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# Operations Research : Recent Questions and Answers (Page 6)

## Formulating these logical constraint in an ILP

I have these two constraints : $z leq My$ $t leq M'y$ where $z$ and $t$ are two integer variables $z, tgeq 0$,...

## Modeling the multiplication of two binary decision variables in undirected graph in python

In an undirected graph, I'm trying to model a constraint that forcing the optimizer to set an edge $(u,v)$ between two nodes to only exist (= $1$) if...

## Flexible Job Shop with Preemption

I'm trying to solve a flexible job shop problem variant that has precedence constraints on jobs along with a few other issues. We have a MIP formulation and also a...

Asked on 01/15/2021 by Robert Hildebrand

## How to handle an equality constraint in metaheuristic algorithms (like GA, PSO)?

Metaheuristic algorithms are generally used to find the optimal solution to unconstrained optimization problems. I would like to maximize $x_1+3x_2-x_3ge0$ while respecting the equality constraint $x_1+x_2=5$. How can...

## What is the difference between min- cut formulation and (bi) partitioning formulation?

I have a min-cut formulation and a bi-partitioning problem.The two problems focus on finding the minimal cut value separating the two partitions?So what are really the differences between...

## Logical constraint in ILP

I want to write the following constraint: Let $z$ be an integer variable such that $0le zle M$, and $t$ be a binary variable where $M$...

## Quasi-convex function must be "partially monotonic"?

$f(x)$ is quasi-convex, $$x^*inargmin_{xin C}f(x).$$ How to prove that, for any $ain C$, $f(x)$ is weakly monotonic in the direction of $(x^*-a)$? Is this...

Asked on 12/13/2020 by High GPA

## Constraint programming resources

I am looking for resources to learn constraint programming. I will divide the resources I am looking for in three types: ModelingIs there resources (books, articles, courses, etc.) that...

Asked on 11/28/2020 by Joffrey L.

## Pyomo variable creation dilemma

I am working on a pyomo model, and need to create a few different sets of variables that are dependent on a solution from a master model. I need...

Asked on 10/31/2020 by Ethan Deakins

## Convexity of the variance of a mixture distribution

$X$ is a random variable that is sampled from the mixture of uniform distributions. In other words:$$X sim sum_{i=1}^N w_i cdot mathbb{U}(x_i, x_{i+1}),$$where $mathbb{U}(x_i, x_{i+1})$...