The multi-objective optimization problem in my case is defined below

Objective 1: Minimize $f_1(X_1,X_2)$= $C_1X_1+C_2X_2+C_3X_1^2+C_4X_2^2+C_5X_1^2X_2^2$

Objective 2: Minimize $f_2(X_1,X_2)$= $D_1X_1+D_2X_2+D_3X_1^2+D_4X_2^2+D_5X_1^2X_2^2$

Objective 3: Minimize $f_3(X_2)$= $E_1X_2$

Constraint 1: $ 0 <= X_1 <= A_1$

Constraint 2: $ 0 <= X_2 <= A_2$

Constraint 3: $ X_1 + X_2 <= A_3$

Here, $C_1,C_2,C_3,C_4,C_5,D_1,D_2,D_3,D_4,D_5,E_1,A_1,A_2,$ and $A_3$ are constant numbers. $X_1$ and $X_2$ are decision variables.

I have used real-coding method for chromosome coding and used NSGA-II for optimization. I used NSGA-II since it is the most commonly adopted method for arriving pareto front. However, to use NSGA-II, is it always required to prove the NP-Hardness of a problem?

To calculate the computational complexity of a NSGA-II problem, we need calculate both the complexity for each generation and the number of generations. (Reference: https://core.ac.uk/download/pdf/82006684.pdf)

Complexity = $O(G*F*P^2)$ = $O(100*3*100^2)$ (Let's say)

Here, $G$ is number of generations, $F$= number of objective functions, and $P$ = Population size

How do we justify the use of NSGA-II for this case?