How can I use gamultiobj to find all the solutions of a nonlinear system?

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kika198513 2014-9-1

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https://ww2.mathworks.cn/matlabcentral/answers/153070-how-can-i-use-gamultiobj-to-find-all-the-solutions-of-a-nonlinear-system

Hi, I would like to solve a nonlinear system having multiple solutions. Instead of using fsolve I would like to obtain at the same time all the numerical solutions. I read that a way to do this is by exploiting the function gamultiobj and to translate the problem into a minimization one. I then wrote the main file:

FitnessFunction=@fun_GA2;
numberOfVariables = 2;
options = gaoptimset('Generations', 100, 'PopulationSize', 100);
[X,FVAL,EXITFLAG,OUTPUT] = gamultiobj(FitnessFunction,numberOfVariables,[],[],[],[],[],[],options)

with

function y=fun_GA2(x)
y(1)=abs(-1/2*x(1)+8*1./(1+exp(-2*(x(1)-1)))-14*1./(1+exp(-2*(x(2)-1)))+10);
y(2)=abs(-1/2*x(2)-2*1./(1+exp(-2*(x(2)-1)))+56*1./(1+exp(-2*(x(1)-1)))+10);

In this way I obtained an X matrix having size 28x2 representing only one solutions. How can I find the other solutions of the nonlinear system?