You prepared a numerical model of your object but, when you compared the obtained results to the experimental data, you found that the discrepancy between the two is too large. How to improve the model?
You have a good numerical model and want to change some parameters in it in order to improve the desired characteristics of the object but, when the changes have been made, some of characteristics became worse. How to achieve the best possible way of changing the parameters in the model?
You managed to formulate an optimization problem in order to improve your object but, when you took an optimization program from a numerical library, you ran into difficulties with linking it to your commercial numerical simulation software. Help!
You managed to make a link between the analysis and optimization software packages but trial runs show that the optimizer is making far too many calls for the analysis program. As each analysis is computationally expensive (perhaps, takes an hour or more on a powerful workstation), the optimization problem becomes unsolvable within any reasonable time. The boss said that the obvious solution - to buy a faster computer - is not an option. What to do?
Your managed to get a VERY fast computer but noticed that the optimization software, which worked so nicely on suggested test problems, does not converge to anything reasonable when linked to your analysis software. At some point, when a current design solution is still not good enough, it either goes into an endless loop or stops with an error message, something like "Check the quality of your gradients".
You realised that the analysis software gives the result spoiled with some considerable numerical noise because the round-off errors are accummulated in a large numerical model, or it involves some non-linear processes and is terminated when a prescribed accuracy is achieved, etc. You tried to play with the numerical model in order to reduce the noise but, still, the noise in the response is too high and cannot be tolerated by your optimization package. What to do?
When the optimizer attempts to run the analysis software at some specific combinations of parameters, the analysis software gives back a meaningless result or simply crashes. When you looked at these combinations of parameters you noticed that they are somewhat strange and should not be analysed in the first place. But how to tell the optimizer to steer clear of such situations? You tried to play with parameters of the optimization program reducing the step size, etc., but it increases the compuation time and does not always help anyway.
You solved the optimization problem but your boss does not like the way it looks. It is hard to formulate why - some gut feeling, perhaps? It would be nice to look through other good alternatives but the optimizer gave you just one - the best - solution so it does not lead you anywhere. Frustrated?
You solved the optimization problem and found that, among many other parameters, the recommended number of reinforcement bars is 4.393745 and the diameter of each is 17.305689 mm. You can only order 15 mm or 20 mm ones so you decided to round everything up to the nearest safe values (i.e. 5 bars 20 mm diameter each). When you did it with all the other values as well, the final result became quite poor. Is there any better way?