# How to convert two conflicting objective functions into a single objective function

I have two objective functions say f1 where I have to minimize (X+Y) and another function f2 where I have to maximize (A-B). The two functions are conflicting.

I need to convert them into a minimization problem involving one single objective function using the weighed sum approach where the final form would become f3 = Min {uf1 (+ or-) vf2} where u+v=1.

I am not sure what would be the sign before vf2 ? I wonder if it should be f3 = Min {uf1 + vf2} or f3 = Min {uf1 - v*f2}.

• Why not simply multiply the maximization problem by -1 (making it a minimization problem), then add? Jun 2, 2017 at 16:05
• I was confused by this definition : Max f(x) <=> -Min -f(x), which sound weird at some point and confused me. So f3 = Min {uf1 + vf2} is that what you meant @NietzscheanAI? Thanks :) Jun 2, 2017 at 16:09
• This depends entirely on what you're trying to achieve. I don't think this question can be answered in any generality. Jun 3, 2017 at 12:38