The multi-objective optimization problem settings are as defined below:
Objective 1: Minimize $f_1(X_1,X_2)=C_0+C_1(1/X_1)+C_2(X_2/X_1)$
Objective 2: Minimize $f_2(X_1,X_2)=D_0+D_1X_1+D_2X_2+D_3(X_2/X_1)+D_4(X_2^2/X_1)$
Objective 3: Minimize $f_3(X_1, X_2)=E_1(X_2/X_1)$
Constraint 1: $ 0 \le X_1 \le A_1$
Constraint 2: $ 0 \le X_2 \le A_2$
Constraint 3: $ k_1X_1 + k_2X_2 \le A_3$
Constraint 4: $ k_3X_1 \le k_4X_2$
Here, $C_0, C_1,C_2,D_0,D_1,D_2,D_3,D_4,E_1,A_1,A_2, A_3, k_1,k_2,k_3,k_4$ are positive constant numbers. $X_1$ and $X_2$ are decision variables that can be real/integer.
Evolutionary algorithms like NSGA-II are considered mainstream algorithms to solve a non-linear multi-objective optimization algorithm (Pareto optimization).
Other than metaheuristics like NSGA-II, PSO, and SMPSO, are there other exact methods that can be applied to solve Pareto optimization problems (i.e., identifying Pareto optimal solutions)?
Which is better to solve the problem illustrated above NSGA-II or exact methods? Does the non-linearity of the problem play a significant role in the selection of solution algorithms?