Questions tagged [optimization]

For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.

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36
votes
8answers
887 views

Why is the programming code of many algorithms not public in the OR community?

In recent years, a huge number of scholars in AI and ML community are using Python to develop their algorithms and then publishing their papers and codes in GitHub. This provides an opportunity for ...
27
votes
9answers
10k views

MATLAB vs. Python in industry

I am a beginning PhD student in math, and I would like to focus on optimization. I am learning programming for the first time, and I have written out some rudimentary optimization algorithms in both ...
27
votes
4answers
315 views

How to avoid having your optimization models rusting?

When designing optimization models for external organizations, I have witnessed the following: We design an optimization model for a given problem. We fine-tune it based on a portfolio of ...
26
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6answers
2k views

Statistical tests for benchmark comparison

Suppose that you have two algorithms for solving an optimization model, and you want to benchmark their performance over a large set of instances (with only one performance metric, for example, the ...
24
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15answers
2k views

Recommended books/materials for practical applications of Operations Research in industry

I have a Masters' degree in Mathematics. I've very fair understanding of methods and techniques of Operations Research. I am looking for a good book/material where I can see a lot of examples on Math ...
24
votes
9answers
3k views

What are Operations Research applications for 'good causes'?

I am looking for applications of OR for good causes, possibly with some literature. I intend a good cause loosely defined in the sense that the scope is that of improving the well-being of others, e.g....
23
votes
4answers
387 views

How to determine if a given problem seems to be a good fit to be solved using combinatorial Benders decomposition

Combinatorial Benders decomposition is a mathematical programming technique consisting into dividing a problem into a master problem and a sub problem. The master problem is solved to optimality (or ...
22
votes
4answers
4k views

What instances can be solved today by modern solvers (pure LP)?

I have found a PowerPoint presentation in which the presentor Hall claims instances could be of the size of 108 in variables and constraints to be solved today. I assume that he meant sparse problems. ...
22
votes
4answers
2k views

OR-backed serious games

A "serious game" is a game (usually a simulation) designed for a primary purpose other than pure entertainment. Games like the beer game or the fresh connection can be considered serious games serving ...
21
votes
10answers
3k views

What are Operations Research problems which occur in everyday life?

What are Operations Research problems which occur in your everyday life? Things that come to mind are for example: driving to work: shortest path problem packing your backpack for vacation: ...
21
votes
5answers
2k views

Validation and verification of mathematical models

Within the subject of simulation I have found some literature on validation and verification (e.g. Sargent's paper). My question is, what techniques do you use to validate and verify your mathematical ...
21
votes
5answers
462 views

Solving ATSP problem for large-scale problem

I want to solve the Asymmetric TSP for a large-scale problem for an industrial application where the company cannot buy a commercial software license. For their applications, it is very important to ...
21
votes
3answers
2k views

Are valid inequalities worth the effort given modern solvers?

In Laurence Wolsey's Integer Programming[1], he presents a well-known procedure for deriving valid inequalities (VI) suitable for integer and mixed integer linear problems (see Section 8.3, and also ...
21
votes
1answer
354 views

Usages of logarithmic mean in optimization

I have recently learned about the logarithmic mean $$\frac{x-y}{\ln(x)-\ln(y)},\quad x,y > 0.$$ It is used a lot in chemical engineering optimization models e.g. see slide 15 of Developing ...
19
votes
7answers
3k views

What kind of optimization problems are solved most often in practice?

I think that the shortest path problem is probably the problem that is solved most often. But if we move to problems where we need more complicated solvers, like Gurobi, Cplex, and Baron? What are the ...
19
votes
5answers
2k views

Ordered list of OR journals

Is there any compact resource that includes a list of all academic journals in the OR/MS space, ranked by journal importance? Although there are some helpful features offered by publisher websites ...
19
votes
3answers
245 views

Variable bounds in column generation

Consider the set covering problem \[ \begin{align} \min&\ \sum_{j=1}^nc_jx_j\\ s.t.:&\ \sum_{j=1}^na_{ij}x_j\geq 1,\quad \forall i=1,\dots,m\\ &\ 0\leq x_j \leq 1 \end{align} \] ...
19
votes
2answers
807 views

How do we decide/plan an SLA for an NP-hard optimization process running in production?

