For multidimensional optimization problems, I want to find which of the variables (to be optimized) are highly influential on the objective function value, so that I can have an expectation on which parameters would be accurately identified by the optimizer.
Given a domain for each variable, the aim is to identify which of the variables (in their respective domain) has the most influence on the overall objective function value.
The complexity also arises due to the fact that I am working on black-box optimization , and the objective function is not algebraic but a finite element computation. So I want to reduce the dimension of the problem.
Thanks for the help.
Dear Dr. Chakraborty,
Have you tried a search engine for your question?
say google, it will let you know all researches recently on the problem.
Hi, I think that in this case it is important to scale all the variables first.
Hi Dr Epenoy, I do scale the variables, earlier I was trying to do a local derivative by perturbation and check the variation in objective function value based on a reference. But in this case, the reference I select has an impact, so I was wondering whether there is a way to determine , for example for 8 design variables (with their respective domain), which have more influence on the objective function , with minimum number of function evaluations.
Thank you for your answer.
Hi Dr. Biazar, thank you for your comment. I did "google" it but generally the analysis which I am referring to are done after an optimum solution is obtained (post-optimization; "sensitivity analysis"). Other methods of reduced order simulation which exists include POD-RBF interpolation of FEM solutions; but I am looking for a different approach. As I mentioned each objective function evaluation is a FEM simulation, there is a restriction in number of function evaluations.
One possible way which is to select random points in the domain and check the local sensitivity, which I refrain from doing since it would require immense function evaluations.
P.S. I am still a student working towards my PhD degree.
Hi, I have found the following paper on this topic:
https://pdfs.semanticscholar.org/66f9/9707d9852bbf252dfefe92460b5b7d200e58.pdf
Hi Liang,
Thanks for the paper. I am working on something very close to what is in the paper.
Hello Aritra,
Actually, I agree with Richard that all your parameters should be first scaled in the intervals you've chosen a priori. In this way, the sensitivity we calculated will be dimensionless and also more meaningful, we say. I have this kind of problem for my newly accepted paper in IJSS. This is right one of the questions asked by the reviewers.So, I will copy at the end the link to the paper.
In fact, in my work, I need to evaluate the influence of two parameters on the objective function. The sensitivity analysis is made, as can be seen in Sect.6.2.
On the other hand, I see you mentioned somewhere the POD methods so as to reduce the dimensionality. This is what I have done in the paper mentioned above. Anyway, the objective function should be manipulated by these parameters, thus POD renders us a more condensed and more efficient description of the objective function. As for you case, I suggest to start with 2 or 3 parameters (in this way, it can be visualised in the Cartesian system), and construct the manifold (a collection of objective functions, either a scalar or a vector) within the reduced order space. Then, according to the form of manifold and the scales of axis, you should gain a better understanding of the influence of each parameter (see Fig.11 for example). Even based on some hypothesis, it works for my case and I guess for yours also.
Hope it can help and good luck!
Liang
Article An insight into the identifiability of material properties b...
Dear Dr. Chakraborty,
I strongly suggest you the so-called analysis of variance (ANOVA) approach.
This method is used to evaluate the influence of each design variable and their interactions to the objective function. Based on the result of the ANOVA, you can succesfully reduce the number of design variables by eliminating those that
have small effect on the whole objective function.
Look at the attached paper.
Hope it can help,
Fabrizio
http://www.ifs.tohoku.ac.jp/edge/Jeong/2004-0118.pdf
There is a classic term for this I haven't noticed that anyone has mentioned: "design of experiments". It's classic. (I am not saying that I recommend it, though.)
Dear Dr. Patriksson,
The ANOVA (and expecially two-way anova) method I suggested is a tool in the huge class of "designs of experiments" to study the main effects of two factors separately and (sometimes) their interaction effect.
Fabrizio
Yeah, I read about the Taguchi method for DOE, and later LHS for sampling but I am thinking of going with Morris method (with a slight modification) for my analysis [link below].
http://www.tandfonline.com/doi/abs/10.1080/00401706.1991.10484804
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