There seems to be a misunderstanding of optimization concepts here: an objective function can be evaluated at many values of X ... including some that are presumably infeasible to a set of constraints. If I tell you that I can earn a profit of $1 by setting x to 100, this is not wrong, but may be infeasible if x

Thank you very much for your answer. Regarding the question whether my problem is convex or non-convex. I think it is hard to say because I do not have an explicit form of the objective function. But for my understanding, once we are dealing with a 'black-box' type simulations, there is no way to prove that the function is convex or not.

Regarding the way I evaluate the objective function, as I have mentioned, there are some values of state variables which lead to divergence in the FEA in ABAQUS (I mean that the FEA simulation is premature terminated). If I still evaluated the objective function as I did for the normal case (the case that the simulation in ABAQUS converges and reaches the end of a load step), the objective function would be small. As a consequence, the optimum result I can get is the infeasible one.

Let me summarize my problem as follows:

I have an objective function, f, that is a black-box. And I would like to find its minimum. Once I plug the values of X (state variables vector) into f, I can have 2 types of output. The first one is the real value of f and the second one is also a value of f together with a message that informs me the given value is not reliable. I then check the value of f in the latter case and recognize that this value is smaller than the real one that I can get in the first case. Therefore, in the second case I set a very big value for f.

If you have any suggestion what I should do in the second case, please kindly let me know.

Hi

As I read your description that "Abaqus cannot coverge for some variable combinations", I guess you imply that the FE solution for a particular case fails as nothing comes out when Abaqus 'crashes'.

The simplest way to think about a case like this is that is a fail.

Therefore, a workaround to your problem, I think, would be to add an output variable to your solution set which is Pass/Fail, i.e. unity or zero. You can use this extra output variable as multiplicator to your solution.

You may object that you are trying to minimize things. If so, the minimize their inverse values in your objective function and you should be able to apply the extra output variable on your objective function.

As you are working on shape optimization, perhaps these papers might be of interest to you as food for thought?

https://www.researchgate.net/publication/256799784_Multi-disciplinary_optimization_of_railway_wheels

https://www.researchgate.net/publication/266214897_2005-01-2342_NVH_optimization_of_truck_cab_floor_panel_embossing_pattern

If you are interested, some ramblings of mine on the subject of simulation/automation/optimization can be found here. 

http://qringtech.com/learnmore/why-simulate-measure-correlate-automate/

Please note that neither paper would be of direct use to the above mentioned problem.

Sincerely

Claes

Article Multi-disciplinary optimization of railway wheels

Article 2005-01-2342 NVH optimization of truck cab floor panel embos...

Dear Tien,

In my practice I often used the Nelder-Mead direct search algorithm for optimization. If during the search the algorithm exceeded some limits or hit an infeasible region, I simply gave a very high number for the traget function, so the algorithm rebounded away from this region. It was a simple, yet effective solution. I don't know however, whether you can implement it.

regards

Andras

Dear Claes and Andras,

Thank you for your answers. Indeed, what you recommended is the way that I am using now (assign a big value for the target function when the algorithm hits an infeasible region). However, I wonder whether this method is so simple and it can probably work out if we have a continuous design space. Unfortunately, I have a discontinuous design space.

Anyway, thanks a lot for your answers.

Regards,

Tien