An issue regarding multi-objective optimisation

[glanke92]

Dear Dr. Johan,

I have an issue with Multi-objective optimisation formulation.

I will summarise it as follows.

I have two objectives coupled together with weighted sum MOOP.

F = w1* f(x,y) + w2*g(x,y)

where decision variables are x and y.

An example could be something like this.

I have two sets of appliances A and B.

For A --> I can define a MOOP with the objectives, cost and discomfort.

For B --> I can do the same thing.

So the final objective = Objective of A + Objective of B

If I am following something similar to this, before assigning the weights I believe I need to normalise the objectives in a correct.

In case of a single obejctive, I know how to do it.

But here I am struggling to do the same for two objectives.

Can you help me with this ?

Thank you.

[Johan Löfberg]

There is nothing magic to do. 

It sounds reasonable to scale the objectives so that they are in roughly the same size, but that will simply mean that you scale the choice of the weights in the end anyway.