具有转换函数的均匀差分进化算法及性能分析

Uniform differential evolution algorithm with transform function and performance analysis

对于求解复杂优化问题,差分进化算法存在后期收敛缓慢、易于陷入局部最优等缺点.为此,从充分利用求解信息和目标信息角度提出了具有转换函数的均匀差分进化算法.首先对3个算子进行分布均匀性分析及设计,使其生成的个体能完全表征解空间特征,并增强种群多样性.其次,为简化优化环境,利用一种适应度转换函数使得当前局部极小点及相关区域拉伸一定高度而优于当前极小点的函数部分保持数值不变.最后通过性能指标的定量评价,结果验证了改进算法在有效性、鲁棒性和效率上的优异性能.

When differential evolution algorithm is applied in complicated optimization problems, it has the shortages of prematurity and stagnation. By efficiently utilizing the information of objective function and solving problems, a uniform differential evolution algorithm with transform function is proposed in this paper. Firstly, three operators are designed to generate individuals which obey uniform distribution. Individuals can fully represent the solution space. So the diversity of populations and capability of global search will be enhanced. Secondly, a transform function used to simplify the objective function is constructed. It stretches the current local minimum and related regions up to a certain height, while keeps the optimized function unchanged under the local minimum. Thus, the number of local minima will be largely decreased with the progress of iterations. Finally, the improved algorithm is quantitatively evaluated by performance indices. The simulation results show that it has perfect property in efficacy and converges faster, and is more stable.