Questions tagged [logical-constraints]

For questions about constraints that can be expressed in (usually propositional) logic.

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3 votes
1 answer
70 views

Creating constraints dynamically in pyomo abstract model

I have a networkX graph with few nodes and these nodes have attributes such as "demand". ...
3 votes
2 answers
56 views

Constrained shift assignment problem using ilogcp solver can´t find an optimal solution

I´ve been trying to solve a contrained assignation problem given a set of constraints based in a real-world problem. I modeled the problem in AMPL as follows: ...
1 vote
1 answer
90 views

PULP : Constraint violation - multiple of expected value

I am developing a linear programming model in PULP that sends material from Origin Facilities to Transfer and Final Treatment Facilities. The objective function is based on summing the transport and ...
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10 votes
0 answers
100 views

which method has been used to automatically reformulate logical constraints in a standard MIP solver?

There are many of the formulations to linearize logical constraints by introducing new auxiliary binary or any appropriate variables and adding the corresponding constraints to the model. It can be ...
  • 6,206
3 votes
1 answer
205 views

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 ...
  • 133
3 votes
1 answer
102 views

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 votes
1 answer
68 views

Disjunctive Constraint , Using Binary Variable to Replace a If or condition

I am trying to use a binary variable based on an inequality. The value of binary variable $q $ is 1 or 0 based on the following equation. [ $q $ = \begin{cases} 0,& \text{if } b \geq \pi ,\\ 1,...
2 votes
3 answers
313 views

How to formulate if-then for two sums in an integer program

I have two sets of Boolean variables, $x_1, \dots, x_n$ and $y_1, \dots, y_m$ and a positive integer $b$. I would like to add the constraint: $$\text{If }\sum_i x_i = b \text{ then }\sum_i y_i > b$...
  • 131
3 votes
3 answers
482 views

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 $(...
  • 77
5 votes
1 answer
109 views

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 ...
3 votes
1 answer
183 views

Disjunctive equality constraints: modelling

I have the following constraint in my model: $$x = 0 \lor \sum_{i=1}^n y_i = 3$$ where $x$ and $y_i$ are all binary variables. How this can be linearized by means of big-M notation? Should I include ...
  • 33
7 votes
4 answers
858 views

is prime? in Operations Research

Is there a way to linearize is prime? in Operations Research? is prime(n) being true if $n$ is a prime number or false otherwise....
  • 533
2 votes
1 answer
57 views

Ensure that scheduled repeating maintenance has to be completed

I'm trying to model the scheduling of maintenance in some machines, and was wondering how I could ensure that, if maintenance is planned to start in period $t$, then it has to be carried out until ...
2 votes
1 answer
175 views

Gurobi add constraint which two variables cant be zero at the same time

I'm currently using Gurobi in python and trying to add a constraint that the variable will not equal to 0 at the same time, say a != 0 or b != 0, both a and b can ...
  • 145
3 votes
1 answer
250 views

Constraint on groups of variables

Assume a LP/MILP with a large number of variables. It is easy to formulate constraints to group variables such that each variable in a group takes the same value, if we know which variables are in a ...
  • 253
3 votes
1 answer
1k views

Complicated constraint with logical operators in PuLP

I have an optimization problem that I am trying to solve with PuLP. All the variables are Booleans. The variables that are "selected" will be true, all others false. Objective function is ...
  • 33
2 votes
1 answer
250 views

mixed integer programming with if then statement for two binary sequences

I have two random binary sequences of the same size, denoted as P1 and P2 respectively here. Let's say they are both the size of ten, like P1 = [1,0,1,1,0,0,0,1,1,1], P2 = [0,1,1,0,0,1,0,0,1,1]. I ...
3 votes
1 answer
133 views

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 ...
  • 143
2 votes
1 answer
93 views

