How can write code of multi objective functions with using optimproblem format?

How can I define functions of multi objective problem with optimproblem format? My mean is using problem based method not using solver based method. ?

For example I have this optimization model:

That this model has two objectives.

I want to write the code of this model with optomproblem.

So I attach my model as above:

In optimproblem we use a phrase like the following sentense to define objective function:

prob.Objective = x(1) + 2*x(2);

But above formolation is for one objective function not multi objective problems.

But I have two objective function in my model and I don't know how can I coded them with this method ☹

[Star Strider]

Reference: Please help me to write the code of this constraint with optimproblem format has significaantly more detail.

[S AsZ]

Ok. Thank you so much. ?

But I don't know which details it need? Do you mean I should put entire my model?

[Star Strider]

My pleasure.

That could help, providing your code is well-documented so we can understand what it does.

Answer 1

[Walter Roberson]

You cannot. Examine https://www.mathworks.com/help/optim/ug/problem-based-optimization-algorithms.html and observe that none of the algorithms are multi-objective . Or look at https://www.mathworks.com/help/optim/ug/optimproblem.html#d117e128953 and see that for problem based optimization, the objective must be scalar.

[S AsZ]

I know that in optimproble, objective function must be scalar and my model is multi objective then it's not could be scalar.

And because my model is multi objective, I must use "gamultiobj" to solve my model. And for this reason I should use "solver based optimization" and I can't use "problem based optimization".

But the examples that explained in gamultiobj are simple examples whereas my model have several summations as can you seen above.

And it is difficult for me to write my model code.

Is there any way that I can convert my model from problem based optimization to solver based optimization?

Or how can I write the above metioned model by using solver based optimization?

[Walter Roberson]

You can create one optimproblem per objective, using the same variables each time. You can use https://www.mathworks.com/help/optim/ug/optim.problemdef.optimizationproblem.prob2struct.html prob2struct() to convert the problem based system to a solver based approach. However,

• there is no guarantee that converting two different objectives with the same variables will use the same parameters in the same order
• you would need to extract the fields from the converted structure to create the multi-objective, and probably check them for consistency with each other
• it is plausible that not all of the objectives will transform into the same solver

But still, it might possibly help to proceed that way.

[S AsZ]

The following sentence is ambiguous for me. Can you give me more information or provide an example for me about this sentence?

"you would need to extract the fields from the converted structure to create the multi-objective, and probably check them for consistency with each other"

[Walter Roberson]

Look at the example for problem2struct() .

%bunch of code
steelprob.Constraints.conswt = totalweight == 25;
steelprob.Constraints.conscarb = totalCarbon == 1.25;
steelprob.Constraints.consmolyb = totalMolyb == 1.25;
problem = prob2struct(steelprob);

Now

>> problem

problem = 

  struct with fields:

     intcon: [5 6 7 8]
         lb: [8×1 double]
         ub: [8×1 double]
         x0: []
         f0: 0
          f: [8×1 double]
     solver: 'intlinprog'
      Aineq: []
      bineq: []
        Aeq: [3×8 double]
        beq: [3×1 double]
    options: []

You would do the same thing for each of the optimproblem that you created. You would need to compare that lb contained the same thing for each, and that ub contained the same thing for each, and likewise Aineq and bineq and Aeq and beq and intcon . Then having verified that those were all the same, you would extract the common ones into variables

    joint_A = problem.Aineq;
    joint_b = problem.Bineq;
    and so on
    

and you would extract the various f fields describing the objective functions and merge them together into one, that might look something like

   joint_obj = @(x) [problem.f(x), problem2.f(x)];

I think you would be ending up with the same nonlcon for all of them rather than having to merge them

and then call

   gamultiobj(joint_obj, length(joint_lb), joint_A, joint_b, joint_Aeq, joint_beq, joint_lb, joint_ub, joint_nlcon, joint_options)

[S AsZ]

Thank you very very much ??????????