fmincon is giving better results than ga for a nonlinear constrained optimization problem.

I used fmincon and ga for the same nonlinear constrained optimization (7-300 variables) but fmincon is giving much better results (all ceq<10^-8) while ga is not able to satisfy equality constraints. Help please.

Also: fmincon results vary with initial guess, step tolerance and constraint tolerance. What step tolerance and constraint tolerance should i choose?

[Matt J]

What help is required? If fmincon responds better to the problem, why not just use that instead?

[Nayan Rawat]

Because fmincon result depends on initial guess. Changing the initial guess is changing the result while the ceq constraints are still very small(1e-8). This means that it may be a local minimum. I want to use other algorithms which give global minimum too (like ga, patternsearch etc).

Answer 1

[Star Strider]

The ga function produces its best results if you override the default population matrix with one of your own. I always use an options structure similar to:

PopSz = 500;
Parms = 6;
opts = optimoptions('ga', 'PopulationSize',PopSz, 'InitialPopulationMatrix',randi(1E+4,PopSz,Parms)*1E-3, 'MaxGenerations',2E3, 'PlotFcn',@gaplotbestf, 'PlotInterval',1);

where ‘PopSz’ is the size (dimension 1) of the population matrix, and ‘Parms’ (dimension 2) is the number of parameters to optimise. It takes a bit longer, however it almost always converges successfully, if a solution exists. I use randi to more efficiently control the range of the random matrix.

[Matt J]

Or/also:

Add one more of the solutions from fmincon to the initial population. Since those solutions satisfy the constraints, they may be good seeds for ga().

[Nayan Rawat]

Thakks for the suggestion. I tried it but GA is not satisfying ceq even after taking 10 times more run time.

[Nayan Rawat]

Thanks, will try.