# Operations Research Stack Exchange Community Digest

## Top new questions this week:

### Do you know production deployments of multi-objective optimization?

In mathematical optimization software, defining the weight and level (hard/soft) of each of the objectives/constraints is often difficult for the business people at software development time, due to ...

multi-objective-optimization

### Product of weighted binary variables equivalent to sum of weighted binary variables?

I'm working on an optimization problem with a non-linear objective function of the form $$\max\prod_{i=1}^{n}(1-a_{i}x_{i}).$$ The objective function represents the combined probability of success for ...

optimization mixed-integer-programming linearization

### Name for this ILP problem type

I am considering automating testing of down-stream testing of packages that depend on other packages. There are test sets $T_1,\ ..., T_n$ which can be tested or not tested, which each have a time ...

mixed-integer-programming terminology packing

### How to modelize a non-overlap constraint between 2 groups of tasks?

Let us consider the following problem : Let $T$ be a set of tasks. Each task $t \in T$ has a duration $d_t$. Let $T_1 \subset T$ and $T_2 \subset T$ such as $T_1 \cap T_2 = \emptyset$ How can I ...

modeling constraint scheduling

### Are simulations a form of multi-objective optimization?

Where is the line when an approach is called multi-objective optimization? For example: Problem Presume I want to optimize an optimization problem, for example nurse rostering, with 2 soft constraints:...

multi-objective-optimization

### Practical open source LP solvers for large linear programming problem with $10^7$ parameters

I have an LP problem of the form $\min\ c^Tx$ subject to $Ax\leq b$ where $x$ consists of 30 million parameters and $A$ is a very very sparse matrix of size 30M by 30M (with only 3 ones per row). I ...

mixed-integer-programming linear-programming convex-optimization cvxpy interior-point-method

### If continuous variable < constant then same variable = 0

When I come across with a situation needs an if-then constraints I visit Larry's post. I am a bit confused with the titled constraint this time because I am not trying to set $y$ based on $x$ but ...

mixed-integer-programming linear-programming linearization

## Greatest hits from previous weeks:

### Solving a knapsack problem with a lot of items

I am wondering what are the fastest ways(faster than classical dynamic programming) to solve the knapsack problem (to optimality) with $n$ items when $n$ is nearly equal to $10000$ ? Apart from ...

dynamic-programming knapsack

### How to innovate in OR

I am a graduate student in OR and I want to build one or two independent projects that go beyond academic projects in my university. I would like to target average people and/or those in the industry ...

applications

### Great Unsolved Problems in O.R

More than 10 years ago, there was during an INFORMS annual meeting a session dedicated to “Great Unsolved Problems in O.R.” (you can find a small report of that session on this webpage). Which are ...

open-problems

### How to represent an integer variable via binary variables?

Suppose we have a model with $N$ integer variables, i.e. $x \in \mathbb{Z}^{N}$ with $L \leq x \leq U$. How can we represent the integer variables via binary variables? Or in other words: how can we ...

mixed-integer-programming modeling binary-variable

### Is it necessary to study rigorous math courses in OR?

I am a business student with engineering background and I am studying papers published in some journals like Management Science, Operations Research, Math of OR and they use some notations and ...

optimization reference-request probability-theory

### Linear Optimization Library for C++ with GPU Support

Does anyone know any linear optimization libraries for C++ supporting GPUs for parallelization? If multiple, which do you recommend? The GPU support is important to me since I am dealing with large ...

optimization linear-programming c++ parallel-computing

### Is there a SQL/English like language that lets you define formulations given some data?

It would be very useful for beginning and non technical users to be able to define models in a way that was natural for them. Further this could perhaps assist generating some kind of generic ...

mixed-integer-programming applications modeling

## Can you answer these questions?

### Building model takes so much time in Cplex

I am a beginner in CPLEX. I have a model with about 1 million constants and 800k rows and 1.6 million columns. I implemented in both GAMS and CPLEX (C# as the platform). The final solution for both is ...

optimization cplex gams c#

### Polynomial Time Solution For a Mixed-Integer Linear Programming Specific Case

Consider the following mixed-integer linear programming (MILP): \begin{equation*} \begin{array}{ll@{}ll} \text{maximize} & 1 & \\ \text{subject to}& x_{i} \geq 0, &i=1 ,\dots, m\\ ...

mixed-integer-programming linear-programming integer-programming algorithms computational-complexity