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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.

dhasson
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S_Scouse
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    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? – LarrySnyder610 Oct 17 '19 at 18:42
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    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. – Ehsan Oct 17 '19 at 18:51
  • 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. – S_Scouse Oct 17 '19 at 19:17
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    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? – Nikos Kazazakis Oct 18 '19 at 04:22
  • The problem is MILP. It iterates very slowly and I am using CPLEX. – S_Scouse Oct 18 '19 at 19:26
  • @S_Scouse: How long does it take to solve the underlying deterministic problem? I'm asking because a MILP model with 15 variables and 18 constraints is considered small and should not take that long (perhaps even solved within seconds, if not under a minute). – Ehsan Oct 19 '19 at 08:05
  • @S_Scouse: Are investment decisions made at the beginning of the planning period or could make some adjustments during the year? Finally, after the initial investment, what kind of decisions are made during the year (i.e., recourse action)? Are they just production decisions or some other decisions could be made to acoount for the effects of uncertainty? – Ehsan Oct 19 '19 at 08:19

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