改进PSO算法及其在函数优化中的应用

针对微粒群算法PSO（Particle Swarm Optimization）应用于函数优化存在的问题，提出一种加入了梯度信息改进的微粒群算法。微粒群算法用于函数的优化，具有简单、效果好等优点。但是研究也表明该方法也存在着一些缺点，如计算时间较长、容易陷入局部最小等，这是由于算法本身的随机性决定的。梯度法是传统的优化方法，典型的特征是在确定优化解的方向时遵循梯度下降原则，因此在寻找优化值时方向比较确定，可以减少优化时间。为了克服PSO的缺点，在标准PSO优化策略中引入梯度原则，设计了一个具有梯度指导的PSO算法。现将改进的PSO算法应用于函数的优化，并与标准PSO算法的效果进行了比较。函数优化实验的结果表明，改进的PSO算法提高了标准PSO算法的收敛时间。

An Improved PSO Algorithm for Function Optimization

For the problems appeared in the function optimization of the Particle Swarm Optimization algorithm(PSO),an improved PSO algorithm attached by the grad information is proposed in this paper.The PSO algorithm can be used in the problems of function optimization with characteristic of simplicity,high effectiveness and so on.The primary study,however,shows that the optimization method has some shortcomings such as slow computing speed,easiness to fall in local peak in large scale problem,which is determined by the randomness of the algorithm.The grad method is a kind of traditional optimization method and has the characteristic that it is along the descending grad direction of optimization values.So the grad method can reduce the time for the optimization values because the direction for optimal values is determined by the grad of grad algorithm.In order to overcome the disadvantages of the standard PSO algorithm,the principle of grads method was included in PSO algorithm.Therefore,the Grads-PSO algorithm(regulated by grad method) was proposed in this paper.The Grads-PSO algorithm was used in the optimization of function in this paper.The results obtained by the Grads-PSO have been compared by the ones of the standard PSO algorithm.The simulation results show that the improved PSO algorithm reduces the computing speed of the standard PSO algorithm.