The non-convex multi-objective optimization problem in my case is defined below:
Objective 1: Minimize $f_1(X_1,X_2)=C_0+C_1(1/X_1)+C_2(X_2/X_1)+C_3X_1+C_4X_2+C_5(X_2^2/X_1)$
Objective 2: Minimize $f_2(X_1,X_2)=D_1X_1+D_2X_2+D_3X_1^2+D_4X_2^2+D_5X_1X_2$
Objective 3: Minimize $f_3(X_2)=-E_1X_2$
Constraint 1: $ 0 \le X_1 \le A_1$
Constraint 2: $ 0 \le X_2 \le A_2$
Constraint 3: $ X_1 + X_2 \le 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 positive constant numbers. $X_1$ and $X_2$ are decision variables.
I want to linearize the objective functions and solve it using LP or MILP solvers for global optimization of $X_1$ and $X_2$. However, I am not sure what is the best method to linearize. For instance, with separable programming I am facing issues with number of breaking points.
Also, I have tried using evolutionary algorithms like MOPSO and NSGA-II for finding global optimum solutions. However, I want to explore if I can reduce the non-linear objective functions to linear and find global optimum solutions with less computation time.