Test function for multi-objective optimization problem

Hi all,

I'm looking for a test function for multi-objective optimization problem, that one of the objective-function is for real data and the other is for binary data.

For more clarify refer to image below.

Thank you.

[Matt J]

It doesn't seem like such a problem belongs in the multi-objective category. If f1 and f2 depend on completely separate variables x and y, you should be able to optimize them independently of one another.

[Amir]

No, they are not independent.

Imagine you have a chromosome with real and binary elements.

[0 0 1 0 , 0.3 0.9 0.78]

[Matt J]

What is a chromosome and what does it have to do with f1 and f2?

[Amir]

Chromosome is an individual in population. (Just like Genetic Algorithm)

pop(i).position = [0 0 1 0 , 0.3 0.9 0.78];
pop(i).Cost     = [f1 f2];

[Matt J]

OK, but that's not the problem you described. You described a problem in which f1 depends on x but not y and f2 depends on y but not x. That is different from saying that both depend on [x,y].

[Amir]

I want to minimize f1 and f2 simultaneous, just like ZDT1 test problem. Only different is part of chromosome is binary not continuous.

I can't minimize them independently, Because f1 and f2 depend to each other (sort of).

[Matt J]

You need to say explictly whether f1 is a function of x, as in your diagram, or whether you are ammending that and f1 is really a function of both x and y. And likewise for f2.

You also need to clarify what the requirements are for the test problem you are looking for. Can we suggest any f1 and f2 that depends on a mixture of discrete and continuous variables?

[Amir]