opt_quadratic.m

遗传算法中二十个非常经典的原代码

function [xo,fo] = Opt_Quadratic(f,x,TolX,TolFun,MaxIter)
% 用二次插值求f(x)最优解
if nargin < 5
    MaxIter =100;
end
if nargin < 4
    TolFun= 1e-8;
end
if nargin < 3
    TolX = 1e-5;
end
%%%根据输入确定三点的初始值，并求出对应的函数值
if length(x) > 2 
    x012 = x(1:3);
else
    if length(x) == 2
        a = x(1);
        b = x(2);
    else
        a = x-10; b = x+10;
    end
    x012 = [a (a + b)/2 b];
end
f012 = f(x012);
%%%%初始化三点值
x0 = x012(1);
x1 = x012(2);
x2 = x012(3);
f0 = f012(1);
f1 = f012(2);
f2 = f012(3);
%%%%%求出插值二项式的取最小值处的x3以及相应的最小值f3
nd = [f0-f2 f1-f0 f2-f1]*[x1*x1 x2*x2 x0*x0; x1 x2 x0]';
x3 = nd(1)/2/nd(2);
f3 = feval(f,x3); 
%%%%判断是否停止迭代
if MaxIter<= 0 | abs(x3 - x1) < TolX | abs(f3 - f1) < TolFun
    xo = x3;
    fo = f3;
else
%%%%%根据求出的多项式值与区间中三点值的大小比较确定相应的新的三点
    if x3 < x1
        if f3 < f1
            x012 = [x0 x3 x1];
            f012 = [f0 f3 f1];
        else
            x012 = [x3 x1 x2];
            f012 = [f3 f1 f2];
        end
    else
        if f3 <= f1
            x012 = [x1 x3 x2];
            f012 = [f1 f3 f2];
        else
            x012 = [x0 x1 x3];
            f012 = [f0 f1 f3];
        end
    end
%%%%%进行新一轮迭代
    [xo,fo] = Opt_Quadratic(f,x012,TolX,TolFun,MaxIter-1);
end