Linearize product of $x\cdot y \text{ with } x,y \in \{-1,0,1\}$ for MILP

I have a problem where I have many products between variables drawn out of $\{-1,0,1\}$. Could you suggest a linearization in terms of variables in $\{-1,0,1\}$ or $B_1 - B_2$ where $B_i \in \{0,1\}$ ...
2 votes
1 answer
68 views

Represent the minimum between two terms as a continuous constraint

Let's consider the following minimization problem: \begin{align} \min_{x,a,b}&\quad X\tag1\\ \text{s.t.}&\quad X = \min(A,B)\tag2\end{align} with $A,B$ functions that depend on $X$. Is there a ...
  • 403
4 votes
1 answer
135 views

Constrain Mixed-Integer problem such that a graph is fully connected

I have a problem (see my questions about Architectural layouts which poses an interesting abstract question) where there exists an implicit (symmetric) graph whose values in the adjacency matrix are ...
3 votes
2 answers
143 views

Assistance in formulating binary constraint(s)

I would like to seek some advice on modeling the following logical condition: Given two groups of binary decision variables $A_{i}, i=1...n,$ and $B_{j}, j=1...m$. $A_{i}=1- B_{j}, \forall i, \forall ...
  • 695
5 votes
2 answers
460 views

In a MIP, how to force a decision variable to be zero unless the sum of specific other decision variables is equal to a certain number?

In an MIP, how can I formulate a constraint such that a decision variable is only greater (or equal to) zero if (and only if) the sum of different decision variables is equal to something. I'm working ...
5 votes
2 answers
423 views

How to linearize specific range constraints?

I would like to know about the linearization of the $(If, Then)$ constraints as follows: $$\begin{array}{l} \text { If: } \\ 15 \leqslant x \leqslant 25 \\ \text { then: } \quad y=\color{blue}{a} x+\...
  • 6,206
3 votes
2 answers
148 views

Write in ILP: If $x$ within range then $s=1$, else $0$

How can write the following function in LP: $$ s= \begin{cases} 1 & 1 \leq x \leq C \\ 0 & \text{otherwise} \end{cases} $$ where $x$ takes only non-negative integers and $C$ is some large ...
  • 33
5 votes
1 answer
408 views

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 =...
3 votes
2 answers
92 views

MILP modelling on minimal disturbance of right-hand-side to make a linear system infeasible

I try to model the following problem: given $z\in\{0,1\}^m$ and a linear system $Ax\le b(z), x\in\Bbb R^n, A\in\Bbb R^{d\times n}, b(z)\in\Bbb R^{d}$, where $b(z)$ means that some entries of $b$ are ...
2 votes
1 answer
45 views

How to write the following constraint? [duplicate]

I would like to write the following constraint, where $varBuyWater$ and $varSellWater$ are decision variables on how much water to buy and to sell. However, I do not want the solver to buy and sell ...
  • 507
3 votes
1 answer
243 views

Linearize x different of y in ILP

I am surprised I couldn't find an already written answer for my question in the internet. I want to linearize $x$ different of $y$ for two nonegative integer decision variables. I am not considering ...
  • 533
4 votes
2 answers
452 views

Modeling a constraint such that a set of binary decision variables do not equate to 1 simultaneously

I would like to seek some advice on modeling the following logical condition: I would like to ensure that a group of binary variables do not equate to 1 simultaneously, i.e., $\omega_{1}=1, \omega_{2}=...
  • 695
6 votes
2 answers
789 views

How to transform this logical if-then constraint?

