genetic algorithm code with more than three variables

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huda nawaf 2022-6-16

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移动：madhan ravi 2023-11-18

采纳的回答： Sam Chak

I need genetic algorithm code with more than three variables

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Sam Chak 2022-6-16

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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)
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
rootx = 1×3
    2.0000    3.0000    5.0000

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Sam Chak 2022-6-21

编辑：Sam Chak 2022-6-21

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Hi @huda nawaf

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.

huda nawaf 2022-6-21