Questions tagged [indicator-constraints]
For questions on constraints controlled by binary variables.
57
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Mixed Integer programming, the big M
In the constraints below, why have they used the big M? What do we look for in order to identify the big M in other questions?
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2
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154
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Matrix lookup modelling variants
As part of a bigger model I have a matrix of variables $x_{ij} \geq 0$ and a "selector" set of variables $y_j \in \{0,1\}, \sum_j y_j = 1$.
From $x_{ij}$ I'd like to get the variables of ...
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if else condition with multiple criteria in MIP
I have problem like below
Decision variable x1 >= 0
But it depends on selection variable s1 as binary variable
If s1 = 0 then x1= 0 and
if s1 = 1 then x1>0
how I can write this as constraint for ...
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2
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1
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Formulation for choosing how many items to manufacture
I am working on a scheduler for a manufacturing plant. I have currently set it up so the decision variables are set up as binary variables:
$x_{m,p,s}$ = 1 if machine m is running part p on shift s
...
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0
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Linearization of Conditional Constraints for MIP using Cplex
I'm currently working on a mixed-integer programming (MIP) problem and I'm trying to implement a set of conditional constraints in CPlex. These constraints involve decision variables that are indexed ...
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The rule of the slack variable in an indicator constraint
In some cases I have seen, the indicator constraint can be written as indcons(expression, binary_var). Then it is interpreted as follows:
$$LHS - slack (\leq = \geq)...
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2
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105
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Modelling a binary variable in LPs
I need your help.
I'm setting up an LP and I'm trying to find constraints to introduce the binary varibale $b_{ij}$. So it should take the value 0 if the sum of all $a_{ij}$ values to the period t are ...
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4
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Rewriting if-then constraints of binary summations
Suppose both $x_{i,j}^{ab}$ and $y_{i,j}^a$ are binaries. Then how can I rewrite the following if-then in linear form?
$\sum_b x_{i,j}^{ab} \ge 1 \implies \sum_{i,j} y_{i,j}^a = 0$
I was thinking of ...
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Assistance in formulating implication constraints for inequalities
I would like to seek some advice on modeling the following logical implications, where $\delta$ is a binary variable, $D_{j}$ and $A_{j}$ are nonnegative discrete variables, and $p_{j}$ are ...
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[OR-Tools][CP-SAT] Implement an indicator function in a constraint
Good morning ! I would like to implement this constraint using CP-SAT (see image below).
x_i,j is a boolean variable, a and b are given. The problem is that I don't know how to implement the ...
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How to enforce logical implication $\sum_j a_j x_j \le b \implies \sum_j c_j x_j \le d$
Some modeling languages and solvers support indicator constraints of the form $$y=\hat{y} \implies \sum_j a_j x_j \le b,$$ where $y$ is a binary decision variable and $\hat{y}\in\{0,1\}$ is a constant....
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Using indicator constraint with two variables
I want to use the sum of two binary decision variables (when their sum equals to one) as the condition of Model.AddGenConstrIndicator https://www.gurobi.com/documentation/current/refman/...
3
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1
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Modelling Question
Let $W^C_t$, $W_t$ be binary variables and $p$ an integer variable with $1 \leq p \leq 3$
The variables are related through the following equation:
$$W^C_t = \sum_{\theta=1}^{p} W_{t-\theta}$$
I can ...
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Is this constraint with an indicator function nonlinear?
We have two variables $x\geq0$ and $y\in\mathbb{Z}^{0+}$.
We have this constraint in our model
$$x = \sum_{i = 0}c_i \mathbb{1}_{\{y=i\}}$$
where $c_i$ is a parameter and $\mathbb{1}_{A} = 1$ if $A$ ...
user10774
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How to write this logical expression with Gurobi + Java, or express it as a big-m formulation
I am trying to write the following expression in Gurobi+Java or Gurobi+python, if it is more practical It could be expressed as a big-M formulation.
\begin{equation} \label{const4}
\text{D}_{uv} =
...
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How to express this constraint efficiently?
Let, $\mathcal{C}=\{1,2,\cdots,C\}$,
$\mathcal{U}=\{1,2,\cdots,U\}$
$\mathcal{S}_u$ is a subset of $\mathcal{C}$ with $u\in \mathcal{U}$
$d_{u,c}$ is a binary variable with $u=1,2,\cdots,U$ and $c=1,2,...
