Optimize two objective functions using fmincon

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safi58 2017-7-26

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评论： Torsten 2022-1-21

I have two objective functions which would optimize same variables. I have done the optimization individually and they are working fine. Now, I need to incorporate those two objective functions in fmincon. Is there any way to do it?

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INDREEYAJEET SINGH 2022-1-21

Even I have same challenge, do you have solution for this now?

Torsten 2022-1-21

If you want to buy a meal of high quality, you get a different food composition as if you want a low-priced meal.

If you define some standard for the quality, you can get the lowest-priced meal with this prescribed quality.

So there is a curve that - given a certain quality of the meal - gives you the meal with the lowest price for this quality. This is called "pareto-optimum":

https://en.wikipedia.org/wiki/Pareto_efficiency

So you must first decide how to weigh the two criteria from your two optimizations to get a common optimum.

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采纳的回答

Walter Roberson 2017-7-26

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https://ww2.mathworks.cn/matlabcentral/answers/350288-optimize-two-objective-functions-using-fmincon#answer_275553

Please read https://www.mathworks.com/matlabcentral/answers/341462-how-to-solve-multi-objective-problem-goal-programming-in-matlab#comment_471312

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Walter Roberson 2017-7-28

在 MATLAB Online 中打开

If each of those functions, OPTM_1 and OPTM_2 emit an eta value (rather than a loss directly), then they will be larger when the loss is least, so you would be wanting to minimize their negative when minimizing individually. However, if you square a negative then you get a positive, so you do not need the negative for the joint minimization:

joint_obj = @(x) OPTM_1(x).^2 + OPTM_2(x).^2;
joint_constraint = @(x) merge_constraints(x, @Constraints_1, @Constraints_2);
[x,fval,exitflag] = fmincon(joint_obj, x0, A, b, Aeq, beq, lb, ub, joint_constraint, options)

togther with

   function [merged_c, merged_ceq] = merge_constraints(x, cfun1, cfun2)
      [c1, ceq1] = cfun1(x);
      [c2, ceq2] = cfun2(x);
      merged_c = [c1(:); c2(:)];
      merged_ceq = [ceq1(:); ceq2(:)];

In the special case where you have no linear equality constraints, instead of the merge_constraints function I show here, you could instead use

VEC = @(M) M(:);
joint_constraint = @(x) deal([VEC(Constraints_1(x); VEC(Constraints_2(x)], []);

This assumes that your constraint functions might return arrays or vectors of uncertain orientation. In some cases you might be able to reduce down to

joint_constraint = @(x) deal([Constraints_1(x), Constraints_2(x)], [])