How to formulate annulus bounds constraints in ga ?

Hello, I am struggling in formulating the lb and ub in my ga code, I need ga to generate locations within an annulus area between a smaller rectangle of 49-by-63 and a larger rectangle of 77-by-91. thanks !!!

Answer 1

[Alan Weiss]

You need to use a nonlinear constraint for this. Something like

function [c,ceq] = myannulus(x)
ceq = [];
c(1) = (-(x(1) - a)*(b - x(1)));
c(2) = (-(x(2) - c)*(d - x(2)));

to constraint x to a < x(1) < b and c < x(2) < d. Of course, you would use your particular numbers for a, b, c, and d.

Alan Weiss

MATLAB mathematical toolbox documentation

[Alan Weiss]

Sorry, I wrote too fast. If you want x(1) to be in

a < x(1) < b OR f < x(1) < g then your nonlinear constraint c(1) would be

c(1) = (-(x(1) - a)*(b - x(1))*(x(1) - f)*(g - x(1)));

Similarly for c(2) and x(2).

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Mamdouh Abdulrahman]

Thanks Alan, :) , so I should leave lb and ub empty [] [] and include these constraints with the other nonlinear constraints ! I will try that

[Alan Weiss]

Now I'm not so sure, sorry again. Is this annulus a round annulus, I mean a section of two circles, radius between a and b? If so, then I think the correct nonlinear inequality constraint is this:

function [c,ceq] = myannulus(x)
ceq = [];
r = norm(x);
c = (-(r - a)*(b - r));

If, instead, this is a rectangular annulus, meaning the area between two rectangles where one rectangle is contained in the other, then I think that my previous answers are not correct. Instead, perhaps this is correct. The outer rectangle is from [xmin,ymin] to [xmax,ymax], and the inner rectangle is from [xmin2,ymin2] to [xmax2,ymax2], where

xmin < xmin2 < xmax2 < xmax

ymin < ymin2 < ymax2 < ymax

Use xmin, ymin and xmax,ymax as the bounds on the components of x. I mean, include them in the bounds. Then include also a nonlinear constraint function:

function [c,ceq] = myannulus2(x)
ceq = [];
cc(1) = (x(1) - xmin2)*(xmax2 - x(1));
cc(2) = (x(2) - ymin2)*(ymax2 - x(2));
c = max(cc(1),0)*max(cc(2),0);

Sorry for the confusion, I wasn't thinking clearly today.

Alan Weiss

MATLAB mathematical toolbox documentation