genetic algorithm code with more than three variables

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I need genetic algorithm code with more than three variables

Accepted Answer

Sam Chak
Sam Chak on 16 Jun 2022
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)
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
rootx = 1×3
2.0000 3.0000 5.0000
  8 Comments
Sam Chak
Sam Chak on 21 Jun 2022
Edited: Sam Chak on 21 Jun 2022
To make it easy for you to visualize a multivariate function in n-dimension, I have simplified the function to only two variables, a bivariate function given by
.
If you haven't noticed yet, is linear functional as shown by the flat surface in the 3D plot below:
[X, Y] = meshgrid(0:12/60:6);
Z = X + 2*Y - 5;
surf(X, Y, Z)
Since the variables are constrained to non-negative values (in this example, from 0 to 6), naturally the minimum of the function must be at , as clearly shown in the plot.
Thus, the Genetic Algorithm will return the solution as close as possible to .
f = @(x) x(1) + 2*x(2) - 5;
nvars = 2; % 2 variables, x1, x2
A = -eye(nvars); % Constraints A*x <= b to force GA to search for solutions on the positive side
b = zeros(nvars, 1);
Aeq = [];
beq = [];
lb = [0 0]; % bounds setup lb < x < ub for x1, x2
ub = [6 6];
xsol = ga(f, nvars, A, b, Aeq, beq, lb, ub)
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
xsol = 1×2
0 0
You are advised to revisit your optimization problem and reformulate the objective function (if relevant, as a Convex function), perhaps together with meaningful constraints as well.

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More Answers (1)

huda nawaf
huda nawaf on 21 Jun 2022
thank u very much

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