# Tag Info

### Stochastic programming MIP solvers

If you have access to MATLAB, I can recommend Marietta (I am a developer of this toolbox), with which you can solve general risk-averse optimal control problems (a ...

### Stochastic programming MIP solvers

Disclaimer: I'm not a researcher in the area of stochastic programming software. But as a researcher in the area of stochastic programming, I've put some time into looking for stochastic programming ...
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### Modeling the uncertainty of the input parameters

In reference to the first question, I think it often comes down to the information you have about the underlying uncertainty. If you only have intervals or ranges, robust is the way to go. If you have ...
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### Difference between stochastic optimization and robust optimization

I think there is no single, uniformly accepted answer. But there are two main factors that distinguish them: In stochastic optimization, it is nearly always assumed that we know the probability ...
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### Scenario Generation and Reduction in Stochastic Optimization

If you have historical data, you might use them as scenario inputs to a scenario reduction algorithm. Some references are available from here and here. Fitting a probability distribution does not ...
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### Stochastic programming MIP solvers

I don't know if it's really what you are asking for, but Julia has a few packages that implement algorithms for stochastic programming (on top of other LP solvers): StochDynamicProgramming.jl (seems ...
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### Modeling the uncertainty of the input parameters

The following papers discuss this extensively with numerical experiments, but they tackle specific examples. Emphasis is mine. Kazamzadeh et al. (2017) This is a comparison of the two techniques using ...
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### Modeling the uncertainty of the input parameters

Regarding your first question, I think other answers have summed it up pretty good. Two things I would add are as follows: Stochastic programming models (besides chance constraint/probabilistic ...
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### How is optimization under uncertainty done in real world applications?

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. "...
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### Why is the sample variance of a Sample Average Approximation calculated in this way?

Since $\hat q_{N'}(\hat x)\approx\Bbb E[Q(\hat x,\xi)]$ and $\Bbb V[\hat q_{N'}(\hat x)]=\Bbb V[Q(\hat x,\xi)]/N'$, we have \begin{align}\hat\sigma_{N'}^2(\hat x)=\Bbb V[\hat q_{N'}(\hat x)]&=\...
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### 2 stage stochastic programming to approximate many stage problems

Let me first distinguish between two-stage and multi-stage models by emphasizing on two issues, namely the type of uncertainty covered by each model and the sources of stochastic parameters. In two-...
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### Benchmark problems for scenario-based stochastic optimization

You can check the Test Sets section of the Stochastic Programming Resources website. It contains different types of problems — two-stage or multi-stage, mixed or ...
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### Can we simplify (perhaps linearize) this constraint?

Assuming the denominator cannot be zero (which would cause the known universe to implode) and that you can provide an upper bound for $y_j$, you can multiply both sides of the equation by the ...
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### Difference between "Online Optimization" and "Stochastic Optimization"/"Robust Optimization"?

Most online problems are sequential decision problems described by the following scheme: Information --> Decision --> Information --> Decision --> Information... We first have some ...
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### Optimal set order to maximize stochastic reward

As it is explained here, this problem is a portfolio selection problem. The player should select the first $n$ booths with the maximum $E(g_i)=p_i \times r_i$ in which $E(g_i)$ represents the expected ...
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### Sources to learn about Sample Average Approximation for practitioners

SAA is a very widely used technique for stochastic optimization problems and as far as I can see there are two frequently used approaches for the implementation of SAA. Please check Homem-de-Mello's ...
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### Alternative definition for the value of stochastic solution

In the paper by Crainic et al.1, the authors stated that "Focusing on two-stage formulations, we show how and under which conditions the reduced costs associated to the variables in the deterministic ...
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### Difficulties with Finding a Proper Penalty Value for the Progressive Hedging Algorithm

This problem is addressed in some detail in Section 2.1 of the paper Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems by Watson and Woodruff (a non-...
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### Optimality in L Shaped or Bender Decomposition

As far as I can see you have binary variables in the first stage and general integer variables in the second stage. This means that classical Benders cuts (based on duality of the subproblems) do not ...
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### Benchmark problems for scenario-based stochastic optimization

Pantelis, It is a great detriment that no such collection of examples exists. One problem is that there is no established format for multistage problems like MPS. (There is SMPS [paper], but this ...
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### Benchmark problems for scenario-based stochastic optimization

"Ruszczynski, Andrzej, and Robert J. Vanderbei. "Frontiers of stochastically nondominated portfolios." Econometrica 71.4 (2003): 1287-1297". This paper provides a large number of test problems which ...
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### Robust/Stochastic optimization deployed in real-world systems/applications

This heavily depends on the application at hand and could vary all the way from milliseconds to months. It all comes down to rigorously defining the specs. Many parameters are in play: How long does ...
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### Difference between stochastic optimization and robust optimization

As Larry said, there is no single, uniformly accepted answer, so I'll make things even more interesting. In mechanical engineering, specifically in aircraft design where I used to work, we used the ...
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### How to evaluate the performance of scenario generation algorithms?

I did a little research and found the paper that I have cited below. I think with 517 citations this paper and the reference therein can be a good source for you. Paper: Kaut, Michal, and Stein W. ...
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### Decomposition methods for two-stage stochastic program with integer variables

To solve stochastic programming models with integer recourse, there are some methods. Most stochastic programming textbooks cover these methods. For example, chapter 7 of Introduction to Stochastic ...
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### How to solve Stochastic Dynamic Program with huge state space?

Just to expand very slightly the comments by Mark: in general exact stochastic dynamic programming scales quite poorly. Value iteration complexity for each iteration is $O(A S^2)$ where $A$ is the ...
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### Accessible introduction to L-shaped methods/Benders decomposition

Given your emphasis on practical and implementation aspects, I think the following two lectures will interest you: Stochastic Programming Modeling by Jeff Linderoth (University of Wisconsin, Madison) ...
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### Optimal set order to maximize stochastic reward

To get $O(2^M M^2)$ instead of $O(M!)$, you could modify the dynamic programming formulation of the traveling salesman problem, with a state for each subset of booths visited so far.
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I hope to provide intuitively-appealing answers to both questions. $\textbf{Question 1:}$ Infinite horizon MDP's do not care about the initial state. They attempt to be optimal in the sense that the ...