# Operations Research Stack Exchange Community Digest

## Top new questions this week:

### Integer column generation without branch & price

Consider the following situation. I have an integer program which I want to solve using column generation. After a suitable decomposition, the master problem has decision variables that select the ...

column-generation dantzig-wolfe-decomposition branch-and-price asked by Curious Score of 10 answered by Kuifje Score of 9

### Nonlinear optimization with constraint involving long product of optimization variables

I solve a nonlinear optimization problem of the form \begin{align} &\max x_0 \text{ such that } \\ &\left[ \sum_{j=0}^N \left(\alpha_j x_0^{j} \prod_{k=3}^j x_k \right)\right]^2 + \left[ \...

optimization nonlinear-programming asked by Dan Doe Score of 7 answered by Erwin Kalvelagen Score of 5

### Additional resources for this type of problem formulation

I'm working on a problem with the following formulation: \begin{align} \min&\quad\sum_{i \in N} \sum_{j \in J} V_{ij}x_{ij} \\ \text{s.t.}&\quad \sum_j x_{ij} = 1 \quad \forall i \in N\\ &...

mixed-integer-programming modeling graphs asked by Bob Jeans Score of 5 answered by Erwin Kalvelagen Score of 5

### Graph coloring problem while counting cliques

Let $G$ be a graph with a set of nodes $V$ and a set of edges $E$. Let $G'$ be a graph with the same set of nodes $V$ but a second set of edges $E'$. For a set of nodes $X\subset V$, we denote $f(X)$ ...

combinatorial-optimization constraint-programming graphs asked by Jin Kazama Score of 5

Consider a Geometric Program (GP), $$\begin{array}{cl} \operatorname{minimize} & f_{0}(x) \\ \text { subject to } & f_{i}(x) \leq 1, \quad i=1, \ldots, m, \\ & g_{i}(x)=1, \quad i=1, \... optimization cvxpy geometric-programming asked by Apprentice Score of 4 answered by ErlingMOSEK Score of 3 ### Software for Feasibility Problems I face a feasibility problem of type$$ c_i(\boldsymbol x) \leq 0, i = 1, \dots, \mathcal{I} \\ c_e(\boldsymbol x) = 0, e = 1, \dots, \mathcal{E} $$where \mathcal{I} + \mathcal{E} \gg \text{dim}(\... nonlinear-programming constraint-programming software feasible-points asked by Dan Doe Score of 3 ### Reformulating undirected to directed edges for MCF As stated in this paper, there is a technique to reformulate a multi-commodity flow problem (MCF) with undirected edges to its equivalent version with directed edges. By quoting them: The ... graphs network-flow asked by Daniele Cuomo Score of 3 answered by David Torres Score of 3 ## Greatest hits from previous weeks: ### 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? optimization modeling constraint asked by A.Omidi Score of 12 answered by dxb Score of 23 ### Are there any COVID-19 (coronavirus) related optimization problems with input datasets that we can "crowd solve"? Is anyone aware of a medicine/vaccine related challenges with a good problem definition and some available input datasets, ideally related to COVID-19? What kind of constraint solving challenges would ... practical-or medical-application asked by Geoffrey De Smet Score of 41 answered by Sebastiaan van den Broek Score of 17 ### List of Implementations for common OR problems For the TSP there famously is the concord solver (http://www.math.uwaterloo.ca/tsp/concorde.html) which is argubly the fastest exact solver for the TSP. There are many other problems that also show ... algorithms online-resources software vehicle-routing implementation asked by PSLP Score of 23 answered by Geoffrey De Smet Score of 23 ### How Close Is Linear Programming Class to What Solvers Actually Implement for Pivot Algorithms As part of a final project for my linear programming course, I have been asked to discuss implementations of pivot algorithms, including which combinations of the ideas we have talked about in class ... linear-programming solver asked by Sean Kelley Score of 14 answered by Mark L. Stone Score of 21 ### No executable found for solver 'ipopt I know that there are some questions concerning this type of error, for example, this link. I first installed the latest version of ipopt through command line into my Pyomo environment and got the &... optimization python pyomo modeling-languages asked by Sik Sik Score of 1 answered by Sik Sik Score of 4 ### Are programming languages necessary/useful for operations research practitioner? This semester I will start teaching Programming in Python to Master students in Supply Chain Management. I would like to start the first lesson with "Why learning programming languages will be useful ... applications software asked by Atilla Ozgur Score of 19 answered by Antarctica Score of 28 ### Can we consider the (Famous) "Trolley Problem" as an Optimization Problem? In the (famous) Trolley Problem (https://en.wikipedia.org/wiki/Trolley_problem) - a runaway train is out of control and unfortunate people are stuck on two different railway tracks. The railway ... optimization asked by stats_noob Score of 9 answered by Sune Score of 37 ## Can you answer these questions? ### Programming product of variables in r I am trying to model a MILP, where in the objective, the product of two variables is introduced. This is solved through the introduction of a new variable according to the following logic: "... r asked by user9867 Score of 1 ### Determining the number of nodes within a cycle for an MILP problem I have a MILP problem that requires knowing the number of nodes within a cycle (there will be multiple depending on inputs). I believe this will involve tracing nodes/values within cycles using the ... optimization mixed-integer-programming gurobi matlab asked by user9899 Score of 2 ### Simplification of nonlinear constraint for optimization I solve a nonlinear optimization problem with constraint$$ \sum_{j=1}^S \ln \Bigg( \Big(1 -x_j c_k + y_j d_k\Big)^2 + \Big( x_j d_k + y_j c_k \Big)^2 \Bigg) \leq 0, \: k = 1, \dots , K  where the ...

optimization constraint asked by Dan Doe Score of 2
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