基于旋转曲面变换的粒子群优化方法

针对粒子群优化算法(PSO)应用于多极值点函数易陷入局部极小值，提出旋转曲面变换(RST)方法.该方法通过将被优化函数映射到一个同胚曲面上，使当前局部极小点变换为全局最大点，并保持被优化函数值在当前局部极小点以下部分的数值不变.当检测到陷入局部极小时，根据具体的优化函数，选择适当的变换参数，进行RST变换，从而得到问题的全局解.并对四个不同的测试函数进行了数值计算实验.结果表明，对于高维函数，当迭代步数相同时，旋转曲面变换粒子群优化算法与其他两种粒子群优化算法相比，具有稳定性要好，收敛速度快.

Particle swarm optimization based on rotate surface transformation

Aimed at particle swarm optimization(PSO) algorithm being easily trapped into local minima value in multimodal function,a rotating surface transformation(RST) method was proposed.The optimal function was mapped onto the homeomorphism surface by RST method,and the current local minima point was transformed into the global maximum point without changing the optimal function values under current local minima point.When PSO was trapped into local minima point,proper transforming parameters were selected according to concrete optimal function,and the global optimum resolution was realized by executing RST.Four benchmark functions were tested using this method.Experimental results show that compared with two conventional PSO at the same iterations for high dimension function,the proposed method converges faster and is more stable.