In the case of your problem, I would advice you to use 'fmincon' function in order to successfully complete multi-objective optimization. This can be done as follows ->
1. We define the objective functions to optimize -
f = @(x) [f1(x); f2(x); f3(x); f4(x); f5(x)];
(here, we are taking input paramters 'x' and returning a column vector of 5 output objectives.)
2. Then, we store the 3 input parameters we need to take in an array, for say -
x0 = [1,2,3] ------------> example inputs
3. Now, if need be can also add constraints, like lower and upper bounds, for say like-
lowerbounds = [0, 0, 0];
upperbounds = [10, 10, 10];
4. Now, we will define a nonlinear constraint function 'nonlcon' that enforces any additional constraints (if constraints are to be put), and we specify the optimization algorithm options in the options variable -
nonlcon = @nlcon;
options = optimoptions('fmincon', 'Display', 'iter', 'Algorithm', 'sqp');
5. Finally, we call the fmincon function to optimize the objective functions using the specified constraints, initial guess, and optimization algorithm options. The function returns the optimized input parameters 'x_opt' and the corresponding objective function values 'fval'-
[x_opt, fval] = fmincon(f, x0, [], [], [], [], lowerbounds, upperbounds, nonlcon, options);
The approach I have provided is a generic one, you will have to add more constraints and can change the approach slightly too by using either weighted sum, weighted product or other types of input/output. But, 'fmincon' function should help you get your desired output.
I hope I was able to help you!
