Questions tagged [robust-optimization]
The robust-optimization tag has no usage guidance.
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Distributionally Robust Stochastic Programming - Help with derivation
I've been working through this book on robust optimization of electric energy systems, and in particular chapter 4 on distributionally robust optimization. In following the derivation of section 4.2.1....
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Lagrange relaxation / subgaradient algorithm Sensivity to input data
I am implementing a Lagarange relaxation with subgradient method to find a lower bound for a minization problem, I tried to find the complicating constraints. I found an upper bound with relatively ...
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Auxiliary parameters for two uncertain parameters Robust Optimization
I have the following constraint for robust counterpart formulation, where two uncertain parameters appear at the same time;
$\sum{QG_{ij}}$*${\theta}$+$\sum_{}\sum{QD_{ij}}*p $ * ${\theta}$
where;
${...
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Number of scenarios in non-deterministic optimization methods
I am investigating an optimization problem under uncertainty and am using scenario-based robust optimization to deal with uncertainties. I have developed a heuristic approach in which I can set the ...
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Recoverable Robustness for an optimization problem
I am relatively new to the concept of recoverable robustness. I am researching the robust version of an optimization problem. I currently have methods to address the problem with perfect knowledge. ...
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Scheduling tasks to minimize the total number of utilized cores
I currently have a scheduling algorithm which computes an approximate solution, say S, for the nominal scenario of a given problem instance, say N. Given that N changes in a way and becomes infeasible,...
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Gamma uncertainty in the RHS of a constraint
I am new to the concept of robust optimization.I am trying to formulate the robust variation of a Binary Integer Program. Suppose we have a constraint of the form $\sum{x_{i,j}} \geq b_j$ for $ i \in ...
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Gamma uncertainty set
I am new to the concept of robust optimization. I am currently trying to use a gamma uncertainty set (Bertsimas and Sim, 2002) for the following scenario. Suppose we have a constraint of the form $\...
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Identifying worst case of realized uncertainty
I have a MILP formulation where one of the parameters in the constraints is unknown but comes from a know uncertainty set (Robust Optimization approach). As far as I researched the first step for ...
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Robust Optimization and Supplier Selection
I would like to incorporate a constraint to my model, this constraint is related to supplier quality or/ reliability selection with respect to efficiency, furthermore, I would like to make the ...
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How to approximate an uncertain constraint?
Suppose $\theta$ is the uncertain vector of parameters and it varies within the interval $\Theta$. We have the following uncertain constraint.
$$
\sum_{i} f_i(x,\theta) \ge \sum_{j} g_j(x,\theta) \...
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Robust optimization for IP formulation
I am researching the robust version of a problem. I have managed to produce an Integer programming formulation which solves the problem with perfect knowledge. From my research on the topic one can ...
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Robust Optimization in Gurobi
I have a research problem where my Mixed Integer Linear Program has data that follow probability distributions. I am approaching this by creating some m instances through realizations of these random ...
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How do I convert existing MILP problem into heuristics? or Shall I add heuristics to my existing MILP problem?
I have formulated a MILP problem & solved it using Gurobi. Below is the link to the description of MILP problem (a brief document) clearly stating its variables, constraints, and objective ...
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Best Case Optimization, which is sort of the opposite of Robust Optimization
TLDR: If George Costanza was supposed to do Robust Optimization, he would instead do Best Case Optimization, which is (sort of) the opposite of Robust Optimization.
Is there a literature or problem ...
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How to find robust counterpart of sum of logit functions?
Suppose function $\mu_i(y):\mathbb{R} \rightarrow \mathbb{R}$ is a logit function, $\mu_i(y)=1/(1+\exp(-y))$. Also, we assume that $\mathbf{x}_i\in \mathbb{R}^d$ and $\theta \in \mathbb{R}^d$. I am ...
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Robust Linear Optimization for avoiding diminishing returns
My engineering problem can be formulated as an LP as shown below
\begin{align}
\max_{\mathbf{x}}~~&\mathbf{a}^T\mathbf{x} \\
\mbox{s.t.}~~~&\mathbf{b}^T\mathbf{x} \leq B~~,~~\mathbf{1}^T\...
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Does YALMIP allow a user-defined function for the objective function and constraints?
I have a robust optimization problem where the decision variable is a matrix, and the uncertain parameter is a vector. My matrix is L, and the uncertain parameter ...
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Difference between "Online Optimization" and "Stochastic Optimization"/"Robust Optimization"?
I just came across the notion of Online optimization (I got a look on Wikipedia page and some other webpages), but it was not enough for me and I am looking for a more elaborated comparison, namely in ...
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Can we take the constraints from one model and plug them into the other model in pyomo?
I am implementing data-driven robust optimization methodology introduced in this article in python. Somewhere of the method, I need to use pyomo for each constraint whose parameters are uncertain to ...
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Derivative of sup(max) functions in distributionally robust optimization
In the distributionally robust optimization problem
\begin{aligned}
\min_{x\in X}\sup_{P\in\mathfrak{P}}\mathbb{E}_P[f(x,\xi)],
\end{aligned}
where $f:\mathbb{R}^n\to\mathbb{R}$ and $P$ is a ...
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Numerical problem regarding to classical benders cut of large scale problem
I am trying to implement benders decomposition for a simple two stage unit commitment problem. I implemented the classic Benders decomposition to add feasible cut and optimal cut to relax master ...
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Identify the specific parameters that reached their worst case in a robustly optimal solution
Assuming that we have a linear math model with $N$ bounded $[0,1]$ uncertain parameters $p_n$ within a typical polyhedral budget uncertainty set that says $\sum_{n}{p_n} \le \Gamma$.
I want to find ...
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How is optimization under uncertainty done in real world applications?
In this post What is robust optimization? there is a nice introduction to robust optimization.
There are many concept for uncertainty in optimization problems like
robust optimization
stochastic ...
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What is intended when we use "robustness", "resilience" and "reliability" in Operations Research?
I will use an example to detail my question but I would like you to keep in mind that I wanted to define:
Robustness,
Resillience,
Reliability
in the most general case within Operations Research.
...
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Is JuMPeR good enough for Robust Optimization problem?
I'm a graduate student studying Robust Optimization (RO).
So far, I've been studied the theoretic point of RO, and now I am looking for an actual tool for solving RO problems, both for practice and ...
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What is robust optimization?
What is the academic definition of robust optimization?
What are examples of robust optimization on:
shift rostering
vehicle routing problem
facility location problem
bin packing
...
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Robust/Stochastic optimization deployed in real-world systems/applications
In an applied project we are working on currently, we want to use robust or stochastic programming in order to enhance the performance of the systems (by reference to certain metrics). As you may ...
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Difference between stochastic optimization and robust optimization
I would like to know whether stochastic optimization and robust optimization are the same and if not, what is the main difference between them. I did an Internet search and I found the following ...
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Robust counterpart: why is dual reformulation not working?
I am trying to solve robust optimisation problems, but I am getting nonsensical solutions most of the time… Here is a very simplified example:
\begin{alignat}{2}\max&\quad x+z&\\\text{s.t.}&...
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Calculating robustness of layout plans
We have tried to design a manufacturing cell which will produce specific families of products. We figure out three layout plans for implementation. For practical reasons, we need to calculate the ...
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Modeling the uncertainty of the input parameters
There are many approaches to deal with the uncertainty such as stochastic programming, robust optimization and fuzzy programming. Finding a suitable approach that is applicable in the real situations ...
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