In this post What is robust optimization? there is a nice introduction to robust optimization.

There are many concept for uncertainty in optimization problems like

  • robust optimization
  • stochastic optimization
  • distributionally robust optimization
  • adjustable robustness
  • ... and many more.

How common are these concepts applied in real-life applications for optimization, and how are the uncertainty sets derived in a practical scenario?

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    $\begingroup$ Among your "many more", I would include "fuzzy optimization", which seems to be used heavily by governments around the world (give or take the "optimization" part). $\endgroup$ – prubin Dec 8 '20 at 22:05
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    $\begingroup$ Most people just use avetage or typical values, and may not even have an appreciation for the consequences of doing so. I am not most people. $\endgroup$ – Mark L. Stone Dec 8 '20 at 22:12

The following is purely personal opinion. I would say a (substantial) majority of non-academic optimization problems do not involve any of the methods you listed, for a number of reasons.

  • "Better is the enemy of good enough." Using fixed, plausible values for parameters and ignoring uncertainty often produce answers that are good enough for management, so why get any more complicated?
  • For large scale problems, any additional complexity could be a back-breaker, so why risk it?
  • Stochastic optimization requires distributional assumptions/estimates that may not be easy to come by.
  • Many OR/MS/IE students get a basic education in LP, graph models, dynamic programming and hopefully MIP, and maybe something a little funkier (optimal control theory?), but do not get much if any classroom exposure to stochastic optimization and especially to robust optimization (which is relatively new). Now shift from "exposure" to "mastery" (a nonincreasing transformation), get them jobs, and you end up with people solving problems who may or may not be aware of those things but in any case are definitely not comfortable with them.

Since a lynch mob is forming outside my study, let me add that there is merit to each of the concepts you listed, and I'm not arguing against their use (except where it would turn a difficult to solve approximate model into an impossible to solve but more exact model). Somewhere down the road, as they become more mainstream academic topics, their use will likely increase.


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