1-insert the objective functions to minimize and maximize at the same time

2-establish the constraints of the variables

3-Plot in 3D Pareto front of optimal solutions

Problem: Multi Optimization of an Turbojet two spool

minimize all this functions , while maximizing others ones under all this constraints.

Objectives	Variable/Function
Minimize
F1 (x) Specific Fuel Consumption
NOx Emissions (LTO) F2 (x)
Fuel Weight F3(x)
Wto F4(x)
Flight time F5(x)
Maximize
Propulsive efficiency F6(x)
Overall efficiency F7(x)
Thermal Efficiency F8(x)
Thurst F9(x)

Constraints

Aerodynamics
Parameters	Values
CL Max CD Min	1.2-1.8
0.015-0.020
Wing weight
Wing planform area
Wing volume
Pitching moment	0

Constraints

Structures
Parameters	Values
Maneuver loads
Load factor	3.5-5.5
Minimum Design Cruising Speed
Maximum Design Cruising Speed
Design Dive Speed
Maneuvering Speeds
Design Speed for Maximum Gust Intensity
Positive stall line
Negative stall line
Gust load factor
Aircraft mass ratio
Gust alleviation factor
Gust load factor
Material Carbon fibre composite Titanium Steel Aluminum Superalloys	Specific dynamic modulus Specific strength Temperature
Range
Endurance

Constraints

Emissions
Inlet mixture temperature Change t05 to t04
Gas temperature leaving the catalyst
Mass flow rate
CO,NOX and UHC emissions

Main MATLAB CODE:

% Define the optimization problem

prob = optimproblem;

% Define the objective functions

prob.Objective = [F1(x); F2(x)];

% Minimize F1

prob.Objective(1).Minimize = true;

% Maximize F2

prob.Objective(2).Maximize = true;

% Define the optimization variables

x = optimvar('x',3);

% Define the objective functions

F1 = x(1) + x(2)*x(3);

F2 = x(1)*x(2)*x(3);

% Define the constraints

prob.Constraints.con1 = x(1) + x(2) <= 10;

prob.Constraints.con2 = x(1) + x(3) >= 5;

prob.Constraints.con3 = x(2) + x(3) >= 5;

prob.Constraints.con4 = x(1) + x(2) + x(3) == 10;

% Define the solver options

options = optimoptions('gamultiobj','PlotFcn','gaplotpareto');

% Solve the problem

[sol,fval,exitflag,output] = solve(prob,'Solver','gamultiobj','Options',options);

Would it be possible for someone to adapt my code so that it works?

or adapt for this example:

https://www.mathworks.com/help/gads/multiobjective-optimization-welded-beam.html

or

https://www.mathworks.com/help/gads/solving-a-mixed-integer-engineering-design-problem-using-the-genetic-algorithm.html#d124e20023

to minimize and maximize two different functions at the same time and plot 3D pareto front with optimal solutions

I've been following this two examples but it's still quite confusing for me since I'm new to matlab.

Could someone give me a hand?

It can be a simple example of this problem but that I can insert other functions, constraints?

Examples in the documentation and forum are not simple enough for me to understand, I just found this code that I understand minimally..

Thanks,

King regards