define a deterministic set of feasible solutions

Answered

David Mejía

• July 08, 2020 21:16

Hi,

 

How can I define a deterministic set of feasible solutions for a variable? For example the solver can only find a solution in the following set of solutions for the variable x: x ∈ {0.1,0.2,0.3,0.4,....}

 

Thanks

0

• 

  Eli Towle

  Gurobi Staff

  • July 08, 2020 21:34
  • Edited

  Hi David,

  You can define a binary variable for each possible value of \( x \), then ensure exactly one binary variable is selected. For example:

  $$\begin{align*} 0.1 z_1 + 0.2 z_2 + 0.3 z_3 + 0.4 z_4 &= x \\ \sum_{i=1}^4 z_i &= 1 \\ z &\in \{0,1\}^4.\end{align*}$$

  In this specific case, since the feasible values of \( x \) form a linear sequence, you could set \( x \) based on the value of a general integer variable. E.g.:

  $$\begin{align*} x &= 0.1 y \\ 1 \leq y &\leq 4 \\ y &\in \mathbb{Z}.\end{align*}$$

  Eli

  1
• 

  David Mejía

  • July 09, 2020 09:13

  

  

  

  Thank you so much for the advice, it worked out perfectly.

  David

  0

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