Consider the binary variables $x, y, z \in \{0,1\}$. I'd like to formulate the two if-then constraints: $$ x + y \geq 2 \implies z = 0, \tag{1} $$ $$ x + y \leq 1 \implies z = 1. \tag{2} $$ Constraint ...
6 votes
1 answer
291 views

ILP Constraint to ensure exactly one constraint from a set of constraints is satisfied

Consider several Integer (0/1) ILP variables, i.e., Boolean variables, $x_i$'s. Consider an ILP constraint $x_1 + x_2 + x_3 \geq 1$ and another constraint $x_4 + x_5 + x_6 \geq 1$. I would like to ...
  • 871
3 votes
1 answer
430 views

If else condition to MILP

I have following problem: $c_i = 1$ if $X + \sum_j^N G_j = T$ else $c_i = 0$ Also there is another constraint which upper bounds equation $X + \sum_j^N G_j \le T$. $c_i$ is binary $X, T$ are ...
  • 1,589
1 vote
1 answer
131 views

Priority Constraint

Suppose I have the following set of binary variables: $X_i$: $I$ ranges from {1,..,4} Highest priority among the three variables $X$ , $Y$ and $Z$ $Y_j$: $J$ ranges from {1,..,3} $Z_k$: $K$ ranges ...
  • 21
1 vote
1 answer
111 views

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 $z$, ...
  • 695
1 vote
1 answer
89 views

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 $y$, ...
  • 695
0 votes
0 answers
56 views

Linearizing max constraint Problem [duplicate]

I want to linearize a max constraint as below: In which x_(i,t),are binary decision variables and T is a constant. How can I linearize this constraint?
6 votes
4 answers
772 views

Can this be formulated as one inequality

I have two binary variables $x_1$ and $x_2$ and a non-negative continuous variable $y$. In addition, I have the following two parameters $u>q>0$. I would like to formulate the following ...
  • 1,011
2 votes
1 answer
64 views

distance specific constraint

I have some points with determined coordinates $(a_i,b_i)$. A vehicle can move between these points based on rectangular distance. In more detail, we consider that the path between points is an ...
  • 445
1 vote
2 answers
316 views

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 ...
  • 695
1 vote
3 answers
356 views

How can I linearize this IF-THEN constraint?

Let $P_{t,u}; t=1,2,\ldots,T, u=1,2,\ldots,U$ be known values $\alpha$ is also a known parameter $X_{t,u}$ an optimization variable I have the following constraint: IF $P_{t,u}\geq\alpha$, THEN $X_{...
3 votes
3 answers
384 views

How to linearize the Min function while letting the binary variable to be fixed for x1==x2 as well?

As discussed here, the min function, i.e $X = \min\{x_1,x_2\}$, can be linearized as follows: \begin{align} X & \le x_1 \\ X & \le x_2 \\ X & \ge x_1 - ...
  • 294
4 votes
1 answer
204 views

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 ...
  • 695
4 votes
1 answer
133 views

Formulating these logical constraint in an ILP

I have these two constraints : $z \leq My$ $t \leq M'y $ where $z$ and $t$ are two integer variables $ z, t\geq 0$, $y$ is a binary variable, and $M$, $M'$ are two big numbers. So basically these ...
  • 117
5 votes
1 answer
192 views

how to apply Big M to model the logic constraint (if-then-else)

I was hoping to get some help in modelling the following logic as an MIP Constraint c_{m,l}^{RC} is binary decision variable. Simplify it:
4 votes
2 answers
361 views

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 ...
3 votes
1 answer
199 views

Logical constraint in ILP

I want to write the following constraint: Let $z$ be an integer variable such that $0\le z\le M$, and $t$ be a binary variable where $M$ denotes big-M. The logical constraint is as follows: if $z \...
  • 117
3 votes
1 answer
369 views

How to express this logical constraint for an ILP?

I am trying to write an ILP for a problem but I have this logical constraint and I'm stuck. In my model I have: two binary variables: $x$ and $y$ One Integer variable: $z$ The logical constraint I am ...
  • 117
3 votes
2 answers
252 views

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
1 answer
71 views

Maximizing 1-norm: using binary variables to relax non-convexity

It is well-known that when we maximize a 1-norm, e.g., $\|Ax\|_1$, we can use binary variables and obtain a mixed-integer convex problem (otherwise maximizing 1-norm is non-convex). I am mentioning ...