# 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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### 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 ...
2k views

### Algorithms vs LP or MIP

Is there a way of writing an algorithm with if-, while-statements to find an optimal solution without using linear-programming (LP)/MIP? If so, what would the benefits be against the LP/MIP? Is it ...
325 views

### Decoding a Deep Neural Network as an Analytical Expression for Optimization Purpose

This post is not really about a specific question but rather a topic I am curious about to know more. We know that when it comes to integrate machine/statistical learning with optimization for the ...
305 views

### Expressing a chain of boolean ORs using ILP involving different variables

How can I express a chain of OR operations in an ILP, given that each operand is an inequality between two binary variables? I have asked a similar question here: Chain of Boolean ORs. In that ...
512 views

### Expressing a chain of boolean ORs using ILP

How to express a chain of OR operations in an ILP in which each expression is a less than or equal constraint and the left hand side variable in all inequalities is always the same? All the variables ...
483 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 ...
2k views

### Performance of a branch and bound algorithm VS branch-cut-heuristics

I was trying to solve a moderate scheduling model using an open-source solver. I did two different ways. A) using pure branch and bound algorithm (disable all options). B) using the default setting ...
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### Run repeatable numerical tests in the cloud

In numerical tests of optimization algorithms, one often reads "We used a XY computer with X GB RAM for the experiments". Usually, when I want to compare my results with theirs, I do not have an XY ...
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### 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 ...
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 ...
870 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{...
161 views

### Model Update for Data Driven Real Time Process Optimization

The question I am about to ask is not a technical one but rather based on following a correct approach, which I am sure would be helpful to many. I am currently working on a project which involves ...
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### 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 ...
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### How to linearize min function as a constraint?

I'm trying to solve an optimization problem including following constraint, and I need to linearize it in a maximization nonlinear programming model. Please help me to reformulate it with mixed ...
285 views

### How to add Binary Variable with condition in LP

Notation $\text{src}_{h,s},\text{dst}_{h,s},\text{ch}_{h,s}$ are constants. $a_{h,s},x_{i,j,s}$ are binary variables. $\text{wt}_{h,s}$ are continuous variables. Problem \begin{align}\min.&\...
880 views

### Linearization of objective function

Notation $\text{src}_{h,s},\text{dst}_{h,s},\text{ch}_{h,s}$ are constants. $a_{h,s},x_{i,j,s}$ are binary variables. $\text{wt}_{h,s}$ are continuous variables. Problem \begin{align}\min.&\...
202 views

### Some theories and laws of Operations Research? [closed]

Can I know some theories and laws of Operation Research which has being widely used nowadays?
597 views

### How to modify EMSR when capacity for each fare class is different

In the normal EMSRa and EMSRb (Expected Marginal Seat Revenue) algorithms, each fare class is utilizes exactly 1 unit of capacity (for example, one seat on a plane). But I have a similar problem for ...
404 views

### Finding minimum time for vehicle to reach to its destination

Given a set of Vehicles with source and destination I need to find the minimum time of travel for all the vehicles, there are also some charging stations and its necessary for vehicles to charge 1 ...
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### Soft constraints and hard constraints

The terms "soft constraints" and "hard constraints" are used in the context of optimization modeling. Is there any standard way to figure out which is which in some of the complicated models?
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### Labour Model - Resource Allocation based off Product Forecasts

at my company, we have a product level forecast that we run through a model which pulls out an hours number for our retail outlets. We do this by binning various products into categories and give ...
406 views

### What is this type of scheduling problem called?

I am currently working on software that deals with a specific type of scheduling problem, and I want to improve the scheduling algorithms that it uses. However, when I tried to research algorithms ...
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### 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 ...
331 views

### Python PuLP - Unable to Model Non-Square Matrix

I am having issues with setting up constraints using both input arrays from excel and variable arrays within PuLP. It appears the model only works with square matrices and my final code has a matrix ...
425 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 ...
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} ...