Hi everybody,

I am currently working on a problem which implies to formulate a MILP problem, but I am a beginner in this field.

The point is, in my opinion, mainly that I don't know if this type of problem has a name, which could help me to find posts here or somewhere else :

I want to minimize the number of unique flow rates values [tex]\dot{m_i}[/tex] with i being the duct number (which is several hundreds), and the flow rate can be equal to any value.

In input (already calculated) I have powers produced by each assembly (to be evacuated by those flow rates) : [tex]\dot{Q_i}[/tex]

I have several linear constraints which are linear, but one is not (I think) :

[tex]\left | \frac{\dot{Q_i}}{\dot{m_i}}- \frac{\dot{Q_{i'}}}{\dot{m_{i'}}}\right | < 10^{-3}[/tex]

with i' taking values of each adjacent duct of the duct i.

I want to minimize would be the number of distinct values of flow rates, or maximize the number of flow rates which are strictly equal. It is very important here to get this linear nature, in order to get THE optimal result.

So, without the non-linear constraint, has this problem a name? Is there a known method to formulate it?

How would you linearize the non-linear constraint?

Thank you!