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What are some methods or algorithms for solving a large-scale stochastic mixed-integer optimization problem that runs on an hourly dataset for a year? Do we employ some kind of decomposition? (the problem in consideration is not bilevel). I am actually looking for general ways/guidelines to tackle these types of problems that are hard to solve even with a large optimality gap but do have an optimal solution.

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    $\begingroup$ Welcome to OR.SE! This question is very broad, and a little imprecise. I think you're really asking about methods for solving multi-stage stochastic optimization problems. ("Stage" = "time period" -- that's the "hourly dataset for a year" part.) Is that what you mean by "large-scale", or do you mean it in some other way? $\endgroup$ – LarrySnyder610 Oct 17 '19 at 18:42
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    $\begingroup$ I agree with @LarrySnyder610 that the question is vague. Please describe the scale of the deterministic problem (i.e., # of variables and constraints of the model when you consider no uncertainty)? In addition, please clarify what you meant by an hourly dataset for a year? Is it a multi-period problem or you just have 24*365 snapshots of the system states? Also, describing your available historical data (e.g., probability distribution or scenarios) would be helpful. Finally, your desired solution time could be relevant. $\endgroup$ – Ehsan Oct 17 '19 at 18:51
  • $\begingroup$ I have a 24*365 snapshot of wind and electrical load data. Based on that, I am considering historical yearly load and wind data for several years to create 15 scenarios combining load and wind profiles. The investment decision is made after running through the yearly data; in that sense, I am not sure if it can be called a multistage stochastic problem. I have 18 constraints and 15 variables. I tried to convert all the parameters to per unit and solve the optimization problem with no luck. It just runs forever. I am new in this field, so excuse me if something doesn't make sense. $\endgroup$ – S_Scouse Oct 17 '19 at 19:17
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    $\begingroup$ A few questions: (i) is your problem MILP or MINLP, (ii) does it iterate slowly or does it have fast iterations but never closes the gap, and (iii) what solver are you using? $\endgroup$ – Nikos Kazazakis Oct 18 '19 at 4:22
  • $\begingroup$ The problem is MILP. It iterates very slowly and I am using CPLEX. $\endgroup$ – S_Scouse Oct 18 '19 at 19:26

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