How to put weight on two objective functions using MATLAB Genetic Algorithm?

Hi,

Say I have to minimize two objective functions -- how can I put weights on each objective function, say for example objective function #1 is 40% and objective function #2 is 60%.

Tried researching and the closest question I got similar to this one was this one (https://uk.mathworks.com/matlabcentral/answers/436951-how-to-choose-weight-for-one-of-functions-in-multi-objective-genetic-algorithm-tool-box) but it did not really answer the question.

Thanks for the help.

Answer 1

[Barnaby Pine]

Hello Phoenix,

By the way you worded the question I assume you are trying to achieve a Pareto front.

Where the objective functins have weights associated to them, satisfying a range of values. These values can then be plotted, on objective function axes. where the x-axis is objective function 1 and the y-axis is objective function 2.

MATLAB has a useful Pareto function which does most of the work for you!

options = optimoptions('gamultiobj','PopulationSize',60,...
          'ParetoFraction',0.7,'PlotFcn',@gaplotpareto);
lb = [0 0]; %lower bound of objective functions
ub = [180 360]; %upper bound of objective functions

[solution,ObjectiveValue] = gamultiobj(@MultiObjectiveFunction,2,[],[],[],[],lb,ub,options);

function f = MultiObjectiveFunction(X)
% x is the input of the objective function as a vector
% f is the output of the objective functions in a vector
f(2) = x(1)^4 + x(2)^4 + x(1)*x(2) - (x(1)*x(2))^2;
f(1) = f(2) - 10*x(1)^2; 
end

More detail on this example can be found through this link: https://uk.mathworks.com/help/gads/pareto-front-for-two-objectives.html

This Requires the Global optimisation toolbox found here: https://uk.mathworks.com/products/global-optimization.html

I know this question was posted in 2019, but I hope that while it may not help you it can help somebody else.

Kind regards,

Barnaby Pine