How do you decide or plan an SLA (Service Level Agreement) for an application that depends on an optimization process when the problems you deal with are NP-hard? That is, if you are developing an ...
18
votes
4answers
887 views

PhD-level textbooks on linear programming

My graduate Linear Programming class uses Bertsimas & Tsitsiklis's Introduction to Linear Optimization. Are there any alternative texts that I could use to supplement this textbook (mainly the ...
17
votes
6answers
1k views

Infeasibility in mathematical optimization models

Sometimes, when solving mathematical optimization models (especially MIPs), they may be infeasible. Is there any comprehensive method to deal with the infeasibility conditions? (especially in complex ...
17
votes
3answers
836 views

What is the connection of Operations Research and Reinforcement Learning?

I know that Markov Chains and Markov Decision Processes have been studied in the OR community too. But, I was wondering what is the relationship of Operations Research (OR) and Reinforcement Learning (...
17
votes
3answers
949 views

TSP with revenue maximization

How to approach a travelling salesman problem with an aim to maximize revenue at each town visited in a certain number of days (total number of towns is greater than what can be visited in the given ...
17
votes
2answers
331 views

Guidelines for Linear Optimization approaches?

When solving a Linear Optimization model (or Linear Program), there are a lot of solution approaches. Just to name a few: Primal Simplex Dual Simplex Ellipsoid Method (as if) ...
17
votes
3answers
2k views

Can an integer optimization problem be convex?

I'm trying to wrap my head around an apparent paradox that I've come across while trying to learn more about optimization algorithms: On one hand several sources state that convex optimization is ...
17
votes
3answers
418 views

As an Operations Research professional, how is your time divided when working on an optimization project?

When working on an optimization project, what is the typical time division (in percentage) between the various tasks that you have to work on: Problem understanding/definition (figuring out what is ...
17
votes
3answers
329 views

How to model nonlinear regression?

As part of my research in statistics, I recently stumbled upon the paper by Wang, 2006, although its primary audience is for those who teach. For simple linear regression, quadratic programming can ...
17
votes
3answers
354 views

Best ways to use machine learning / AI as an OR scientist

I have come across GUROBI's webinar "Mathematical optimization and machine learning". In essence, Mathematical Optimization (MO) and Machine Learning (ML) are different but complementary technologies....
17
votes
1answer
721 views

The difference between max-min and min-max

I am solving two-stage optimization problems in the form of $$\max_{x \in X}\min_{y \in Y} f(x,y),$$ where $f(x,y)$ is the solution of a mixed integer linear program (MIP). As the constraints of the ...
16
votes
7answers
2k views

Does there exist an aggregation of videos on optimization?

Is there a website or otherwise maintained list of talks regarding mathematical optimization? This would be a big help for the community it seems. I'm most interested in those relating to integer ...
16
votes
3answers
647 views

What are some real-world applications of QUBO?

QUBO (Quadratic Unconstrained Binary Optimization) is the minimization of a quadratic function of binary variables. It has been used for computer vision, Ramsey numbers, factoring numbers, the ...
16
votes
2answers
193 views

Can we replace a binary variable with a continuous variable using a quadratic equality constraint?

Is it possible to replace a binary variable $x$ with a continuous variable that satisfies the quadratic equality constraint $x^2 - x=0$? The function $f(x) = x^2 -x$ is not a convex function. Can ...
15
votes
2answers
240 views

Search approach to solve optimization problem with only a minimum where time series get scaled

Currently, I am working on a relatively simple optimization problem: There is a set of time series (red) that get summed up to a cumulated time series (blue). The red time series have different forms ...
15
votes
4answers
694 views

Optimization models for portfolio optimization

What are the mainstream models for portfolio optimization? We have Markowitz mean-variance model and CVaR-based models (e.g., max return subject to a CVaR constraint). What else is out there in terms ...
15
votes
3answers
323 views

Benchmark problems for scenario-based stochastic optimization

$\newcommand{\E}{\mathbb{E}}$I am working on numerical algorithms for solving convex large-scale multistage scenario-based problems and I am looking for some standard benchmarks problems. I have so ...
15
votes
1answer
274 views

Convexity of Variance Minimization

$X$ is a discrete random variable taking value $x_n$ with probability $1/N$ for $n=1, \ldots,N$. I would like to set the $x_n$ values in an optimization problem. My objective is to minimize the ...
15
votes
2answers
409 views

Are there any real-world problems where quadratization helps to solve something that couldn't have been solved without quadratization?

