How can I add 2 different variables into NSGAii toolbox?

For a NSGAii optimization problem withi 8 variables which are: x(1) +x(2)+x(3)+x(4)= 8 and x(5) +x(6)+x(7)+x(8)= 100, How I can add in NSGAII toolbox?

Answer 1

[Shishir Reddy]

Hi saman

To incorporate constraints into an NSGA-II optimization problem using a toolbox like the one available in MATLAB, the constraints need to be defined within the problem setup.

Kindly refer the following steps to understand how to set this up:

Step 1: The objective functions have to be defined in a separate MATLAB function file. This function should accept a vector of decision variables and return the values of the objectives.

function f = myObjectiveFunction(x)
    f(1) = ...; 
    f(2) = ...; 
    % Add more objectives if necessary
end

Step 2: Constraints can be defined in a similar way by creating another function for them.

function ceq = myConstraints(x)
    ceq(1) = x(1) + x(2) + x(3) + x(4) - 8;
    ceq(2) = x(5) + x(6) + x(7) + x(8) - 100;
end

Step 3: Setting up the NSGA-II Solver.

options = optimoptions('ga', ...
    'PopulationSize', 100, ...
    'MaxGenerations', 200, ...
    'Display', 'iter', ...
    'UseParallel', true, ...
    'PlotFcn', {@gaplotpareto});

% And then finally call the solver
lb = zeros(1, 8);
[x, fval] = ga(@myObjectiveFunction, 8, [], [], [], [], lb, [], @myConstraints, options);

This setup allows you to incorporate your constraints into the NSGA-II optimization process effectively.

I hope this helps.