The Research Of Particle Swarm Optimization Solving Nonlinear Programming Problems

Particle Swarm Optimization (PSO) algorithm is a novel evolutionary algorithm. PSO algorithmhas been widely used in constrained optimization, optimal design of fuzzy controller, neural network op-timization, filter design and so on for its simple concept, fast convergence and low domain knowledgerequired. Compared with other evolution algorithms, PSO algorithm is more effective to solve optimiza-tion problems, but there are many aspects to be improved, such as theory and practice areas. So we shouldkeep on researching it and extend its application aspect.This article concentrates on PSO algorithm by the analysis of constrained optimization algorithm’sunified framework, the PSO algorithm is used for solving unconstrained optimization, 0-1 linear program-ming, constrained optimization and multi-objective optimization problem and the simulation experimentsare carried out. Main contents of this article can be summarized as follows:(1) A kind of particle swarm optimization algorithm with local information strategy is given. Theresults show that this algorithm has fast convergence, high precision solution and robustness.(2) By the penalty function method,we transform zero-one nonlinear programming problems intounconstrained 0-1 integer optimization problems. A particle swarm optimization algorithm with chaosand gene density mutation is given to solve unconstrained the 0-1 nonlinear program problems. We usechaos to initialize populations and use the 0-1 integer operation in updating positions to produce 0-1 in-teger points. We adapt the fitness variance and gene density strategy to determine whether the populationpremature phenomenon or not. If it appears that we use the gene density mutation to increase the popula-tion diversity or restart and reset the population by chaos technique. Numerical simulations show that theproposed algorithm for most test functions is feasible, effective and has high precision.(3) Considering the current global optimal particle and current individual optimal particles on theeffect of particle swarm search ability,then the update velocity formula is improved; Then we use mod-ified feasibility-based rule to update the individual optimal and global optimal, thus guiding infeasibleparticles as reach feasible area, in order to increase the diversity of population and improve the globalsearch ability. Numerical simulations show that the algorithm of this paper for most test functions is ef-fective, steady, and is a potential global optimization algorithm.(4) The elitist strategy is used in external archive in order to improve the convergence of this algo-rithm. The new diversity strategy called dynamic crowding entropy strategy and the global optimizationupdate strategy are used to ensure sufficient diversity and uniform distribution amongst the solution ofthe non-dominated fronts. The results show that the proposed algorithm is able to find better spread ofsolutions with the better convergence to the Pareto front and preserve diversity of Pareto optimal solutionsthe more efficiently.In general, the hybrid and application of PSO algorithm are analyzed comprehensively. Finally,whole research contents are summarized, and further research directions are indicated.