如何提取非支配解（帕累托前沿） [英] How to extract the non-dominated solutions (Pareto front)

问题描述

我曾多次尝试使用MATLAB为两个目标函数编写提取非主导（或主导）的

解的代码。

我有两个简单的目标函数：

J1 = x。^ 2

J2 =（x-2）。^ 2

我有一个x值的范围，比如-5到5，例如，100个解决方案是在指定范围内随机生成的

。

我想提取非支配来自这些解决方案的解决方案。

我没有任何上述操作的问题。我到目前为止所做的是：

 ％在-5和5之间随机生成100个解决方案：
 
X = -5 + 10 *兰特（100,1）; 
 
％计算两个目标函数，每个解决方案的J1和J2：
 
 J1 = x。^ 2; 
 
 J2 =（x-2）。^ 2; 
  

现在，我面临如何将概念转化为书面代码的问题。

我知道如何提取非支配解和Pareto前沿的概念。

我可以手动完成，但是这个需要很长时间。

我尝试使用if语句，但结果不准确。

我认为最好提取主导解的指数，然后将它们从主矢量x中移除以获得非主导解。$ b $

预先感谢

解决方案

你介意来自FEX的文件吗？ 这个作品完美无缺：由Yi Cao创作的Pareto Front p>

为您提供了主导解决方案的 x 指数。

然后你只需要像这样使用它：

  x = -5 + 10 * rand（100,1）; 
 J1 = x。^ 2; 
 J2 =（x-2）。^ 2; 
 
 idx = paretofront（[J1，J2]）; 
 xdi =〜ismember（idx，1：numel（x））; 
 
图（1）
持有
分散（J1，J2,10，'red'）; 
 scatter（J1（idx），J2（idx），50，'blue'）; 
 scatter（J1（xdi），J2（xdi），50，'green'）; 
延期
 
 legend（'all solutions'，'dominating solutions'，'non dominating solutions'）
  

导致：

这正是它应该看起来的样子。否则，您需要澄清您的问题。

I have tried so many times to write the code of extracting the non-dominated (or dominated)

solutions for two objective functions using MATLAB.

I have two simple objective functions:

J1=x.^2

J2=(x-2).^2

and I have a range for x values, say from -5 to 5 and there are, for example, 100 solutions to be

generated randomly within the range specified.

I want to extract the non-dominated solutions from these solutions.

I have no problem of all above operations. What I have done so far is:

   % generating 100 solutions randomly between -5 and 5:

   x=-5+10*rand(100,1);

   % calculate both objective functions, J1 and J2 at each solution:

   J1=x.^2;

   J2=(x-2).^2;

Now, I faced the problem of how to translate the concept to a written code.

I know the concept of how to extract the non-dominated solutions and Pareto front.

I can do it manually but this will take very long time.

I tried using if statements but the results were not accurate.

I think it is better to extract the indices of the dominated solutions and then remove them from

the main vector x to get the non-dominated solutions.

Thanks in advance

解决方案

do you mind files from FEX? This one works perfectly: "Pareto Front" by Yi Cao

giving you the indices of x of dominating solutions.

Then you just have to use it like this:

x=-5+10*rand(100,1);
J1=x.^2;
J2=(x-2).^2;

idx = paretofront([J1,J2]);
xdi = ~ismember(idx,1:numel(x));

figure(1)
hold on
scatter(J1,J2,10,'red');
scatter(J1(idx),J2(idx),50,'blue');
scatter(J1(xdi),J2(xdi),50,'green');
hold off

legend('all solutions','dominating solutions','non dominating solutions')

leads to:

which is exactly how it is supposed to look like. Otherwise you need to clarify your question.

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