Linked Questions

0 votes
2 answers

Conditional milp formulation

I have two binaries, $\alpha_{ts,it}$ and $\alpha_{ts,gshp} \in \{0,1\} $, and two reals $T_{it}$ and $T_{ts}$ which have upper and lower bounds. How can I model $\alpha_{ts,it}=1$ if the following ...
2 votes
1 answer

Covering a graph with M cliques maximizing total edges weight

I am working on a problem that involves distributing a set of N supplements across a predefined number of meals (M) in a way that maximizes the total number of positive interactions and minimizes ...
1 vote
1 answer

Boolean Integer Linear Optimization/Programming

Trying to solve an ILP optimization problem with a number of potential boolean variables and then express constraints on these variables based on those boolean results. Let's say I am doing 5 coin ...
1 vote
1 answer

Maximum reachable checkers on a checkerboard

This is a problem inspired by a video game that I've been thinking about for a long while, and I haven't convinced myself that I can do any better than brute force + pruning techniques, which would ...
3 votes
1 answer

Finding a minimal set of package versions in a dependency graph with constraints

Suppose you have a dependency graph of "packages" registered in the ecosystem of a given programming language. We can model each package as a tuple ...
5 votes
1 answer

Nesting algorithm for rectangular-based, fixed-orientation polygons

I'm looking for an algorithm that is closely related to the 2-dimensional nesting problem (also known as lay planning, bin packing, and the cutting stock problem). The main differences between this ...
1 vote
1 answer

Having a 2D matrix with three typed elements, how to efficiently cover one of the types and NOT cover the other one?

I have a matrix with three possible elements: A, B and C. The size of the matrix could be a maximum of 15x16. $$ \begin{bmatrix} A & A & C & A\\ A & C & B & C\\ A & C & ...
1 vote
1 answer

Find the placement of gates on 2D points that minimizes the total distance of all paths to be made

Suppose we have a 6 vertices graph. We also have 6 gates. Each gate is attributed a path. For example, Gate 'A' will have to go to 'B'- 'C' - 'D' and 'E' Gate 'B' will have to go to 'D' Gate 'C' will ...
-1 votes
1 answer

Integer Linear programming formulation if then condition

I want to create constraints such that I can implement the following condition: Let A be an integer variable >= 0 with an upper bound of 12 I want to introduce the following variable B also an ...
0 votes
0 answers

ILP - Maximize the number of pairs of variables with the same value

I have a 0-1 integer linear program for a set of $2n$ variables $S = \{x_1, ..., x_n, y_1, ..., y_n\}$. My objective is to maximize the number of pairs $(x_i, y_i)$ such that $x_i = y_i$, $i = 1, ..., ...
0 votes
1 answer

Encoding a binary sequence with shift in MILP

I would like to know if it's actually possible to encode a (binary) sequence with rotations in MILP/MIP. Given a binary sequence $(0,1,1,0,0,0,0,1)$ and variables $x_0,x_1,x_2,x_3,x_4,x_5,x_6,x_7$ I ...
4 votes
5 answers

"Greater than" condition in integer linear program with a binary variable

How can one model the following condition in an integer linear program? $$A = \begin{cases} 1 & \text{if } B > C\\ 0 & \text{otherwise}\end{cases}$$ where $A \in \{0,1\}$ and $B, C \in \...
1 vote
1 answer

Minimum Cost Arrangement

I want to find an arrangement to evenly place 12 items ($a_1, a_2, ..., a_{12}$) into 4 boxes ($b_1, b_2, b_3, b_4$) such that the cost is minimal. Let $b(x)$ be the index of the box that contains ...
0 votes
1 answer

Non-convex linear program optimisation with infinite number of OR constraints

I am aware that when we have a linear problem subject to OR constraints, the LP would be a non-convex optimisation problem. For example, ${x = 0}$ OR ${1<=x<=2}$. My question is in such a ...
1 vote
2 answers

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, ...

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