The Pseudo-gradient Technology And Its Application In Swarm Optimization

The simplex method (SM) is an optimization algorithm for directly searching which is simple and effective in local search and has been successfully applied in many fields. It doesn't require whether the objective function is analytical. But it has some disadvantages such as low search speed, bad convergence, limited global search capability.Evolutionary algorithms, such as Particle Swarm Optimization (PSO) and Genetic algorithm (GA), are random search methods inspired by biological evolution. They are simple, robust and are fit to be used in the parallel computation. Evolutionary algorithms are very effective in global search, and have been successfully applied in many engineering. However, the common evolutionary algorithms have some disadvantages such as premature, bad local search capability.The SM and evolutionary algorithms are analyzed deeply in this thesis. The main works are as follow:Firstly, based on the high efficiency of the gradient search in local search, the conception of pseudo-gradient is presented and applied to the SM. Then, a pseudo-gradient SM is proposed. It accelerates the convergence and meliorates the quality of the optimization.Secondly, the idea of the space partition by means of the SM is introduced in the GA, so that the individuals of the population are operated in the SM form. The experiments show that the proposed method can prevent premature convergence.Thirdly, the idea of the SM is introduced in the PSO, so that the particles in the swarm are located in the SM form. Under the same condition, the experiments show that the SM-PSO algorithm improves the convergence and the quality of the optimization.At the end of this thesis, the Evolutionary algorithm modified by the SM is applied to the optimization of the dynamic routing of the telecommunication network.