A few of your statements I think need some clarification. While my former (I'm retired) @Byron_JMP 's comments are on the spot...the one stop shop for all your optimization needs in JMP resides in the Prediction Profiler, a few of your statements I think need some clarification or additional commentary.
1. "Will JMP be able to optimize the uncertainty of the random discrete inputs..." The answer to this is 'no.' if, by 'uncertainty' you mean the distributional properties of the input variables. JMP does not 'optimize uncertainty of the random discrete inputs'. You specify the uncertainty of the random inputs. JMP finds an optimal solution for a number of user specified inputs...among them...distribution shape of the inputs, central tendency, and limits of exploration across the prediction space.
2. "...search for strategies that allow minimizing risks while achieving the objectives." What are the risks? Practical, statistical, compliance, etc. Evaluating a minimal risk solution is impossible without knowing the exact nature of the risks and more importantly consequences associated with failure/noncompliance, etc.
3. What do you mean by '...multi-objective optimization.'? In a modeling sense do you mean multiple 'y' variables? Or do you mean something else, like 'on aim with minimum variance for a single 'y'. Or for that matter, 'on aim with minimum variance for multiple 'y's.'? Tactics you take within the Prediction Profiler will vary based on these answers. What role might JMP desirability function capabilities play here?
Monte Carlo simulation is a rich set of capabilities within JMP as well. Exact tactics you take will depend on much of what I've written above. I encourage you to finish watching all the links provided by @Byron_JMP
