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I am investigating an optimization problem under uncertainty and am using scenario-based robust optimization to deal with uncertainties. I have developed a heuristic approach in which I can set the number of scenarios to large values. For example, I am currently using 1,000 randomly generated scenarios, and the algorithm seems efficient for large-scale instances in terms of CPU time. Commercial solvers might not be computationally efficient when the number of scenarios is large.

I was wondering what scientific and systematic approaches would be recommended for determining the number of scenarios in a scenario-based optimization algorithm.

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Generally if aiming for robust I'd try to get scenarios that would fall within 95% (95th percentile if distribution is discrete) of cases or choose the worst-case scenarios. Depending upon distribution you can constrain your relations to satisfy cases in that chosen range (chance constrained).
Other than that, sample average approximation is used where may be N samples are generated & average of those samples is taken as the parameter.

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  • $\begingroup$ Focusing on your example of SAA, could you please elaborate more on how you determine the value of N? $\endgroup$
    – mdslt
    Apr 6, 2023 at 12:08
  • $\begingroup$ That why I mention N, since you'd take the average, N could as large as 2k or 10k, since larger the value of N, closer will be sample average to real average. You can also do repeated random/stratified sampling & take average of sample averages. $\endgroup$ Apr 6, 2023 at 13:58

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