一类不依赖于局部极小解个数的填充函数

A CLASS OF FILLED FUNCTIONS IRRELEVANT TO THE NUMBER OF LOCAL MINIMIZERS FOR GLOBAL OPTIMIZATION

求解无约束总体优化问题的一类单参数填充函数需要假设问题的局部极小解的个数只有有限个,而且填充函数中参数的选取与局部极小解的谷域的半径有关.本文对填充函数的定义作适当改进,而且对已有的这一类填充函数作改进,构造了一类双参数填充函数.新的填充函数不仅无须对问题的局部极小解的个数作假设,而且其中参数的选取与局部极小解的谷域的半径无关.

A class of singly-parameterized filled functions developed for unconstrained global minimization problem needs the assumption that the optimization problem has only a finite number of local minimizers, and has parameters which are heavily restricted by the minimal radius of the S-basin of some local minimizer of the problem. In this paper, we modify the definition of filled function and present a class of doubly-parameterized filled functions such that the two weaknesses are overcome.