network optimization when constraint calls a function

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sina 2017-5-27

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评论： Walter Roberson 2017-5-29

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I am trying to optimize a network using GA. The objective function is to minimize x(3). The formulation is as follows:

x(0) is known.

Constraint file:

% equality
c_eq(1) = x(0) + x(4) - x(1);
res_fun = f(x(1));
c_eq(2) = x(2) - res_fun;
c_eq(3) = x(2) - x(4) - x(3);
% inequality
c(1) = x(0) - x(3);
[x,fval] = ga(ObjectiveFunction,nvars,[],[],[],[],LB,UB, ConstraintFunction);

And my question is that the formulation is correct?

Thank you.

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John D'Errico 2017-5-27

编辑：John D'Errico 2017-5-27

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This is not linear, but the product of two unknowns:

ceq = a*b - x(1)*x(2)

It cannot go into Aeq. As for the other case,

ceq = x(2) - f(x(1))

Again, if f is a nonlinear function, then this is a nonlinear constraint. But I don't see what is your problem. Functions can call other functions! If f is an m-file, then WTP? If f is a function handle, defined somewhere, then you can either pass it around as an argument, or learn to use nested functions. nested functions can see variables in the workspace above them, and a function handle is just a variable. Again, WTP? Or make f an m-file sub-function. Again, no problem. The constraint function will be able to see sub-functions.

Of course, f must be differentiable for fmincon to work properly, but you never told us what is inside f.

Use the linear equality and inequality constraints to the extent that you can. So some of your constraints should go there. Best would be if all of your constraints are linear.