genetic algorithm to optimize the variable of linear regression(a,b1,b2)

I need some codes for optimize my prediction(using linear regresion) in MATLAB. I am new to genetic algorithm so if anyone has a code that can do this that would help me start off will be greatly appreciated.

Answer 1

[Abdolkarim Mohammadi]

First of all, you should use regress for multiple linear regression. However, if you want to know whether it is possible to use ga for it, the answer is "yes".

First let's create a dataset for a multiple linear regression analysis in the form of .

rng (0);
OriginalA = 2;
OriginalB1 = 1;
OriginalB2 = -4;
X1 = (0:10);
X2 = (5:12);
[DataX1, DataX2] = meshgrid (X1, X2);
DataY = OriginalA + OriginalB1*DataX1 + OriginalB2*DataX2 + 4*rand(numel(X2),numel(X1));

Define the objective function. Regression models minimize the mean squared error of the estimation (MSE).

function f = MSE (x, DataX1, DataX2, DataY)
a = x(1);
b1 = x(2);
b2 = x(3);
YHat = a + b1*DataX1 + b2*DataX2;
f = mean((DataY-YHat).^2, 'all');

Run the Genetic Algorithm to .

fun = @(x)MSE(x, DataX1, DataX2, DataY); % minimize MSE 
nvars = 3;
A = [];
b = [];
Aeq = [];
beq = [];
lb = [-10,-10,-10];
ub = [10,10,10];
nonlcon = [];
options = optimoptions ('ga', 'MaxGenerations', 1e3);
[x,fval,exitflag,output] = ...
	ga (fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,options);

Investigate the results.

RegressionA  = x(1);
RegressionB1 = x(2);
RegressionB2 = x(3);
RegressionY = RegressionA + RegressionB1*DataX1 + RegressionB2*DataX2;
hold on
scatter3 (DataX1(:), DataX2(:), DataY(:), 18, ...
	'Marker', 'o', ...
	'MarkerEdgeColor', 'none', ...
	'MarkerFaceColor', 'k', ...
	'DisplayName', 'Original data');
surf (DataX1, DataX2, RegressionY, ...
	'FaceAlpha', 0.8, ...
	'EdgeColor', 'none', ...
	'DisplayName', 'Regression model')
text (-3, 9, -28, ...
	sprintf("MSE = %f\na = %f\nb_1=%f\nb_2= %f", fval, RegressionA, RegressionB1, RegressionB2));
hold off
xlabel ('x_1');
xlabel ('x_2');
xlabel ('y');
view ([-120,25]);
grid ('on')
box ('on');
legend ('Location', 'Northwest');

[John Juston]

Very grateful for this example, a gateway to solving more complex nonlinear functions

Answer 2

[Alan Weiss]

While you CAN solve a linear regression using ga, it is unwise to do so. Your answers will be faster and more accurate while using less memory by using the MATLAB mldivide function (\). For an example, see Overdetermined Systems.

Alan Weiss

MATLAB mathematical toolbox documentation