How to obtain the optimised decision variable in the lower-layer when using genetic algorithm for a two-layer optimisation problem?

I have a two-layer optimisation problem with some decision variables, and the number of the lower-layer decision variables (DV_Low) is dependent on the upper-layer decision avriable (DV_Up). The structure of my function looks like this:

[DV_Up_Opt,Obj_Up_Opt] = ga(@Objective_function_Up,...);
function [Obj_Up] = Objective_function_Up(DV_Up)
    [DV_Low_Opt,Obj_Low_Opt] = ga(@Objective_function_Low,...);
    Obj_Up = Obj_Low_Opt;
    function [Obj_Low] = Objective_function_Low(DV_Low);
        ... (the size of DV_Low is dependent on the values of DV_Up)
    end
end

I want to know if there is any way for me to obtain the optimised lower-layer decision variables (DV_Low_Opt) that correspond to my optimised upper-layer decision variables (DV_Up_Opt)?

Answer 1

[Alan Weiss]

You can write these to an array, if you like. Something like this:

function [DV_Up_Opt,Obj_Up_Opt,lowhistory] = myfun()
lowhistory = []; %%%
[DV_Up_Opt,Obj_Up_Opt] = ga(@(x)Objective_function_Up(x,lowhistory),...); %%%
function [Obj_Up,lowhistory] = Objective_function_Up(DV_Up,lowhistory)
    [DV_Low_Opt,Obj_Low_Opt] = ga(@Objective_function_Low,...);
    Obj_Up = Obj_Low_Opt;
    lowhistory = [lowhistory;DV_Low_Opt]; %%%
    function [Obj_Low] = Objective_function_Low(DV_Low);
        ... (the size of DV_Low is dependent on the values of DV_Up)
    end
end
end

Alan Weiss

MATLAB mathematical toolbox documentation

[Xuming Yuan]

Hi Alan, thank you very much for your answer. I have tried your suggestion and I found that my optimisation problem does not have a feasible solution. I noticed that when I used the parallel pool, the codes can give me back the error saying ''function to evaluate must be represented a string scalar, character vector, or function_handle object'', but when I didn't activate the parallel pool, it just show me that the GA could not find any feasible solutions in the current generation and continued to run. Is there any issues with the parallel pool when I use the method you suggest here?

[Alan Weiss]

That is a very interesting finding. I am not sure how the nested objective function behaves with the lowhistory data passed the way you do it.

As you probably know, ga in parallel distributes the objective function to various workers to evaluate. When doing so, it packages lowhistory as data along with the evaluation point. Because of the way you pass lowhistory as input and output from Objective_function_Up, I am not completely sure what happens, whether things are getting passed the way you want to the various workers, or whether things somehow get mixed up because the workers have different versions of lowhistory. I do not have time right now to investigate, sorry, but it might be worth trying to figure out what you want lowhistory to represent in a parallel computation. Do you want the workers to have different versions of lowhistory? How do you want to recombine them into a sensible history? Or do I misunderstand entirely?

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Xuming Yuan]

Hi Alan

I just want to obtain the optimal lower-layer solution that correspond to my optimal upper-layer solution. If it is possible to keep a record of the history of the optimised decision variables, it is even better, but this is not very necessary to me.

Best Wishes

Xuming Yuan