A Multi-objective Particle Swarm Optimization Algorithm Based On Self-organizing Map Network

There are some problems in theoretical research and practical application which have conflicting objectives to be optimized at the same time,called multi-objective optimization problems(MOPs).When solving MOPs,we obtain non dominated solutions set which known as the Pareto solution Set(PS)in the decision space and the corresponding fitness values in the objective space form the Pareto frontier(PF).Multi-objective particle swarm optimization(MOPSO)algorithm is a population based method with random search mechanism.It has been widely applied to solve multi-objective problems because of its fast convergence by learning from history and memory storage.The balance between convergence and diversity for multi-objective particle swarm optimization algorithms is very important.A lot of improved strategies have been proposed.Some divide the objective space into grids and map solutions into them.Some use specific indicators to select leaders.Also,mutation strategy is adopted to avoid falling into local optimum.But the above strategies rarely use the characteristics of multi-objective optimization problems,namely,under certain conditions,PF in the object space and PS in the decision space form m-1 dimensional pieces of continuous flow pattern for m target multi-objective problems.To sum up,this thesis proposes a self-organizing multi-objective particle swarm optimization algorithm.The self-organizing map network topology is used to discover population distribution structure and builds neighborhood relationships,so as to guide the particle flying for global and local search.First of all,self-organizing map network is used to find the distribution of individuals in current population and points in external archive in the decision space.Based on the characteristics of self-organizing map network that clustering similar samples into the same neighborhood,the neighborhood relationships are built with the help of self organizing map network for multi-objective particle swarm optimization algorithm.Leaders of particles are selected in their corresponding neighborhood,which help to promote local searchSecondly,in order to avoid the algorithm being trapped in local optimal position,the elite learning strategy is applied under a certain probability after produce offspring.The algorithm is able to keep the diversity of solution in the course of evolution to operate mutation on the elite position.Then,in order to verify the performance of the proposed algorithm in this thesis,the proposed algorithm is applied to a series of test multi-objective functions with different characteristics of the Pareto frontier,and compared with some state-of-the-art multi-objective optimization algorithms.The experimental results proved its superiority in dealing with multi-objective problems.The rationality of the neighborhood relationships in the algorithm is analyzed.The influence of network topology to the performance of the algorithm is also analyzed.Finally,the proposed self-organizing mapping multi-objective particle swarm optimization algorithm is applied to the multimodal multi-objective test functions.Self-organizing multi-objective particle swarm optimization algorithm builds neighborhood relationship in decision space,which provides the chance to solve the multimodal problems.In order to maintain the particles which have small crowding distance in the objective space but have a big crowding distance in the decision space.Algorithm combines the special crowding distance mechanism which considers both the crowding distance in the decision space and the crowding distance in the objective space.Experiments results show that the neighborhood relationship built by self-organizing map network can avoid the influence of niching parameters.The proposed algorithm can solve multimodal multi-objective optimization problems well and provides multiple alternative choices for decision makers.