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?
You may be interested in the following paper because it uses chance-constrained programming and bi-objective optimization together in a transportation application:
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:
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: