All Questions
Tagged with linearization constraint
26
questions
0
votes
0
answers
37
views
What's the linearization of the product between a discrete variable and a continuous varibale?
I am trying to linearize the product $z=xy$, where $x$ is an integer variable and $y$ a continuous variable, both non-negative, for an optimization problem. I have tried the SCIP formulation:
$v_{bn} \...
0
votes
1
answer
76
views
PULP: Optimization Assignment of Bicycle production per month
Q1. If bicycles of types A and H are produced, then bicycles of type C can be produced with 20% shorter working hours, while selling profit of bicycles type H can be 20% higher.
Q2: If bicycles of ...
3
votes
1
answer
194
views
Reformulate constraints
I have the following constraints and am wondering whether I can formulate the whole thing more narrowly and with fewer constraints. $x_{itk}$ is binary and $u_{it}, v_{itk}\in [0,1]$. $M$ is a Big-M ...
0
votes
2
answers
90
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linearizing a constraint involving an absolute function
I would like to know what is the best way to linearize a constraint involving an absolute function. More precisely, imagine I have three binary variables and their relationships is as follows:
|x-y| = ...
- 97
1
vote
1
answer
125
views
How to linearize the following constraints
Given the following two expressions:
$ x - \frac{1}{T}\sum_{i} y_{i}$
$ x - \frac{1}{Q}\sum_{i} \beta_{i} y_{i}$
where $x \in \mathbb{Z}_{+}$, $y \in \mathbb{R}_{+}$, and $T$, $Q$ and $\beta_{i}$ ...
- 113
0
votes
1
answer
186
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Production scheduling
I'm formulating a scheduling problem with the following decision variables:
$$X_t \space \text{is power sold to market in time period t} \\
Y_t \space \text{is power used for production in time period ...
1
vote
2
answers
263
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Linearizing if else conditions in ILP
We are given three binary indicator variables $X_{ij}, Y_{jk}$ and $Z_{jl}$. Write linear constraints such that,
a) if $X_{ij}$ is equal to 1, then for that $j$ when $X_{ij} = 1$, exactly one $Y_{jk} =...
- 917
1
vote
3
answers
125
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How to linearize a chain of if-then constraints?
How can I express the process of converting a series of if-then constraints into a linear form?
Let's assume that we have integer variable $x_i$, non-negative variables $y_i^d$, and binary variables $\...
- 177
3
votes
3
answers
268
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Equivalence between constraints in ILP
Let's have binary variables $x$ and $y$. I'd like to define a helping binary variable $z$ such that
$$ z = 1 \; \;\; \mathrm{iff} \; \; \; x + y = 2.$$
If I wanted to express the equivalence between ...
- 133
1
vote
1
answer
195
views
Linearize conditional constraint
Consider a variable c from the domain {-1,0,1}. I have the following constraint:
IF $c = 1 \Rightarrow x = 1 $ ELSE $x = 0$
How do I linearize this constraint?
- 19
2
votes
1
answer
674
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Optimization problem with if condition as constraint
I am trying to solve an optimization problem where the constraint contains absolute values and I am not sure how I can express this in a 'Pyomo-friendly' way.
Consider the following optimization ...
- 185
6
votes
1
answer
352
views
Absolute value in an equality constraint
What is the best way to model or represent an equality constraint which includes an absolute term in the expression:
$$ x = |y| $$
$x \in \mathbb{R^+}$ and $y \in \mathbb{R}$
- 113
2
votes
1
answer
138
views
Lifting a 3rd order polynomial into a higher dimensional space
An MINLP from a paper I am reading has the following expression in its constraints:
$$
p_{l,s}=z_lb_l\Delta\theta_{l,s}+b_l\lambda_{l,s}u_l\Delta\theta_{l,s}
$$
Where from left to right:
$p_{l,s}$: ...
- 113
2
votes
1
answer
146
views
How to optimize multiple linear regressions based on cost?
I have an optimization problem where I'd like to maximize revenue and I have separate variables for cost and revenue.
Building a single unit of a product takes 100 hours of labor
I have a list of ...
- 197
6
votes
2
answers
143
views
Linearise $\max\{ y_{t-1} + a_t - z_t ,0\}$
I'm trying to linearise these constraints, but I am not able to do correctly do it.
$$y_t = \max\{ y_{t-1} + a_t - z_t, 0 \} $$
My attempt was this:
\begin{align}y'_t &\geq a_t - z_t\\y'_t &\...
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