Research Of Particle Swarm Optimization And Its Application

Particle swarm optimization (PSO) is a kind of optimization algorithm based on swarm. Because of its fast convergence and simple operation, etc, PSO is widely used in many fields such as engineering and business management. Now it has become a hot topic in intelligence research.However, similar to other intelligence algorithms, PSO is also vulnerable to premature convergence, and PSO originally proposed for single objective optimization problems has no mechanisms of dealing with constraint conditions and many objectives. In order to solve these problems, this paper mainly includes the following parts:(1) The analysis of particle trajectory and PSO convergence behavior Firstly, the state change of single particle is analyzed by linear discrete dynamic system equations; secondly, adopting necessary and sufficient condition of Lyapunov stability sense gives the conditions of particle motion stability and defines the condition of PSO convergence to provide theoretical support for PSO algorithm improvement.(2) The research of two improved single objective PSO PSO based on dynamic neighborhood and comprehensive learning strategy (DNMPSO) is proposed. The DNMPSO thought is the following: firstly, a dynamic topology is proposed, and the advantages of dynamic neighborhood topology and the effect of the interval iteration of reconstructing neighborhood on the algorithm are analyzed, respectively; secondly, a comprehensive learning strategy is proposed and the learning strategy is analyzed from the search behavior; thirdly, by analyzing the reason that PSO gets into the local optima, a parallel hybrid mutation is used to work for local search, which will improve the ability of escaping from local optima; finally, to further enhance the DNMPSO ability at solving complicated multi-modal problems, the local search algorithm is introduced and the realization of the local algorithm is also analyzed. Simulation results show that DNMPSO is better than the others in accuracy and robustness.The dynamic multi-swarm PSO based on K-means clustering algorithm (KDMSPSO) is proposed. The KDMSPSO thought is the following: firstly, a dynamic multi-swarm strategy is proposed based on K-means clustering algorithm and to increase the message exchange of sub-swarms, the sub-swarm is dynamically constructed;secondly, the diversity of population is analyzed and the effect of interval iteration of reconstructing multi-swarm on PSO is discussed; thirdly, by analyzing the learning exemplar of each particle, an improved learning strategy is proposed, i.e., the learning exemplar of social part for each particle is not the best performing particle in each sub-swarm but the center particle in the corresponding sub-swarm; finally, in view of the advantage of dynamic multi-swarm, KDMSPSO is used to solve the optimization problem with constraint conditions. In order to deal with the constraint condition, the task allocation strategy of each sub-swarm (here, the constraint conditions represent the optimization task), the choice strategy of the members for each sub-swarm and the particle comparative rules between particles are discussed, respectively, as a result, a solving constraint optimization PSO is proposed (DMCPSO). Simulation results show that DMCPSO may obtain the better optimal solution in less function evaluation times.(3) The research of two multi-objective PSO and three strategies to improve PSO performance efficiencyACG-MOPSO is proposed. The thought is the following: firstly, according to the key points (learning exemplar selection and size control of the external archive) for solving multi-objective problem, the adaptive grid is used to research density message, crowding distance and the strategy of size control of the external archive; secondly, how to determine the global best particle by the information of density and crowding distance is discussed; thirdly, from how to make full use of the best previous position of each particle (pbest), the update strategy of pbest is discussed; finally, a new multi-objective particle swarm optimization (ACG-MOPSO) is proposed based on adaptive grid and the crowding distance. Simulation results show that ACG-MOPSO obtains the better distributivity and convergence property of solution compared with other algorithms in dealing with, convex, concave, discontinuous and multi-peak problems of Pareto front.εDMOPSO is proposed. To improve the efficiency of PSO in multi-objective optimization problem, a multi-objective PSO (εDMOPSO) is proposed. The algorithm has the following characteristics: firstly, the classic Pareto dominant improvement,εdominance is used to discuss dominant relationship of particles, which not only ensures the distributivity and convergence property of solution in the external archive but also automatically limits the size of external archive byεvalue that improve algorithm efficiency; secondly, the modification DNMPSO learning strategy for multi-objective problems is adopted to improve diversity of swarm, further to improve the swarm flight probability to the true Pareto front. Simulation results show thatεDMOPSO obtains higher efficiency and quality higher solution compared with other algorithms.Three strategies to improve PSO performance are proposed, they are orthogonal initialization swarm, the mutation operator of the non-dominated solutions away from Pareto front, and the crossover of the boundary points and sparse parts on Pareto front based on uniform design. The mixing of the three strategies are also studied, namely, orthogonal initialization + mutation, orthogonal initialization + uniform crossover, and orthogonal initialization + mutation operation + uniform crossover operation. At last, three strategies are introduced in ACG-MOPSO andεDMOPSO, respectively, and the simulation experiment is conducted in a high dimensional test functions DTLZ1, DTLZ2, DTLZ3 and DTLZ7. Simulation results show that these strategies have a positive effect on improvement of distributivity and convergence property.(4) The practical application of the proposed PSO in this paper This part mainly includes three applications, namely, DNMPSO application in curve of soil water movement (Van Genuchten equations), PSO with constraint handling techniques based on K means clustering strategy (denoted as DMCPSO) in solving the CCMV model with the boundary constraints and the number of assets, andεDMOPSO application in solving portfolio model with risk constraints. Simulation results show that the proposed improvement PSO can effectively solve the above three practical problems.