# Questions tagged [binary-programming]

An optimization problem in which the decision variables are binary.

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### Testing functions for binary optimization

It is well known that it is hard to find optimum of some functions, mainly those with lot of local extremes, discontinuities etc. To assess quality of optimization algorithms (particularly heuristics),...
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### Disjunctive Constraint , Logical Constraints, 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,...
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### Question on designing a binary (integer) programming problem

Given a vector $c\in\Re^n$ and a vector $b\in\Re^n$, I would like to design a binary programming problem, \begin{equation} \max_{x\in\{1,0\}} c^\top x \end{equation} and for constraints, I need all ...
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### Linear program with exponential decay between variables

I'm trying to create a linear program to solve a scheduling problem, below is a description of the problem, I'll try my best to keep it short but comprehensive. The core of the problem is that a daily ...
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### Constrained coloring of bigraph nodes

I have a graph $G(U,V,E)$ representing a set of documents ($U$) and queries ($V$). Every document has 1-5 queries it is connected to, and every query has 1-50 documents it is connected to. There are ~...
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### Finding a binary vector that satisfies non-linear constraints

I’m looking for good heuristics for finding at least one (of a probably large set, although possibly none) high dimensional ($|v|>5000$) binary vector that satisfies a set of non-linear/non-...
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### Linear programming mathematical model

The problem: There are $N$ cities $(1, 2, \dots, N)$. There are roads connecting $M$ pairs of cities in $N$. Stores need to be build in way that for each city $X$ store is in city $X$ or in ...
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### Conditional constraints in binary integer programming problems

I am confronted with the problem of writing conditional constraints in a binary integer programming problem. Let us consider a typical knapsack problem. The constraint is that if items $1$ and $2$ are ...
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### How can I solve a binary quadratic program in MATLAB?

I'm not an expert in MATLAB. Can I use MATLAB function fminimax to solve the problem below? Let's say I have matrix $\mathbf P$ and let's say $\bf Px = b$. My ...
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### Model the constraint ‘Only if decision 1 is yes and decision 2 is no, then decision 3 is allowed to be yes’ [closed]

Model the constraint ‘Only if decision 1 is yes and decision 2 is no, then decision 3 is allowed to be yes’ as a set of linear constraints that should simultaneously be satisfied. Add binary variable(...
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### Linearize absolute value constraint

I want to linearize the following absolute value constraint for MILP: $\sum_{l=1}^{n} |x_{gl} - x_{hl} | > k$, where $x_{g}$ and $x_{h}$ represent different types of bit strings of length $n$ ...
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### Creative solution to set of nonlinear equations

I have a set of $N$ equations and $N$ unknown variables $x_{i}$ like $0 = x_{0}x_{1} - 1 - x_{0}x_{2}$. That's an example. Realistically the equations will be much larger. Each $x_{i} \in \{0, 1\}$. ...
I'm trying to solve a problem for $x$ which is a vector of length $n$ with only binary elements, i.e. each $x_{i}$ is either $0$ or $1$. There are two constraints on $x$, one quadratic and one linear: ...
If I have a set of binary variables that indicate whether something is active or not (in my case this is for employee scheduling) like so: $$x_1E_1 + x_2E_1 + x_3E_1 + x_4E_1$$ where $x_i$ is a ...