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2
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How to model the following "if, then" constraint
There are two matrices:
Matrix $S^{v\times v} \in \{0,1\}$ this is a know parameter.
Matrix $X^{v\times p} \in \mathbb{N}$. Elements of $X$ are the variables.
I want to model:
$$\textrm{if }s_{v v'} =...
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How to model logic constraint: $y=1$ if $a\le x\le b$ and $y=0$ otherwise?
I am trying to formulate indicator-type of constraints. $y$ is binary $0$ or $1$ and $x$ is a continuous variable.
$$ y =
\begin{cases}
1, & \text{ if } a \leq x \leq b \\
0, & \...
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Piecewise function with two variables
I have a square like region centered at the origin, which is divided into 4 sub-regions. Region 1 can formed from by the diagonal of a square, $x + y \leq 0$. Region 2 is formed by joining the center ...
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gurobi bigM constraint vs. epsilon
I am new to mathematical programming and I am trying to implement case specific constrains in Gurobi with Python.
I am wondering about how I can implement my constraints in the fastest or most common ...
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3
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Converting if conditions to linear constraints
I have an optimization problem and I want to convert the following if conditions to linear constraints:
If $(y_1 > U_1)$ and $(m_1)$ and $(E_1)$ then $x_1=1$
If $(y_2 > U_2)$ and $(m_2)$ and $(...
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152
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Binary variable to indicate zero probabilities
I have a finite probability distribution $p_1, p_2, \ldots, p_n$ (but these are variables of an optimization problem). Moreover, we have monotonicity, $p_1 \geq p_2 \geq \cdots \geq p_n$.
Assume we ...
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1
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Robust way to implement $(x=0) \Rightarrow (y=0)$, with $x$ nonnegative and $y$ binary
I am formulating a MILP in which there is a continuous variable x and a binary variable $y$.
In the program formulation there are the following constraints:
$Ay\leq x \leq By$ (with $0\leq A\leq B$). ...
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2
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how can I modify my LP to activate the most constraints possible?
Suppose I have a linear program (LP) that has many optimal solutions. Of those optima, I want to find the optimum that activates (aka, "pegs" or "bumps") the largest number of ...
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If-then condition formulation to avoid variable multiplication
I'm trying to formulate the following logic:
If $y_i =1$, then $c_i \leq x_i$
If $y_i =0$, then $c_i \leq 0$
Where $y_i$, $c_i$, and $x_i$ are decision variables.
The easy way would be to write:
$$c_i ...
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Can you calculate the mean of some MIP variables using linear constraints?
got a lingering question from a graduate course in integer programming that's been bugging me ever since.
Is it possible to find the mean of some variables in a MIP without resorting to quadratic ...
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Conditional constraint with a strict inequality
It's almost this question: Formulating the conditional constraint
But there they have non-strict inequality. I have $x_i$ a boolean decision var and $Q_i$ as a nonnegative integer decision variable ...
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0
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Multiple conditions in indicator constraint of Gurobi
I'm working on a vehicle routing problem, in which a vehicle need to pick up amounts of things in some nodes. I'm trying to solve it by Gurobi optimizer. Except for meeting the time windows of each ...
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Model "if and only if" indicator constraints in Linear programming
Apologies if this question has been asked, but I haven't been able to find it. I'm modelling something with Gurobi and want to do the following:
\begin{align}\text{cond} < \dfrac{1}{3} &\iff x =...
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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:
...
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How to couple a binary variable to a continuous variable to indicate values greater 0
I have a continuous variable $x_t$. A binary variable $b_t$ should be coupled to $x_t$ such that $b_t$ has the value $1$ if $x_t$ has a value greater than $0$ and $b_t$ has the value $0$ if $x_t$ has ...
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MILP constrained by the minimum number of satisfied constraints
I have an MILP where we have
$$
t_k = \sum_i P_i\cdot C_{ik} : P_i\ \in \{0,1\}, C_{ik} \in I^+
$$
and our model is constrained by the number of times $t_k$ is bigger than a certain value $T_k$.
$$
\...
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1
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475
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if-else query depending on optimization variable in Gurobi (Java)
I am looking for the most elegant solution to the following problem:
I have an if-else query that depends on my optimization variable $x_i$.
If $a \leq b_i + x_i$, the parameter $c$ should take the ...
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2
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If-then constraint with continuous variables
I was usually using if-then constraints with integer variables but ended up using continuous variables and got confused. I have variables $x_{ij}\in\mathbb{R}_{\geq 0}$, and would like to force the ...
