I am looking to solve a multi-objective chance-constrained blending problem. Are there any suggestions about the software to use to try and solve a problem like this?
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1$\begingroup$ Would you see the multi-objective optimization laboratory which was founded at University of South Florida? $\endgroup$– A.OmidiCommented Apr 14, 2020 at 11:47
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1$\begingroup$ I have edited your title to include multi-objective optimization, and also to avoid the word "best", since your question doesn't ask for the "best", and since such a question would be subjective (and therefore not a great fit for OR.SE) anyway. Feel free to re-edit the title if I've introduced any errors. $\endgroup$– LarrySnyder610Commented Apr 14, 2020 at 13:18
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$\begingroup$ @LarrySnyder610 Thank you for the edit, and thank you for the advice! $\endgroup$– danielchartersCommented Apr 15, 2020 at 10:54
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You may be interested in the following paper because it uses chance-constrained programming and bi-objective optimization together in a transportation application:
https://link.springer.com/article/10.1007/s10288-019-00429-7
I would suggest to do the followings for your problem:
1- If you have bi-linear terms in your formulation then try to linearize them using for example "Piecewise mccormick relaxation".
2- Generate a reasonable (and tractable) number of scenarios to generate/expand the chance constraint(s) in your formulation.
3-1- If your problem has two 2 objective functions then you can pass your formulation to the "triangle splitting method" (which is an exact method) embedded in the following julia package to solve it:
https://github.com/alvsierra286/OOESAlgorithm.jl
(*) https://onlinelibrary.wiley.com/doi/abs/10.1111/itor.12692
3-2- If your problem has more than two objective functions then you can pass your formulation to the following julia generic heuristic package to solve it:
https://github.com/aritrasep/FPBH.jl
(*) https://www.sciencedirect.com/science/article/abs/pii/S0305054819301947
