Efficient techniques for multiobjective optimization for a beginner I want to minimize a function $f(x)$ at multiple positions of $x$, e.g., from $x_1$ to $x_4$, $x_{17}$ to $x_{20}$, $x_{51}$ to $x_{54}$ etc. Each value of $x$ is an independent sinusoidal function. The value of $f(x)$ depends on amplitudes of $x_1, x_2, \ldots$. Since there is an upper constraint on $x_i^2$, I want to find the optimal values of the $x_i$'s to minimize $f(x)$. I know little about optimization and have solved this problem to get minimum value at single range of values ie. $x_{1}$ to $x_{4}$. Being new to optimization, I am not sure whether I can call it multiobjective optimization? To get minimum value, which optimization technique will be feasible for the problem? 

The actual functions must be known beforehand in order to assess whether conflicting objectives exist.
As a simple test, you can check whether increasing f1 reduces f2. If it is so, then you can apply multiobjective optimization.
In order to get further details, you can refer to the following article.
http://dx.doi.org/10.1016/j.ins.2020.05.019
OR
https://www.researchgate.net/publication/341752284_Pareto_dominance_based_Multiobjective_Cohort_Intelligence_algorithm
