[Multi-objective optimization] the maximum number of optimization solutions is very small.

A randomly generated 100bcell group, how many of which are the optimal solutions to the problem?
My answer is very few, almost zero, and sometimes only one or two. Obviously, I think I have made a mistake somewhere.
We say that bcell A is superior to bcell B. if and only when a is not inferior to B in each target, and at least one target is superior to B, this is the definition of the optimal solution of the solution. Therefore, the non-inferior solution in a group must be superior to other 99 individuals. This probability is very small. Or

It is proved that up to one of the 100 groups has a maximum of one optimal solution.
: If a group has at least two optimal solutions, set them to A and B as defined (set the optimization goal to two ),
1. A. obj1> = B. obj1 A. obj2> = B. obj2 and at least one equal sign is invalid.
2. B. obj1> = A. obj1 B. obj2> = A. obj2 and at least one equal sign is invalid.

Apparently there is a. obj1 = B. obj1 A. obj2 = B. obj2, and at least one equal sign is invalid. Obviously, there are contradictions.
Therefore, according to my understanding, there is only one front-end with the optimal proxyproblem. This is a problem that I need to solve.

However, according to the source code provided by the procsor xxcui, of course, this code is incorrect and it is not expected to run, but the concept should be good. // you can judge whether the non-negative solution omitting the relevant code and only summarize part of it.

For (INT I = 0; I <pop_size; I ++)
...{
Flag = 1; // true in the original text is obviously incorrect.
For (Int J = 0; j <pop_size; j ++)
...{
If (I! = J)
...{
If (R [I] [0]> r [J] [0] & R [I] [1]> r [J] [1])
...{
Flag = 0;
Break;
}
}
}
}

According to the analyzer's judgment method, it seems that there is nothing wrong with what I understand. Is it true that the number of front-ends of the company is very small?
One decision can generate only one?

Confused ......................