Hi @huda nawaf
Maybe this example would give you the basics of using the genetic algorithm (GA) to minimize a multivariate function. The problem to find the roots of a Cubic function given by
.Since the cubic function has no global minima, and the GA only minimizes a given function, then the root-finding problem must be reformulated to become a convex optimization problem.
x = linspace(1, 6, 501);
y1 = x.^3 - 10*x.^2 + 31*x - 30; % cubic function
y2 = abs(x.^3 - 10*x.^2 + 31*x - 30); % absolute value of cubic function
subplot(2, 1, 1) % 1st subplot
plot(x, y1, 'linewidth', 1.5)
title('Roots of a Cubic function')
subplot(2, 1, 2) % 2nd subplot
plot(x, y2, 'linewidth', 1.5)
title('Absolute value of the Cubic function')
To setup the fitness function for GA, you can do as follows:
f = @(x) abs(x(1).^3 - 10*x(1).^2 + 31*x(1) - 30) + abs(x(2).^3 - 10*x(2).^2 + 31*x(2) - 30) + abs(x(3).^3 - 10*x(3).^2 + 31*x(3) - 30);
nvars = 3; % 3 variables
A = -eye(nvars); % Constraints A*x <= b to search for solutions on the positive side
b = zeros(nvars, 1);
Aeq = [];
beq = [];
lb = [1.0 2.5 4.0]; % bounds setup xlb < x < ub for x(1), x(2), x(3)
ub = [2.5 4.0 6.0];
rootx = ga(f, nvars, A, b, Aeq, beq, lb, ub)
