In most metaheuristic algorithms like Genetic Algorithm, Simulated Annealing, or particle swarm optimization, it is required to generate random variables under some control parameters. For example, we can generate a sample of z value controlled by % load balancing and its boundary limits using this algorithm:
z1 = z got from % Maximum load balancing, i.e., 120%;
z2 = z got from % Minimum load balancing, i.e., 70%;
To compute z1 and z2, a particular function is required to convert % load balancing and drape value into z value. for example
MATLAB CODE:
%
% compute z from given balance load
% use for generating valid chromosome
%
function o = z_from_wbal (w_bal,F,Area,h,zend,ispan)
global L b bw
num_spans = length(L);
drape = w_bal/100*L(ispan)^2*24*Area/8/F;
if ispan == 1 || ispan == num_spans
z = 1/2*(zend+h-0.05)-drape;
else
z = h-0.05-drape;
end
o = z;
end
Then compare z with its boundary values.
% bound of z from wbmin, wbmax, lb_z, ub_z
z_low = max([lb_z, z_from_wbal(wbmax,F,e(i),Area,h,zend,i)]);
z_high = min([ub_z, z_from_wbal(wbmin,F,e(i),Area,h,zend,i)]);
z(i) = max([z_low+(z_high-z_low)*rand,lb_z]);
disp([z_low,z_high,z(i)])
The result of z is guaranteed to lie within the boundary between wb_max and wb_min, but in extreme cases, they are also controlled within the [zmin, zmax] range.
In PT-OP, software for design optimization of PT slab developed for Posteck Prestressing, we employ the above method to control the depth of tendon z, so that the % balance load stays within the control parameters.
Figure Percentage of Balance Load control [70%, 120%] in PT-OP
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