Questions tagged [robust-optimization]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
0 answers
18 views

Supremum of a probabilistic function with ambiguity distribution set using Wasserstein metric

There is a proof of how to derive distributionally robust chance constraints with ellipsoid bound. $$\inf_{\mathbb{P}\in\mathcal{D}^{WD}} \mathbb{P}\{\|\mathbf{A\zeta-b}\|_2 \leq 1\} \geq 1-\epsilon$$ ...
Kaiming Zhang's user avatar
0 votes
0 answers
43 views

Lagrange Duality in Robust Optimization

I am learning Robust Optimization and been stuck on this example. I've brushed up on my knowledge of Lagrange duality and referred to a couple of textbooks on Linear Programming but not able to ...
stuckinlocal's user avatar
4 votes
1 answer
136 views

Need help understanding robust optimization formulation

I am reading these notes from Stanford called "Optimization with uncertain data". In section 2.2, Example 2 (page 7), the author mentions the following portfolio problem $(P)$: $$ \max \; t $...
Kuifje's user avatar
  • 13.3k
1 vote
0 answers
56 views

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....
asfiwefewrno's user avatar
0 votes
0 answers
60 views

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 ...
ABDE's user avatar
  • 1
1 vote
0 answers
36 views

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; ${...
Abde's user avatar
  • 81
1 vote
1 answer
39 views

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 ...
mdslt's user avatar
  • 615
2 votes
0 answers
37 views

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. ...
Pia MiA's user avatar
  • 392
1 vote
1 answer
96 views

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,...
Pia MiA's user avatar
  • 392
0 votes
0 answers
60 views

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 ...
Pia MiA's user avatar
  • 392
3 votes
1 answer
135 views

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 $\...
Pia MiA's user avatar
  • 392
3 votes
1 answer
62 views

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 ...
Pia MiA's user avatar
  • 392
3 votes
1 answer
96 views

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 ...
Abde's user avatar
  • 81
4 votes
2 answers
163 views

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) \...
Amin's user avatar
  • 2,150
6 votes
2 answers
246 views

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 ...
Pia MiA's user avatar
  • 392
2 votes
3 answers
554 views

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 ...
arvind rathore's user avatar
1 vote
2 answers
221 views

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 ...
Margi Shah's user avatar
4 votes
0 answers
57 views

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 ...
Mark L. Stone's user avatar
3 votes
0 answers
129 views

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 ...
Amin's user avatar
  • 2,150
6 votes
0 answers
84 views

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\...
dineshdileep's user avatar
2 votes
0 answers
119 views

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 ...
makansij's user avatar
  • 129
8 votes
3 answers
712 views

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 ...
Betty's user avatar
  • 544
2 votes
1 answer
454 views

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 ...
Sik Sik's user avatar
  • 133
3 votes
0 answers
83 views

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 ...
Keith's user avatar
  • 155
2 votes
1 answer
168 views

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 ...
Lee Adolin's user avatar
4 votes
1 answer
77 views

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 ...
user4168715's user avatar
11 votes
1 answer
520 views

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 ...
user3680510's user avatar
  • 3,655
6 votes
1 answer
736 views

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. ...
JKHA's user avatar
  • 679
6 votes
1 answer
326 views

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 ...
Seok's user avatar
  • 166
8 votes
1 answer
2k views

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 ...
Geoffrey De Smet's user avatar
3 votes
1 answer
162 views

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 ...
Betty's user avatar
  • 544
23 votes
3 answers
5k views

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 ...
PeterBe's user avatar
  • 1,642
14 votes
1 answer
267 views

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.}&...
dourouc05's user avatar
  • 998
7 votes
0 answers
95 views

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 ...
A.Omidi's user avatar
  • 8,882
16 votes
4 answers
1k views

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 ...
Mehdi's user avatar
  • 683