# Genetic algorithm and system of nonlinear ODE

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Artyom on 4 Jul 2012
Hi everyone. Here is the question. Can I using genetic algorithm from Global Optimization Toolbox optimize next problem: There is a system of differential equations (example):
y(1)=x(1)^2
y(2)=x(2)^2*x(1)
With constraints:
x(1)>=0;x(2)>=0;
x(1)+x(2)<=y(2);
x(2)<=y(1);
y(2)>=0;
x(i) - unknown values. I'm solving system with ode45 on t=[0,1]. Than solve it again (t=[1,2]), but with modified constraints (because y(i) were changed). Goal - maximize x(2) on T=[0,2].

Alan Weiss on 5 Jul 2012
I don't understand your question. Are the y(i) supposed to be the derivatives of x(i)? If not, where is the differential equation? If the independent variable is time, are the constraints supposed to be true for all values of time, or just for some initial or other values? And what does your goal mean, is this a multiobjective optimization? If not, can you give a formula for your objective function that evaluates to a scalar?
Alan Weiss
MATLAB mathematical toolbox documentation