# Questions tagged [mixed-integer-programming]

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### Binarization for optimization problems

I have a nonlinear mixed-integer optimization problem, and because of very high complexity when solving it using methods like Branch and Bound, I resorted to solve it using alternating method and ...
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### Efficient solver of a Integer programming

I am solving an Integer programming using MATLAB, yet the efficiency is low. Here is the problem: Suppose $v$ is a $N \times 1$ vector. For $v_i \in v$, $v_i \in \{0,1\}$. $D$ is a 0-1 matrix, which ...
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### Cplex C++ Interface: How to add many constraints quickly?

I noticed that adding constraints to an IloModel one by one can be prohibitively slow. (I am referring to the construction of the model, not the optimization.) ...
35 views

### How to solve a system of linear equations with binary variables mod 2 with a constraint that is not mod 2?

I am trying to solve a system of $H \leq 4^n$ polynomial equations of degree $H$, where the variables $(x_1, x_2, \ldots, x_{2n}) \in \mathbb{Z}_2^{2n}$ are binary. The problem was that these ...
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### Split classroom sizes in half linear integer programming

I work for a school who is looking to split students into two groups for COVID related reasons. Ultimately we need to split the students by class section and try to keep families to be in the same ...
92 views

### How to speed up the Mixed-Integer Quadratic Program process?

Currently, I am solving a problem in the format: M is an integer as well. The problem that troubles me is that X is a vector in {0,1} with a size of 7000. I use the solver in https://github.com/...
116 views

### Using MILP to place a set of primers along a genome

Define variables $p_i,u_i\in\{0,1\}^G$, for $i=1,\ldots,8$ and $G=30000$. Let $v$ be a constant vector also in $\{0,1\}^G$, with approximately 25% of its entries equal to $1$ (randomly located). Let ...
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### Ways to speed up solving an LP with Google's ortools

I'm having an issue solving an LP of the form: $$\min z = c^Tx$$ $$\text{s.t.}$$ $$Ax \geq b$$ $$x\geq p$$ $1 \leq a_{ij} \ll b_i$, $p \leq 0$, and $c \geq 0$ The specific problems I'm running into ...
1k views

### C++ mixed integer nonlinear programming (MINLP) solver

Doing research project in material involving (mixed integer nonlinear programming) MINLP problem, we want to implement MINLP based on C++, because the majority of our project is based on C++. What ...
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### Constraints 'exactly/at most one non-zero element' without binary variables

In a much larger MINLP problem, I have set of variables $\{a_{ij}\}_{m,n}$, such that $0 \leq a_{ij} \leq 1$ for all $i$, $j$, which I could think of as a matrix, for which I have two requirements: ...
98 views

### $L_2$ projection with integer constraints and prescribed sum

Suppose I am given a vector $v^0\in\mathbb{R}^n$ and integers $k,\ell\in\mathbb{Z}$. Assuming $k$ is close to zero (e.g. $0\leq k\leq5$), is there an algorithm for solving the following integer ...
24k views

### What's the fastest software(open source) to solve mixed integer programming problem

I have a mixed integer programming problem. And I am current using GLPK as my solver. But I found that GLPK is good for Linear Programming problem, but for Mixed Integer programming, it requires much ...
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### Relaxing a variable in MIP

I have this MIP optimization problem, with couple of binary variables; however when I relax one of the binary variables the optimal solution of the objective does not change. But the solving time ...
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### Resources for large-scale MILP optimization

With the advent of "big data" applications, different algorithms have to be used to efficiently solve optimization problems, even in the convex case (e.g. the recent success of stochastic gradient ...
366 views

### Solving nested MILP problems

I want to solve a family of MILP problems (indexed by $k \geq 0$) of the following type: \begin{align} \max \; c^Tx \;\; s.t. \\ Ax \leq b \\ d^Tx \leq k \end{align} In other words, the ...
173 views

### enhancing a MIP formulation of Ising model [closed]

I want to construct a MIP formulation for Ising model. For simplicity, I will only include terms involving nearest-neighbor pairs and triangular terms. I propose one formulation and ask whether there ...
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### Comparison of the time efficiency of an optimization problem formulated as a Network Flow model and Mixed Integer Programming

In combinatorial optimization, there are many problems that can be formulated as either Network Flow model or Mixed Integer Programming (MIP), e.g. supply chains, transportation, and graph-base ...
334 views

### MILP formulation and optimization

For $i=1, \dotsc, K$, we have $n_i$ ordered real numbers: $$x_i(1) \leq x_i(2) \leq \dotsc \leq x_i(n_i)$$ I want to solve the following optimization problem: \begin{align} \mathrm{maximize} \; \...
505 views

### Mixed-integer quadratic programming, state of art [closed]

I used Gurobi with a MIQP with 26 binary variables and 26*4 interaction term without any other constraint. The speed is very slow already.... I want to ask what is the state of art of MIQP solvers. ...
660 views

### Solver for a MIQP with an indefinite coefficient matrix

Do CPLEX or Gurobi handle MIQPs with indefinite coefficient matrices? The problem I am dealing with has quadratic terms in which one variable is binary and the other variable is continuous. The ...
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### learning Gurobi for MIP calculation [closed]

I am a new learner of Unix, python and Gurobi for MIP calculation. I basically finish reading the quick start guide in Gurobi website but still feel that I need more training to use this combination ...
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### Constrained System / Combinatorial Problem

Let $x\in \mathbb{R}^{n}$, $Y\in \mathbb{R}^{mxn}$. We can then define: $row_{i}(Y)=$ $i^{th}$ row of $Y$ $column_{i}(Y)=$ $i^{th}$ column of $Y$ $x_{i}=i^{th}$ element of $x$ $sum(x)=$ sum of ...
190 views

### Solve chemical formula (number of molecules in reaction)

In order to balance atom count in chemical equation: a O2 + b C12H24O11 → c CO2 + d H2O I make linear equation: ...
71 views

### How to model a pump behavior using MILP?

The behavior of a pump is the following: If $h \geq h_{start}$, then pumped flow is a constant $Q_p$. The pump works as long as $h > h_{stop}$ If $h \leq h_{stop}$, then pumped flow is 0. The pump ...
201 views

### Good approximate solutions for a MILP problem

The company I work for has been developing an application for real-time control of sewer networks. Every 5 minutes, a MILP problem is built or updated, then solved using Gurobi. For mid-sized cities, ...
187 views

### Optimization algorithm selection for 3 variable integer

I have a cost function: $f(x,y,z) \rightarrow \mathbb{R}$ it is very expensive to evaluate $x,y,z \in \mathbb{Z}$ 0 < x < 10 0 < y < 30 0 < z < 100 I thought it was convex, not sure ...
563 views

### Binary Integer Programming Problem Subject to a Set of First-Order DEs

Recently, I came across an optimization problem with binary decision variables which was constrained with a set of first-order differential equations (resulting from a continuous-time Markov chain ...
306 views

### Closest interior point on integer grid to a vertex of a convex polyhedron

I have a 3 dimensional convex polyhedron whose vertex coordinates are rational. For one of these vertices, I would like to find the nearest integer grid point (under the Euclidean metric) that is ...