how to plot a fitness or objective function with optimum values

We want to minimize a simple fitness function of two variables x1 and x2

min f(x) = 100 * (x1^2 - x2) ^2 + (1 - x1)^2;

x

such that the following two nonlinear constraints and bounds are satisfied

x1*x2 + x1 - x2 + 1.5 <=0, (nonlinear constraint)

10 - x1*x2 <=0, (nonlinear constraint)

0 <= x1 <= 1, and (bound)

0 <= x2 <= 13 (bound)

it can be solved by

ObjectiveFunction = @simple_fitness;

nvars = 2; % Number of variables

LB = [0 0]; % Lower bound

UB = [1 13]; % Upper bound

ConstraintFunction = @simple_constraint;

[x,fval] = ga(ObjectiveFunction,nvars,[],[],[],[],LB,UB, ...

ConstraintFunction)

how to plot the objective function with both variables simultaniously with marking the optimim values?

Answer 1

[Fabio Freschi]

objFun = @(x)100.*(x(:,1).^2 - x(:,2)).^2 + (1 - x(:,1)).^2;

conFun = @(x)[x(:,1).*x(:,2)+x(:,1)-x(:,2)+1.5, 10-x(:,1).*x(:,2)];

LB = [0 0];   % Lower bound
UB = [1 13];  % Upper bound

% resolution
n = 1000;

% regular grid
x1 = linspace(LB(1),UB(1),n);
x2 = linspace(LB(2),UB(2),n);
[X1,X2] = meshgrid(x1,x2);
x = [X1(:) X2(:)];

% evaluate the fitness
Y = objFun(x);

% correct with constraints
Y(any(conFun(x) > 0,2)) = NaN;

% plot
figure;
hold on
s = surf(X1,X2,reshape(Y,size(X1)));

% correct the boundary values

% maybe remove the grid
s.EdgeColor = 'none';

% run GA
% up to you

% plot the best solution
% plot3(x(1),x(2),fval);

[Fabio Freschi]

Edit to make the contraint calculation compatible with ga

Answer 2

[Matt J]

Sounds like you want this?

options = optimoptions('ga','PlotFcn',{'gaplotbestf','gaplotbestindiv'});

[x,fval] = ga(ObjectiveFunction,nvars,[],[],[],[],LB,UB, ...
    ConstraintFunction,[],options);

Or, you can write your own custom plot functions as described here,

https://www.mathworks.com/help/gads/genetic-algorithm-options.html#f14474