Linked Questions

2 votes
1 answer
315 views

Modeling equality in an ILP

Lets say we have integer variables $a \in\mathbb{Z}^n$ and $M \in\{0,1\}^{n\times L}$. I am promised $a_i \leq L$, for some fixed constant $L$. I want to model the constraint $$M_{i,j} \iff (a_i=j)$...
Throckmorton's user avatar
1 vote
1 answer
265 views

How to model a logical indicator when two inequalities hold in Integer Programming?

I have an IP program where $\forall i \in I, j \in J$ my decision variables are $x_{i,j}$. I have two sets of inequalities (one inequality for every $i,j$ pair) that are of interest which are $$a_{i,j}...
WBM's user avatar
  • 113
-1 votes
1 answer
335 views

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 ...
Tobias Dekker's user avatar
3 votes
1 answer
257 views

Students in classroom problem - Flow in network

I have room, which is opened some days in week, in different hours each day. I have multiple students, each has time some days in week, in different hours. Each student have to visit the room ...
Peter's user avatar
  • 31
4 votes
1 answer
190 views

Integer Problem Solving with two boolean selection variables

I am trying to solve a two dimensional combinatorial problem. Hereis my input space {{RA1,RA2},{RB1,RB2},{RC1,RC2}} and i have to choose two out of three elements{A,B,C} and one out of two possible ...
Jiterika's user avatar
1 vote
1 answer
174 views

Integer Programming - packing wolves and sheep

I'm new to linear/integer programming and I'm trying to solve a little problem I made up. I want to "pack" animals into a minimum number of bins where some of the animals cannot co-exist (wolves and ...
mj_'s user avatar
  • 115
0 votes
2 answers
264 views

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 ...
SR89's user avatar
  • 1
1 vote
1 answer
175 views

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 ...
Christopher Boo's user avatar
3 votes
1 answer
121 views

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 ...
tom's user avatar
  • 133
0 votes
1 answer
153 views

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 ...
Amal Sailendran's user avatar
4 votes
1 answer
82 views

Optimising an exhaustive search for a card game

I'd like to search for a combination of resources that when used, would produce at least up to a threshold of different kinds of materials. For the majority who are not in the know, I'll use an ...
Felix's user avatar
  • 143
2 votes
1 answer
104 views

Choice of algorithm for hierarchical clustering for minimizing network communication costs

Suppose I have a large distributed task running on a cluster system where part of the workload is compute bound and part depends on network performance. Data transfer is not completely homogeneous ...
Aaron Altman's user avatar
2 votes
2 answers
48 views

Growing a set given constraints

I am trying to solve the following: Given a set $S_0$, find min $|S|$ where $S_0 \subseteq S$ subject to: $\forall s \in S$ $\exists$ $s_a, s_b \in S $ $|$ $ ( s_a \neq s, s_b\neq s ) \land ( s = ...
da_steve101's user avatar
1 vote
1 answer
117 views

ILP representation of the number of maximal 1 sequences in a row

I am currently using an ILP to model events which occur on some input sequence from $1...n$. These events modify the input sequence in order to obtain a desired sequence. Each event can happen on some ...
Throckmorton's user avatar
2 votes
0 answers
145 views

Relaxations for MILP with logical constraints

I have an LP with a (non-fixed) number of logical constraints in the form of $X_1 \rightarrow X_2$ (where $X_1$ and $X_2$ are linear functions inequalities of the $n$ input variables). To express ...
galoosh33's user avatar
  • 121

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