Particle Swarm Optimization Algorithm

Optimization problem is an ancient problem, has a strong application background, and appears widely in scientific research, technology, economic management and engineering and technical fields. The classic methods for solving optimization problems, such as conjugate gradient method, hill climbing method, Power method and so on, have good convergence performance, but only for smooth problems. However, many practical problems is non smooth. Differing from the traditional optimization algorithm, intelligent optimization algorithms such as genetic algorithm, ant colony algorithm and particle swarm algorithm suitable for practical problems, and does not require the function of smooth. Thus these algorithms have more practical, and can solve complex optimization problems.This thesis studies particle swarm optimization algorithm. The algorithm is inspired by the swarm intelligence of bird migration, by analyzing the flight coordination between the flock and collective collaboration to simulate bird migration process. Like other evolutionary algorithm, the algorithm no special requirements on the specific form of the objective function, thus it does not require gradient information. In addition, particle swarm optimization algorithm is simple and need to few parameters, so the algorithm has been widely used in function optimization, neural network training, fuzzy control system and so on. However, particle swarm optimization algorithm converges slowly, and is prone to premature convergence in the multi-modal function optimization. To overcome these shortcomings and improve the speed of convergence of the algorithm, the improved particle swarm optimization algorithm proposed, such as the inertia weight method, compression factor method and adaptive weights method. Although these methods are better to solve the premature convergence problem, there are still the drawbacks of slow convergence and high-dimensional problems are difficult to calculate. Based on deeply studying particle swarm optimization algorithm, by increasing the time factor to flight speed, this paper presents a particle swarm optimization algorithm with the time factor. The main idea is introduced time factor to accelerate the flight speed and improved the performance of the algorithm. Numerical experiments show that the faster the convergence speed of the particle swarm optimization algorithm with the time factor, the higher the operator to achieve the accuracy, run more stable, and can effectively overcome the local minima.