Is this resource-pattern branching rule exact in a branch-and-price algorithm...
I am implementing a branch-and-price algorithm for a scheduling problem. The compact formulation is decomposed by a Dantzig–Wolfe reformulation. Patients with identical characteristics are aggregated...
View ArticleEffect of nonnegativity constraints on solving ILPs
Consider the integer linear program (ILP)$$\max \{ c^T x \mid Ax = b, x \in \mathbb{Z}^n \},$$where $A$ is a totally unimodular matrix. It is well known that in this case, the ILP can be solved in...
View ArticleVariation of the multiple-choice multiple knapsack problem
I'm looking for an algorithm, preferably exact, to solve the following variation of the multiple-choice multiple knapsack problem: Given a set of items $N := \left\{1, \ldots, n \right\}$ partitioned...
View ArticleIs a block upper bidiagonal $\{-1,0,1\}$-matrix TUM for all $T$ if its...
Crossposted on Mathematics SESetupFix positive integers $p$ and $c$. Let $E \in \{-1,0,1\}^{p \times c}$, $P_1 \in \{0,1\}^{p \times c}$, and $P_2 \in \{0,1\}^{p \times c}$ be matrices satisfying the...
View ArticleWhat are the solvers that give a feasible solution within a given time?
What are the solvers that take the maximal computation time as a parameter and gives the best found feasible solution within this time.
View ArticleIs there any solver intended specifically for integer and binary variables...
Any solvers which can be integrated in python where we can quickly solve if we have integer and binary variables alone in our model other than normal solvers for MIP, MILP?
View ArticleCplex callback to cache the value of variables in the optimal solution for...
I am using Cplex version Version 22.1.1 (I know there are lots of other solvers).I am solving a lexicographic multi objective optimization problem using the c++ API.I would like to retrieve the value...
View ArticleWhy this ILP and LP are equivalent?
Let's consider a competition with $n$ questions. Each question has a price $p_i$ and a score $v_i$. To advance to the next round of the competition, we need to accumulate a minimum score of $D$. We can...
View ArticleCan I decompose all MIPs to 1 IP (Master problem) and multiple LPs...
Can decomposition (Benders) methods divide any MIP into 1 IP and multiple LPs? I know there should be some structures (e.g. block-angular) in the MIP to get benefits from decomposition methods....
View ArticleWhat are the differences between integer programming and constraint programming?
At first glance, integer programming (IP) and constraint programming (CP) appear to be very similar. What are the major differences between IP and CP?
View Articlelp_solve gives a very infeasible solution
I am trying to solve the following integer linear program using lp_solve: (there is no objective, so this is just asking about feasibility)min:;lhs = 133x + 142.4y + 125z - 266.13a - b - 25c;rhs =...
View ArticleNumber of Subtour Elimination Constraints for ATSP (DFJ Formulation)
In the DFJ formulation of the symmetric TSP, the subtour elimination constraints are typically written as:$$\sum_{\{i,j\} \in E: \ i \in S, j \notin S} x_{ij} \geq 2, \qquad \forall S \subset V, \; 3...
View ArticleAnyone have an explanation for QUICKXPLAIN that a mere mortal can follow?
I have been using CBC for some years solving various optimization problems, where each variable is a boolean. Sometimes I get an infeasible result. I'd like to compute a "reason" for the infeasible...
View ArticleMajorize instead of maximize
In my very limited knowledge of optimization there is always an objective function to minimize or maximize.I have a problem where there are binary and integer variables. The objective is to find a...
View ArticleNo good cuts for thousands of integer solutions thousands of times
I have tiny neat ILP which depends on the parameters $n,m$. I am interested in finding all solutions to this ILP which have a distinct ${\color{blue}{(S_i)_{i\in\{1, \dots , 6\}}}}$. However i need the...
View ArticleConditional constraint with a strict inequality
It's almost this question: Formulating the conditional constraintBut there they have non-strict inequality. I have $x_i$ a boolean decision var and $Q_i$ as a nonnegative integer decision variable such...
View ArticleHow to linearize min/max function of a large number of values as a constraint?
Assuming I have 100 variables $r_1 \dots r_{100}$ which can be positive or negative and I try to find the minimum of all of them in a MILP problem and bind that to a variable $y$.$$y = \min_{i \in \{1...
View ArticleHow to give a sufficient or necessary condition of a ILP's relaxation?
I have a class of ILP questions in the form of:\begin{align*}\text{Max} \quad & c^T x \\\text{subject to} \quad & Ax \leq b \\& A \in \{0,-1,1\}^{(m+n+mn)*(mn+n)}\\ & x \in...
View ArticleOutput Presolved model in AMPL
My question is related to this:https://discuss.ampl.com/t/obtain-presolve-output-reduced-model-without-solving-the-problem/2176Is there a way to export a 0-1 Integer Programming presolved model (output...
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Miller-Tucker-Zemlin subtour elimination constraints to obtain a minimum...
I need Miller-Tucker-Zemlin subtour elimination formulation for symmetric traveling salesman problem (STSP) to use to construct a minimum spanning tree. Ie,I need Miller-Tucker-Zemlin formulation for...
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