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Logical equivalencies to modeling an indicator decision variable in transportation problem
I am formulating a model that seeks to minimize the cost of shipping goods from factories to warehouses, where the cost of shipping is independent of the type or amount of goods being shipped (except ...
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Modeling the product of two variables
Suppose we have two continuous nonnegative variables $X_{1}$ and $X_{2}$ both bounded by the number $M$ from above.
I would like to model the following:
If $X_{1} > 0$ then $X_{2} = 0$
If $X_{2} &...
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How to model this chain of logical implication II
I would like to seek some advice on modeling the following (chain of) logical implication:
For instance $\omega_{xz}$ might indicate precedence, i.e., $x$, $z$ being the nodes $x$ and $z$, ...
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How to model this chain of logical implication
I would like to seek some advice on modeling the following (chain of) logical implication:
For instance $\omega_{xy}$ might indicate precedence, i.e., $x$, $y$ being the nodes $x$ and $y$, ...
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0
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Indicator function for integer variable with inequality constraint
I have $n$ integer variables $\vec{x}$ with the following integer programming problem.
$$
COST = \sum^{n-1}_{i = 0} a_i x_i + \sum^{n-1}_{j=0} b_j I(x_j > 0)
$$
Here, $a_i, b_j \in \mathbb{R}_+$ ...
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470
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Portfolio optimization with indicator function constraint in CVXPY
I have the following portfolio optimization problem that I want to solve using CVXPY: \begin{align}\min_w&\quad w^\top\Pi\\\text{s.t.}&\quad\sum_{i=1}^nw_i=1\\&\quad w^\top\Sigma w\le\...
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2
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420
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Switching of decision variables to be larger than or equal to a decision variable according to an indicator variable value
I would like to seek some advice on modeling the following:
I have two integer decisions variables, $x, x'$, that are either equal or greater than zero and either of them is greater than or equal to a ...
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260
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Switching of decision variables to be equal to a certain decision variable according to a binary (indicator) variable
I would like to seek some advice on modeling the following:
I have two integer decisions variables, $x, x'$, that are either equal or greater than zero and either of them is to be equated to a third ...
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1
answer
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Formulating indicator constraint set
I am having difficulty formulating the indicator constraints for the following:
Consider a set of $A_{n}$ decision variables such that $A_{1},A_{2},⋯,A_{n}<A$. While all of them are integers that ...
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1
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Reformulating to locate the second largest decision variable of a set of decision variables
Consider a set of $A_{vn}$ decision variables such that $A_{v1},A_{v2},\cdots,A_{vn}<A$. While this is the standard formulation finding the maximum value of $A_{vn}$, I would also like to find the ...
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Linearize sum of continuous and boolean variable
For maximizing the objective function $\sum_i{d_i y_i}+ A x - B \cdot \mathbb{I}_{x>0}$, how can I linearize $ A x - B \cdot \mathbb{I}_{x>0}$ term where $d_i, A$ and $B$ are positive constants ...
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Formulating the conditional constraint
I want to develop a model extension of capacitated location problem.
The variables are a binary $x_i$ and a continuous $Q_i$. The following condition must be satisfied:
if $x_i = 0$, $Q_i$ must be ...
4
votes
2
answers
307
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Model "If, then" constraint
How to model the following "If, then" type constraint?
If $\sum\limits_{i \in I}x_i = 0$ then $\sum\limits_{j \in J}x_{j} = n$
where $x$ are binary variables, $n$ is a known parameter and $...
4
votes
3
answers
745
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Faster implementation of "or" constraints in ILP
I have implemented a set of "or" constraints in my ILP using binary decision variables (as in this method). It works fine for smaller problems, but when I try to increase the number of ...
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1
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Indicator function in math programming
Let $x$ be an integer variable that takes the values $1$, $2$ or $3$.
Let $y_1$ and $y_2$ be binary variables.
I want to express the two following logical constraints:
if $x=2$ then $y_1=1$
if $x=3$ ...
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votes
1
answer
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How to optimize with "if" constraints
The minimizing problem is the following :
$$ \underset{w}{\operatorname{argmin}} \sum_{i=1}^{n}\left[w_{i}\times (\frac{Vw}{\sigma})_{i} - b_{i}\right]^{2}$$
with $V$ a $n\times n$ matrix (covariance ...
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