# Multi objective optimization into single objective.

I read that it is possible to convert a multi-objective optimization problem into single objective by using weighted sum method. I wanted to know if it is a good idea to convert a two objective optimization problem into single objective by multiplication. for example:

Goal: minimize $f_1(x)$, maximize $f_2(x)$. So is it a good idea to calculate $f_2(x)/f_1(x)$, and use it as an optimal value.

• First thing that comes to my mind is that multiplying or dividing the objective functions you may end up with non-linear objective. Is that relevant to you to have a linear objective function? Oct 2, 2013 at 6:11
• No. I don't mind having a linear or a non-linear objective function . Oct 2, 2013 at 11:57
• You may have a look at this: theory.stanford.edu/~megiddo/pdf/rational.pdf Oct 2, 2013 at 12:49
• @Libra thanks for sharing the link. In case the link expires the the paper is: "COMBINATORIAL OPTIMIZATION WITH RATIONAL OBJECTIVE FUNCTIONS" By NIMROD MEGIDDO from Tel Aviv University Nov 16, 2022 at 17:34

In a multi-objective optimization, the objectives to be optimized are conflict. For the convenience of the description, supposing all the objectives are to be minimized, because the maximizing problem can be transformed to the minimizing problems by multiplying $-1$.