# Tag Info

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### What is robust optimization?

In colloquial terms, Robust Optimization (RO) is a methodology (including modeling approach and computational methods) for handling optimization problems with uncertain data. Many times data aren't ...
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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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### Robust counterpart: why is dual reformulation not working?

I think there are two small mistakes in your formulation: In the final formulation, the roles of $x$ and $z$ should be reversed. Except for the first constraint and for the non-negativity of the ...
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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 ...
• 1,317
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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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### 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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### What is intended when we use "robustness", "resilience" and "reliability" in Operations Research?

I think these terms are all rather vague and imprecise, and different people use them slightly differently. Some papers try to draw clear lines between them—for example, in my dissertation in 2003, I ...
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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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### 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 ...
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### 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 ...
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### Robust optimization for IP formulation

I think this is a relatively easy but still general paper to start with: https://arxiv.org/pdf/1501.02634.pdf
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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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### 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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### Gamma uncertainty set

I think you meant $\sum_{i\in I} a_{i,j} x_i \ge b_j$ for all $j \in J$. In section 14.1 of Bertsimas/Weismantel, Optimization over Integers (2005), your first question is addressed by introducing a ...
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### How to approximate an uncertain constraint?

Yes, it is always mathematically guaranteed that $$\sum_i \min_\theta a_{i, \theta} ≤ \min_\theta \sum_i a_{i, \theta} \tag{1}$$ and that \sum_i \max_\theta a_{i, \theta} ≥ \max_\theta \sum_i a_{i, \...

### Difference between "Online Optimization" and "Stochastic Optimization"/"Robust Optimization"?

Pedrinho covered the Online part of your question very well, so I'll answer the other two. Strictly speaking, when we pose an optimisation problem, solving it means finding its global solution. If the ...
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### Identify the specific parameters that reached their worst case in a robustly optimal solution

A robust optimal solution has to satisfy all constraints for each choice of the uncertainty parameters. Thus you might not be able to point out one particular set that is active for an optimal ...
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### How do I convert existing MILP problem into heuristics? or Shall I add heuristics to my existing MILP problem?

There is a Gurobi video Faster MIPs Using Custom Heuristics MIPs often solve faster with good integer feasible solutions. Thus, Gurobi contains a variety of MIP heuristics to create integer solutions ...
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### Is JuMPeR good enough for Robust Optimization problem?

As you mentioned that you looked for python packages for RO before and didn't find any you might want to have a look at RSOME. You can custom build uncertainty sets using affine constraints as well as ...
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### Can we take the constraints from one model and plug them into the other model in pyomo?

Yes, this can be done in pyomo. Pyomo implements ConcreteModel() as a Block() object, so you could just place one over the other....
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### Difference between stochastic optimization and robust optimization

Let's make it more clear. Stochastic Programming is not Stochastic Optimization. When you say Stochastic Programming the above answer of @Larry is explaining more about "stochastic programming&...
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### Modeling the uncertainty of the input parameters

Stochastic Optimization (SO) requires the probability distributions (PDF) of the uncertain variables which are usually hard to fit. Then, a large number of scenarios are required to be sampled from ...
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### Numerical problem regarding to classical benders cut of large scale problem

CPLEX treats certain small values as negligible for purposes of constraint satisfaction (including satisfying integrality constraints). That does not mean it automatically rounds small values to zero. ...
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### Robust Optimization and Supplier Selection

RO is still in academic research area and several methods have been proposed. What I would do is this( not using any math programming model as you have already formulated already) Solve for q=0 Solve ...
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### Robust Optimization in Gurobi

Robust optimization ($+/-$) is still a research area and I am not sure if Gurobi has an automated way unless you want to follow this example from Wolfram. In case it's stochastic programming one way ...
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### How do I convert existing MILP problem into heuristics? or Shall I add heuristics to my existing MILP problem?

Please see if this answer helps you. Heuristics will have perturbation (changing values, first randomly, then based on a pattern if direction of min/max is ascertained) of variables, checking the ...
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### How to approximate an uncertain constraint?

My simple logic says your constraint states that the lowest of the lhs should always be greater than/equal to the highest values possible in the rhs within the given interval. If you take sum then you ...
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