To minimize a function $f(X)$ subject to constraints $g(X) \leq0$, there are multiple optimization techniques that can be used (convex optimization if $f$ is convex, differential evolution DE for global optimization etc.)
However, I am confused as to what are the criteria to justify using multi-objective (pareto optimization) optimization if $f(X)$ can be split into multiple sub-functions, which usually it can be.
For example, if we want to optimize the Gomez-Levy function given by
$$ f(x,y)=4x^2-2.1x^4+\frac{1}{3}x^6+xy-4y^2+4y^4 $$
this can be optimized using DE.
What is to stop me saying the Gomez-Levy function is given by two functions
$$ f_1(x,y)=4x^2-2.1x^4 $$ $$ f_2(x,y)=\frac{1}{3}x^6+xy-4y^2+4y^4 $$
and now we need to switch to a multi-objective optimization paradigm to minimize $f_1$ and $f_2$? Similarly, what is to stop me going in the reverse direction i.e. I start with a multi-objective function paradigm with multiple functions $f_1(X),f_2(X),...f_N(X)$ and I simply sum them all together $F(X)=f_1(X)+f_2(X)+...+f_N(X)$ and then minimize $F$?
Some online sources say that multiple objective functions are generally "conflicting" without giving a strict definition as to what that means.