Operations Research Stack Exchange
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TSP with Repeated City Visits

Suppose that we have a standard TSP, except that it is required to visit each city at least once instead of exactly once. The challenge is: how to transform this problem to a standard TSP? To that end, one construct a new network with arcs…
DSPinfinity
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Solve nonlinear programming problems practically

In an exam, I studied Theoretical approaches to converting constrained minimum problems into unconstrained minimum problems. Specifically: KKT conditions Projection Gradient Descent Penalty and Barrier Methods But how are nonlinear constrained…
Francesco Ladogana
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1 answer

Java in OR: Which non-constraint solving libraries do you use?

If you're programming OR challenges in Java, besides using constraint solvers, which other libraries do you typically use? Maybe for common tasks such as data reading, etc. Why? How do they make your life easier?
Geoffrey De Smet
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Python for OR: Which non-solver libraries do you use?

If you're programming OR challenges in Python, besides using mathematical optimization software (= constraint solvers), which other libraries do you often use? Maybe for mundane tasks such as data parsing, etc. Why? How do they make your life…
Geoffrey De Smet
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Prove that $x^*$ is an optimal solution where $f_0$ is $C^1$ and convex and $f_i$ are $C^1$ and strictly convex functions

Let $x^*$ be a feasible solution of the following convex optimization problem \begin{align}\min&\quad f_0(x)\\\text{s.t.}&\quad f_i(x)\leq0,i=1,\ldots,m\end{align} where $f_0$ is $C^1$ and convex and $f_i$ are $C^1$ and strictly convex functions.…
convxy
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Gurobi and CPLEX cannot exploit more than 32 cores of machine

I have some attempts to solve a scheduling problem using the Gurobi and doCPLEX API in python and .NET on Ubuntu-server installed on a hyper-computing cluster with 64 physical cores. Unfortunately, both solvers cannot exploit more than 32 cores and…
Mohammad Namakshenas
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0-1 knapsack with non-linear objective function

There's efficient algorithms for solving the 0-1 knapsack problems when the objective function is just a sum of profits. I am dealing with the following problem with non-linear objective function: $$\max_{S \subseteq N} \frac{\left( \sum_{k\in S}…
mike
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Shortest path problem with underlying continuous variables

I recently got interested in the following variation of the shortest path problem. I've looked in the literature for days but I couldn't find any paper studying this problem. I'd like to ask if you have seen this problem (or any similar problem)…
Tobia Marcucci
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How to model bicycle sharing scheme?

One of the problems I have recently considered is the problem of rebalancing bicycle stations for bike-sharing schemes all over the world. It is not a secret that the demand for bikes across the city varies (some people, including myself, prefer to…
bajun65537
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Counting the number of matchings in a complete bipartite graph

I am trying to count the number of matchings in a complete bipartite graph (perfect as well as imperfect). It's relatively easy for me to convince myself that there is $n!$ perfect matchings in the graph $\mathcal{K}_{n,n}$. However, I cannot seem…
Djames
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Is the order of edges in graph is changing the optimization result?

I am solving an optimization problem using Pulp and NetworkX. The problem is similar to the Minimum Vertex Set (MVS) problem. I have noticed that the optimizer is Scanning the edges according to their order in the entry of set edges and deciding…
Amedeo
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PAVA-like solution to simple QP

Let $l,u\in\mathbb{R}^n$, and consider the QP: $$\min_{l\le x\le u} {(\Delta x)^\top (\Delta x)}$$ where $\Delta x=[x_2-x_1,\,x_3-x_2,\,\dots,\,x_n-x_{n-1}]^\top$. I.e. we want to minimize the squared change in the elements of $x$ subject to $x$…
cfp
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Is there a way to use lazy constraints with Baron?

I am solving a non-linear mixed-integer programme with BARON. The objective function looks like $\big( \sum_i x_i \big) \cdot \big(\prod_i e^{-y_i}\big)$ (binary $x$ and real-valued $y$) and it has some quadratic constraints. My problem is that I…
Alberto Santini
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How to determine if this problem is NP-HARD or NP-COMPLETE?

Suppose that I have a pool with N nodes and I have to move the nodes one by one to another pool. For each move, consider a value on the edge linking the two pools. The goal is to find a order of nodes (for the N nodes) that minimizes the overall cut…
fathese
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Substituting inequality by equality constraints

Let $\mathbf{A}=\left(a_{ij}\right)$ be a $n\times J$ matrix with $a_{ij}\geq 0$, $n>J$ and such that no row or column has all its entries equal to zero. Let also $\mathbf{k}=\left(k_j\right)$ be a $J\times 1$ vector of non negative coeficients and…
Patricio
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