# Questions tagged [mixed-integer-programming]

For questions about mathematical optimization problems involving both continuous and binary or general integer variables.

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### Guides for strong MILP Formulations

When developing MILPs, often there are different alternatives possible to express a constraint. The question then arises, which of the alternatives is better, meaning, which alternative is expected to ...
488 views

### MILP - stronger models

Let $y, x_1, x_2, x_3$ be binary variables. The following holds: $y=1 \implies x_1=1, x_2=1, x_3=1$ I can model this by requiring (1) \begin{align}x_1 &\ge y\\x_2 &\ge y\\x_3 &\ge y\end{...
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### 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 ...
85 views

### Minimax problem with a large high dimensional feasible region

How to solve minimax mixed integer problem with a large high dimensional feasible region? \begin{aligned} \max_{\vec{x}}\min_{\vec{y}} \quad & \vec{r} \cdot \vec{x} + \vec{s} \cdot \vec{y}\\ \...
116 views

### Is that Ok to exclude fixed components from an objective function?

Suppose we have the following objective function with one decision variable $x_i$ where $p_i$ is a fixed parameter for each $i$ and also, $a$ is a constant for the problem \begin{align} \label{eq} \...
265 views

I'm totally new to the world of optimization and I have an optimization problem that I think it can be formulated as Mixed Integer Quadratically Constrained Quadratic Program (QCQP) but I'm not sure ...
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### Linearization of a quadratic model, what is the difference while using gurobi?

I have a quadratic model of parking $N$ cars in $S$ separate lanes as follows. Each car has an arrival time and a departure time. Departure follow the last in first out principle. The objective is to ...
253 views

### CPLEX log always the same after hours ("Gap" and "Best Integer" always blanks)

I'm using the Java API of CPLEX 12.6.1 (with license) to solve a MILP (Mixed-Integer Linear Programming) maximization problem. The point is that, after 21 hours, CPLEX has consumed 32 GB of RAM and ...
152 views

### Solver Recommendation : Discrete Variables and Quadratic Constraints

I would like some solver recommendations to solve a problem with boolean/integer variables, mostly linear constraints but also some quadratic constraints. I also have an objective to minimize which is ...
194 views

### Simplified risk game: writing a pratical Minimax objective for mixed integer programming

Problem To ensure fairness of the game, I am writing a bot that plays against itself. I have trouble rewriting a minimax objective to a practical maximization in mixed integer programming. The amount ...
89 views

### Benders Decomposition for deterministic MILP

When I think of Benders Decomposition, I typically think of two-stage stochastic programs. However, I was wondering if there is any application to decomposing a large scale deterministic MILP with ...
35 views

### behaviour of CPXsetincumbentcallbackfunc

I am using the incumbent callback CPXsetincumbentcallbackfunc to identify integral solutions that do not satisfy nonlinear constraints that are not explicitly part of the constraint set. When such a ...
93 views

### Problems with a MILP

I need some advice, any hints will be appreciated. I have a MILP and I am using Gurobi to solve it. I have a feasible integer solution. When I use mipstart, after ...
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### CPLEX Indicator Constraints in Java API

I'm using the Java API of CPLEX (12.6.1 version) to solve a MILP problem. This is how I create 'normal' constraints: ...
111 views

### The precision of the decimal number of the Cplex

I have faced a little weird problem when I use Cplex to solve my test problem. Basically, some of my data are float numbers up to three decimal numbers (For instance, 0.627). But, when I print out the ...
120 views

### Water quality component optimization

I have an optimization problem that I'm attempting to tackle. As you can see in the image below, there's a graph network through which water flows. I've drawn out the problem in the image to explain ...
269 views

### What is a good way to penalise LP relaxation?

I have a binary integer program. It is of a large size and the solver is taking longer time. I am thinking of relaxing the binary integer variable and making it a continuous variable. How can I ...
107 views

### Docplex, CPLEX Warning 1036 :

I am trying to solve a large-scale MIP problem. I have the following errors, I know, it's about the data, but I can't change the data. Is there a method to deal with it? ...
146 views

### CPLEX ignores a feasible solution given as start one

Assume we have 100% feasible solution for the model with decision variable a[i]. Then we are changing the objective function on something similar to ...
92 views

### Approximately evenly-spaced subsequence

Suppose you have $n$ time series data where the times are in arithmetic series with difference $d$, and suppose further that some of the data are missing at random (say, $p=.30$). Now suppose you want ...
240 views

### Forbid transformation of max(x,y) into MILP

The function $\max(x,y)$ can be linearized by making use of additional binary variables. I suppose global optimisers are implemented to perform this transformation automatically. Is there a global ...
133 views

### Combinatorial Optimization Problem using IBM ILOG CPLEX

Consider the combinatorial optimization problem described as below. Let $D=(V,A)$ be a directed graph with $V$ the set of vertices and $A$ the set of arcs, i.e., $A=\{(i,j)\mid i,j\in V\}$. On each ...
111 views

### Multiple If else constraints in Mixed integer programming

How to formulate the following as constraints in MILP? a = y, if x= 0, a = 0, if x != 0, . . . . a[i][j] = b[i][j-1] + y, if x[j]=i, a[i][j] = a[i][j-1], if x[j] != i, ... . . . b...
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### How to model this multi-commodity flow problem with a twist?

Problem description I am working on a variation of the multicommodity flow problem on a graph $G=(V,E)$. I have requests $r_{uv}$ for pairs of nodes $(u,v), u\in V, v\in V$, which means that $r_{uv}$ ...
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### For docplex, it's possible to set the number of iterations without improvement?

When running the cplex model, I noticed that the CPLEX repeats the same gap value several times. I ask if there is a parameter in docplex that limits the number of iterations without improvements or ...
83 views