Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments

I run the code with seperately set the function and f1, f2, f3, and f4. Why I still got the orange warning. Moreover, could you please check my code. Is it correct?

clear all
%Assignment 2 Multi-Objective functions with Pareto Frontier
%Objective functions
f1 = @(x) (x(1).^4) + ((2.*x(1).^2).*x(2)) + x(2).^2 +3;
f2 = @(x) (x(1).^2-1)^2+x(2).^2-3*x(2)+1;
FITNESSFCN = @(x) [(x(1).^4) + ((2.*x(1).^2).*x(2)) + x(2).^2 + 3, (x(1).^2-1)^2+x(2).^2-3*x(2)+1];

f3 = @(x,y) x.^4 + 2*x.^2.*y + y.^2 +3;
f4 = @(x,y) (x.^2-1)^2+(y.^2)-(3*y)+1;
%Input values
nvars = 2;
A = [];
b = [];
Aeq = [];
beq = [];
nonlcon = [];
lb = [];
ub = [];

%Plot pareto frontier
options = optimoptions(@gamultiobj,'PlotFcn',{@gaplotpareto});
[x, fval] = gamultiobj(FITNESSFCN,nvars,A,b,Aeq,beq,lb,ub,nonlcon,options);

Optimization terminated: average change in the spread of Pareto solutions less than options.FunctionTolerance.

xlabel('f1')
ylabel('f2')
title('Pareto Frontier in Objective Space')

figure 
hold on
% Plot Pareto Frontier in Design Space
fcontour(f3, [-30 30 -20 20], 'LineColor', 'red')
fcontour(f4, [-30 30 -20 20], 'LineColor', 'blue')

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments.

scatter(x(:,1),x(:,2),10,[0 0 0],'filled','black')
xlabel('x1')
ylabel('x2')
title('Pareto Frontier in Design Space')

Answer 1

[Torsten]

f4 = @(x,y) (x.^2-1).^2+(y.^2)-(3*y)+1;

instead of

f4 = @(x,y) (x.^2-1)^2+(y.^2)-(3*y)+1;

[Patis Thepsorn]

thank you so much

[Patis Thepsorn]

thank you so much