective optimization algorithm,this paper proposes a novel clustering algorithm,and employs a global particle swarm optimization algorithm with a leader particle to update velocity and position of particles.A decision variable clustering method is developed to divide whole population into multiple subpopulations.Each subpopulation evolves independently and search different regions.Thus,it avoids repeatedly searching one region and economizes computing resource.During the process of updating velocity and position of particles based on a leader particle,it not only accelerates the convergence of subpopulations,but also save amount of Pareto-optimal solutions.Thus,this method improves effectively the search ability of algorithm.Simulation experiment indicates that developing the leader update mechanism can enhance obviously the performance of algorithm.(2)To promote the local search ability of multimodal multi-objective optimization problems,a ring topology structure was established by combining niche technologies between the subpopulations.The local search ability of each subpopulation is improved and the diversity of the whole population is maintained by employing local model particle swarm optimization algorithm to update global optimal particles of each subpopulation.Meanwhile,the distribution of Pareto-optimal solutions in decision space is more uniform.(3)Comparing with the other the state of the art algorithms,MMO_CLRPSO algorithm obtains better result on all the test benchmark functions.Pareto-optimal solutions in the decision space are uniformly distributed.The performance of MMO_CLRPSO algorithm in objective space is very similar to its comparison algorithm.Therefore,the performance of MMO_CLRPSO on decision space and objective space are compared with some multimodal multi-objective algorithms,which reveals that MMO_CLRPSO algorithm is very competitive.