The closest thing I know is the computer vision problem, in which an image is de-blurred and/or de-noised by quadratizing a quartic problem into a quadratic optimization problem (QUBO) and then the ...
15
votes
4answers
273 views

Tool/Editor to visualize optimization problem files and solutions

Is there a tool with a graphical user interface which helps to visualize optimization problem files (e.g. lp/mps) and solutions? Let's say you have an optimization problem and a solution and want to ...
15
votes
1answer
215 views

Was there something specific that caused graph cuts to lose popularity in the last 5 years?

Almost every graph-cut paper I look at seems to have exactly the same pattern of monotonic growth in citations and then monotonic decline starting around 5 years ago: For privacy I've cut the all ...
14
votes
4answers
251 views

Does this $0-1$ integer program have any speciality?

Given matrix $A \in \{0,1\}^{m \times n}$ and vector $b \in (\mathbb{Z^+})^m$, where $\mathbb{Z^+}$ is the set of positive integers, $$\begin{array}{ll} \text{maximize} & c^\top x\\ \text{subject ...
14
votes
4answers
518 views

Online Education for OR and Developing Decision Support Systems

I am looking for educational programmes which can be conducted online, such as full MSc., degree certificates, postgraduate courses/modules, MOOCs. Topics I am looking for are on advanced ...
14
votes
4answers
188 views

How would you characterize “optimization data?”

We often hear that in practice, not enough data of sufficient quality, consistency, recency, etc. is available for feeding into mathematical optimization models. Example: my university wanted to plan/...
14
votes
2answers
237 views

How can I approximate a chance constraint in a computationally tractable way?

I want to solve an optimization model that contains a constraint like $$ \Pr[F(x,\xi)\leq0]\geq1-\varepsilon $$ where $x$ are my decision variables, $\xi$ is a random vector, and $\varepsilon\in(0,1)$ ...
14
votes
3answers
136 views

Strategic planning based on average values

If you have strategic planning problems like hub location problems, the input data often consists of average values for shipping volumes etc. When planning capacities, it is risky to ignore the ...
14
votes
1answer
106 views

In the context of LASSO regression, how to introduce a constraint for max number of selected betas?

In lasso, we have a regularization term in the loss function: $$\sum \|y-\hat{y}\|_{2} + \lambda \sum\|\beta\|_{1}$$ As the loss function is minimized, some $\beta$'s will become zero. That's what ...
13
votes
7answers
849 views

What are the examples (applications) of the MIPs in which the objective function has nonzero coefficients for only continuous variables?

I'm specifically looking for real applications of the following form of MIP: $$\max\,Cx$$ subject to: \begin{align}Ax +By &= D\\Ax &= E\\By &= F\\ x &\ge 0\\ y &\in \mathbb{...
13
votes
2answers
468 views

Simulation optimisation: Monte carlo simulation, regression, optimise within regression model?

Can you help me identify if this technique has a standard name to help me explore the literature? Suppose I have a black-box stochastic simulation parameterised by $X=[x_1,...,x_p]$ with some single ...
13
votes
2answers
714 views

What is the difference between optimization software APIs based on performance and speed?

The state-of-art solvers like CPLEX or Gurobi and some of the open-source solvers have had the different APIs (like Python, C/C++, Java, etc.) in which users could write their MP model in own ...
13
votes
3answers
206 views

Protein folding and protein design relation

I understand from this active COVID-19 question: Are there any COVID-19 (coronavirus) related optimization problems with input datasets that we can "crowd solve"? that the protein folding ...
13
votes
1answer
290 views

Categorization of optimization models

For many families of optimization problems there is some sort of classification scheme. I am thinking about the triple notation for machine scheduling introduced in "Optimization and approximation in ...
12
votes
3answers
725 views

What is a “hard problem” in the context of Mixed-integer programming?

As a practical (real-world problems) point of view, it's important we could solve optimization problems as quickly as possible (for instance, to release a daily schedule). Maybe a problem with many ...

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