MATLAB實現蒙特卡羅方法

1.首先編寫M文件mengte.m定義目標函數f和約束向量g

%%%蒙特卡洛法
%%定義目標函數和約束向量函數
function [f, g] = mengte(x);
f = x(1) ^ 2 + x(2) ^ 2 + 3 * x(3) ^ 2 + 4 * x(4) ^ 2 + 2 * x(5) - 8 * x(1) - 2 * x(2) - 3 * x(3) - x(4) - 2 * x(5);
g = [sum(x) - 400
    x(1) + 2 * x(2) + 2 * x(3) + x(4) + 6 * x(5) - 800
    2 * x(1) + x(2) + 6 * x(3) - 200
    x(3) + x(4) + 5 * x(5) - 200];
end

2.編寫M文件mainint.m，求問題的解

%%%通過迭代求解
rand('state', sum(clock)); %產生5個0-1之間的隨機數
p0 = 0;%p0代表目標值z，x0代表目標x
tic
for i = 1 : 10 ^ 6  %采集10^6個點
    x = 99 * rand(5, 1);%0<= x <= 99
x1 = floor(x); x2 = ceil(x);%x1是x向下取整，x2是x向上取整
[f, g] = mengte(x1);%對x1求值
if sum(g <= 0) == 4%若滿足4個則符合條件
    if p0 <= f
        x0 = x1;
        p0 = f;
    end
end
[f, g] = mengte(x2);%對x2求值
if sum(g <= 0) == 4
    if p0 <= f
        x0 = x2;
        p0 = f;
    end
end
end
x0, p0
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