19
votes
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 ...
15
votes
Accepted
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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13
votes
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 ...
- 2,473
12
votes
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 ...
- 1,317
11
votes
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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10
votes
Accepted
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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10
votes
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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10
votes
Accepted
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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9
votes
Accepted
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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8
votes
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)]&=\...
- 5,452
8
votes
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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8
votes
Accepted
Is Benders decomposition and the L-shaped method the same algorithm?
In the paper that proposed L-shaped method, you can find
In section 2, an algorithm which is essentially the same as the
algorithm developed by Benders[3] is described and a geometric
interpretation ...
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7
votes
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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7
votes
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 ...
- 1,726
7
votes
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Robust Optimization in Gurobi
One way to do this is to rewrite the objective somewhat.
I'm going to start from an objective of the following form:
$$ \min_x c(\zeta)^\top x, $$
with $c(\zeta)$ a cost vector depending on a random ...
- 241
6
votes
Accepted
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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6
votes
Accepted
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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6
votes
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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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6
votes
Accepted
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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6
votes
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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 ...
- 1,701
6
votes
Accepted
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 ...
- 40.1k
6
votes
Robust Optimization in Gurobi
The following formulation is more or less the same as the formulation used in How to represent a constraint on the kth-smallest function?. So thanks to @RobPratt for providing a comment which improved ...
- 13.8k
5
votes
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 ...
- 51
5
votes
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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4
votes
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 ...
- 12.2k
4
votes
Accepted
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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4
votes
Accepted
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 ...
- 12.2k
4
votes
Stochastic programming MIP solvers
We recently had a review paper on the software packages for Benders decomposition and dual decomposition. We did some benchmark studies on their performance as well through the stochastic programming ...
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4
votes
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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4
votes
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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