Linked Questions

3 votes
1 answer
1k views

How to solve an ILP problem with conditions in an objective function?

I have came accross this link. I have an integer linear programming (ILP) problem $$\max_{(x_1, x_2,\ldots, x_n)}\sum_{i=1}^n x_i\cdot f(x_i),$$ $$\text{subject to } \begin{cases} ..., &(1)\\ L≤...
Nick's user avatar
  • 175
2 votes
3 answers
248 views

Integer linear programming formulation of formula in DNF

I have multiple sets, e.g., $$\{1, 2\}, \{2, 3, 4\}, \{1, 4\}$$ Each variable $1, 2, 3, 4$ is binary. I need to represent the following condition without additional variables $$(1 \land 2) \lor (2 \...
Tom's user avatar
  • 185
1 vote
2 answers
674 views

Applications for boolean logic operations in zero-one integer linear programming (ILP) [closed]

It is nice to know that every boolean formula can be expressed by zero-one integer programming by this answered question. But are there any applications? To be more precise: Are there papers which ...
user avatar
1 vote
1 answer
764 views

Linear programming, Checking a constraint based on condition

I have a constraint $X \ge Y$ in a Linear programming formulation, where both $X$ and $Y$ are binary. I want to check this constraint on a condition like: ...
asm_nerd1's user avatar
  • 229
4 votes
1 answer
332 views

Card-buying algorithm

I'm trying to make an algorithm to calculate what combination of cards from what buyers I should get to get the cheapest deal. Taking the shipping costs into consideration. It's for a website called ...
The Oddler's user avatar
3 votes
1 answer
888 views

From CNF to ILP?

Can we transform a CNF to ILP without introducing new variables? My question can be seen as a follow up to Express boolean logic operations in zero-one integer linear programming (ILP) as the ...
Moati's user avatar
  • 33
4 votes
1 answer
250 views

Maximum minimal set coverage

Suppose we are given a universal set $U$ and a family of subsets of $U$, denoted by $F$ (elements in $F$ are subsets of $U$). We assume that all elements in $F$ can cover $U$, i.e., $U\subseteq \...
Alex's user avatar
  • 215
0 votes
1 answer
515 views

NP-completeness proof via reduction

I'm aware that 0-1 integer programming problem is NP-complete, where the problem is stated as: Given some integer matrix A and some integer vector b, determine whether there exists a vector x ...
user3280193's user avatar
1 vote
1 answer
631 views

Reduce Min-Cut to 0/1 Integer Program

Given an undirected, weighted graph $G=(V,E)$ and two nodes $s,t \in V$ and weight function $w: E \rightarrow \mathbb{N}$. The weight of a (s,t)-cut $ (U, U^C)$ is given by: $$ w(U,U^C) := \sum_{\{i,...
Tobias's user avatar
  • 27
3 votes
2 answers
393 views

Model disjunction in a $\{0,1\}$ integer linear program

How can I model logical OR as an integer linear program? $$(y_3 + y_4 + y_5 + y_6 = 2) \lor (y_2 = 1)$$ where $y_i \in \{0, 1\}$, $1$ = True and $0$ = False.
Marcello S's user avatar
1 vote
1 answer
454 views

Representing chained XOR operations as linear inequalities

I'm trying to solve an integer linear program (ILP) in which a constraint of the following kind must be met: $x_1 \oplus x_2 \oplus \cdots \oplus x_n = 1$ where $\oplus$ is the binary xor operator. ...
José Eduardo Bueno's user avatar
0 votes
1 answer
340 views

How to model equality in Integer Linear Programming

How to implement v=(a==b) using Linear Programming? $$ v= \begin{cases} True, a=b\\ False, a≠b\\ \end{cases} $$ Until now I tried the big M-Method. To show a≤b: $$a-b+Mv≤M$$ $$-a+b-Mv≤-1$$ To show ...
Adamos2468's user avatar
2 votes
1 answer
185 views

Modeling $(x > 0 \wedge y > 0) \Leftrightarrow z > 0$ in a linear program: impossible?

In this question, we see how to model boolean logic in $0 - 1$ ILPs. Moving to a relaxation, modelling $(x > 0 \vee y > 0) \Leftrightarrow z > 0$ with $x,y,z \in [0,1]$ with linear ...
G. Bach's user avatar
  • 2,019
1 vote
1 answer
374 views

Restrictions that set binary variable to 1 when integer variable equals x, 0 otherwise

I have this problem: I'm building an integer linear program, which I'm going to give to an ILP solver. I have a binary variable Y which can be either 1 or 0 and an integer variable MONTH which takes ...
Heathcliff's user avatar
1 vote
2 answers
213 views

Linear program for min-length pair of edge-disjoint paths problem

Consider a problem: we have an undirected graph $G = (V, E)$, function $l: E \to \mathbb{Z}_{+}$ where $l(e)$ is edge's length $e \in E$, and two vertices $s$ and $t$. And we want to find a pair $(A, ...
envy grunt's user avatar

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