基于适应值曲面分析的全部局部极值搜索算法

为求得类似仿真函数的黑箱函数优化问题的全部局部极值点,提出了一种基于适应值曲面分析的新算法。首先,对适应值距离相关系数(fitness distance correlation, FDC)进行了改进,探讨了改进FDC指标与适应值曲面崎岖度的对应关系。在此基础上,设计了基于FDC的重复对分区域法(FDC based repeated split region, FRSR),对可行域依据崎岖度进行分解,得到满足崎岖度要求的若干子区间,并在这些子区间上依据FDC指标设置初始点,然后利用模式搜索算法进行寻优。通过对比FRSR法与传统的均匀分配初始点法以及其他现有方法,验证了FRSR法能够以较少的初始点得到全部局部极值,在速度上和解的质量上都优于传统方法。

Algorithm for locating all local optimum based on fitness landscape analysis

To locate all local optimum of the black box function, such as the simulation function, a method based on fitness landscape analysis is proposed. Firstly, the fitness distance correlation (FDC) is modified according to the characteristics of our problem, and the relationship between the modified FDC and the roughness grade of the fitness landscape is explored. Based on the relationship, an FDC based repeated split region method (FRSR) is designed to breakdown the whole feasible region into several acceptable sub-regions according to the FDC value, and a certain number of initial search points are assigned in each sub-region based on the FDC value of the sub-region, followed by an optimization procedure using the pattern search algorithm. Experimental results show that the proposed method can locate all local optimum with feuer initial points, and comparison study shows that it performs better than traditional methods, such as the uniformly generating initial points method and other known methods, both in speed and in quality of the solution.