Hybrid Particle Swarm Optimization For Solving Optimization Problems

Nonlinear optimization problems often appear in economic management, engineering technology, transportation, science and national defense etc. Their theory and algorithm have great significance in promoting the development of these areas. For complex nonlinear problems, the traditional methods based on gradient information easily fall into local optimal and are not suitable for non-smooth problem. Inspired by the process of biologic evolution, algorithms based on population evolutionary search was proposed since the 1950s, these include particle swarm optimization (PSO) algorithm, ant colony optimization (ACO) algorithm, differential evolution (DE) algorithm, genetic algorithm (GA), fish-swarm algorithm (FSA) and so on. Since they are doesn’t required the conditions of continuous and differentiable in solving optimization problems, and become one of the hot spot of research.PSO algorithm is widely used in function optimization, nonlinear system identification, neural network training and other fields such as GA, owing to its concept concise, less parameters settings, fast convergence speed and convenient implementation. Since it come from the simulation of biological phenomena, there exists some drawbacks, such as premature convergence and slow convergence speed in the late evolution. In order to overcome these drawbacks, this paper by using the thought of "complementary" to integrate PSO algorithm and DE algorithm, to enhance the detection and development capabilities of PSO algorithm. The main work is as follows:(1) PSO algorithm is proposed by integrating adaptive chaos DE. First, chaos map is introduced to DE algorithm, and the obtained results are correction variation and correction options, then, chaos DE algorithm embedded PSO algorithm, thus increasing the differences in the particle of particle swarm in the optimization process and global search ability of PSO algorithm. Numerical experiments show that the optimization effect of this method is good, the precision is high.(2) To solve the optimization problem with constraints conditions and enhance the population’s ability to jump out of local optimal solution efficiently, adaptive penalty function is firstly used to deal with constraint condition, and then, using diversity assessment function to evaluate the diversity of population, i.e. if the population diversity is less than a certain adaptive threshold, the optimal position of particles is updated by using the DE algorithm; otherwise, white Gaussian noise is used for disturbance the global optimal particle of hasn’t been updated in continuous several generations, to enhance the ability to jump out of local optimal. The experimental results show that the proposed algorithm can effectively solve a class of constrained optimization problems.