I am working on a problem for design optimisation. I would like to ask if for an uncertain problem, should design optimisation under uncertainty techniques be used for the design optimisation?
You may not get an answer to your question because it is so vague. Are you designing house, space station, artificial heart, entrance exam, or what?
Hi Shahroz,
I agree with Dudly.
However, a few points can be made to steer the discussion. We can think of a theoretical problem and assume that a maximand can be developed. In the alternative, some ranking may all that can be dome, regardless of of the nature of the problem. By this I mean that a partial order can be developed using axioms (e.g., transitivity and so on) for the preferences This may provide an initial answer without worrying about optimality as such. But you need a set of axioms and make sure that those axioms are met (btw, this raises impossibility issues but for now you need not worry about these -- you can force the problem to fit some axioms and discard the other axioms).
If the problem is itself vague, then I doubt if you can jump into an optimization technique (e.g., linear programming, dynamic programming, decision theoretic solutions etc.) because you do not seem to not have the state variables due to the vagueness of the problem statement. Worrying about uncertainty (and how to model it) before clearly understanding the problem increases vagueness. Try to make the problem explicit using first principles, if you can, try some linear assumptions (including quasi-linearity), use two or there state variables. I would temporarily forget uncertainty -- which can be defined from probabilistic to fuzzy to ... you decide, and get to the essence of your actual problem.
Much more to be said after you formalize your question and give a sense of the application your are thinking of.
All the best and thanks for the question!
Paolo
Dear Shahroz,
As per ASME code of ethics "Engineers shall perform services only in the areas of their competence". So in my opinion, if problem is not theoretical and related to some engineered product (and that also of mechanical in nature) it will be better to do some R&D and reduce the degree of uncertainty about your product, instead of thinking about optimization.
Regards
Naveen Bhatt
You should use "design optimization under uncertainty techniques" when you intuit or observe that uncertainties (variations in problem parameters you do not control) impact substantially the performance of the design (safety, economics, ....) over a substantial range of design parameters (problem parameters that you control). As Dudley answered, it would help to precise a bit your question.
For some problems the problem domain "stochastic mathematical program with equilibrium constraints" (SMPEC) might be very useful. The set-up is an extension of a bilevel mathematical program, where the lower-level problem has stochastic data. It was first described thoroughly in two tandem papers in 2010 in JOTA (Journal of Optimization Theory and Applications), by me and Christoffer Cromvik.
You should use design optimization under uncertainty techniques if the problem is uncertain. However, it is problem specific what you can do. What are you designing? The following links might help answer your question:
Article Multi-fidelity design optimisation strategy under uncertaint...
Conference Paper System Engineering Design Optimisation Under Uncertainty for...
The below paper might be helpful:
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjggMiS19_vAhVUwTgGHRB4C80QFjABegQIAxAD&url=http%3A%2F%2Fcepac.cheme.cmu.edu%2Fpasilectures%2Fsahinidis%2FNVSpaperthree.pdf&usg=AOvVaw1lumukPI9IlZEZsJHM7uLJ
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