“S”型曲线的优化模拟

本文介绍了用直接求优法模拟S型曲线的方法,并从微分方程dy/dx=Ey-Fy~2出发,给出了三参数取值范围的确定方法。本方法由于直接以Q=∑_(l=1)~n(y_-C/(1+Ae~(BX_1)))~2对实际观察值取最小为目标,因此克服了0.618法(即优选法)在对S型曲线进行模拟时的局限性,从而在对S型曲线进行拟合时,将明显地优于0.618法。

THE OPTIMIZATION METHOD FITTING THE S-MODEL CURVE

This paper introduces a method fitting S-MODEL CURVE by seeking optimization directly,and shows a method determining the range in which three parameters exist by solving differential eauation dy/dx=Ey-Fy~2.The method takes the formularQ=sum from i=1 to n(y_i-C/(1+Ae~(-Bx1)))~2 setting minimal value for the real observational value,as the objection fuction,so it overcomes the limitation which appears when S-MODEL CURVE is fitted in the 0.618-METHOD(that is optimum seekingmethod), therefore this method is muc...