How to write 2 functions both in 2 variables that will be the objective functions of a Multi-objective Genetic Algorithm?

This part below is a file code that will be the input for the multi-objective (in my case a bi-objective) genetic algorithm. I don't know exactly who the function should be written. "f1" and "f2" are the function that have to be maximixed/minimized by the algorithm. "x" and "y" are the variables that I want to find as optimum results. Can anyone help me understanding exactly how to write this part?

function z = multiobjective(f1,f2)
 
    Ratio1 = x/(x+y);      %D/(D+E)=0.5277
    Ratio2 = y/(x+y);     %E/(E+D)=0.4723
    Re = 0.1022;
    Rd = 0.0167;
    t = 0.169;

    % WACC Formulation:
    f1 = Ratio2*Re+Ratio1*Rd*(1-t);
 
    EBT = 3487;
    Fc = 231; %finance costs
 
    NI = ((EBT+Fc)-(2*(e-08)*x^3-0.0003*x^2+2.0057*x-3928.9))*(1-(t));
 
    % ROE Formulation:
    f2 = NI/y;
 
end

This part below is instead a simple code where the file "multiobjective" (the code above) is the input. I'm not sure if this is the correct way or if I should create 2 different files (one for each function to maximize or minimize).

FitnessFunction = @multiobjective; % Function handle to the fitness function
numberOfVariables = 2; % Number of decision variables
lb = [0 0]; % Lower bound
ub = [100 100]; % Upper bound
A = []; % No linear inequality constraints
b = []; % No linear inequality constraints
Aeq = []; % No linear equality constraints
beq = []; % No linear equality constraints
options = optimoptions(@gamultiobj,'PlotFcn',@gaplotpareto);
 
[x,Fval,exitFlag,Output] = gamultiobj(FitnessFunction,numberOfVariables,A,b,Aeq,beq,lb,ub,options); 

Answer 1

[Athul Prakash]

Hi Andrea,

I think your approach with the 'multiobjective' function is wrong.

The input 'FitnessFunction' should be returning multiple values - the values of each objective function - aggregated as a vector.

Therefore, in your example, 'multiobjective' should calculate the values of 'f1' and 'f2' from their inputs and return a vector of the calculated values.

Add the line

z = [f1 f2]

to the bottom of the 'multiobjective' function.

Further, the function should accept the variables 'x' and 'y' as inputs, not 'f1' and 'f2'.

Hope it Helps!