surf can not be drawn/how triple objective function is written in same page with ga solver?

I define this triple objective function in separate sheet ,but how I can define this with ga solver in same sheet?

%%%%%multiobjective(triple) optimization problems
function Z= tripleobjectivefunction(x,y)

f1 = 0.5.*(x.^2+y.^2) +sin(x.^2+y.^2);
f2 =((3.*x-2.*y+4).^2./8)+((x-y+1).^2)/27+15;
f3 =1/(x.^2+y.^2+1)-1.1.*exp(-(x.^2+y.^2));
Z=[f1,f2,f3];
end

I want to have surf but this is not possible since the function Z is unrecognized.

clc;
clear all;
close all;

nvars = 2;
lb = [-3 -3];
ub = [3 3];

%initial population
%crossover and mutation
options=optimoptions("gamultiobj",'InitialPopulationRange',[1;100],"PopulationSize",50,"MaxGenerations",100,"MaxStallGenerations",100,"FunctionTolerance",1e-4,"MutationFcn",{@mutationadaptfeasible,2},"CrossoverFcn",{@crossoverintermediate, 2},"PlotFcn",{@gaplotpareto ,@gaplotselection ,@gaplotbestf});
[x,fval,exitflag,output,population,score] = gamultiobj(@(x) tripleobjectivefunction(x(1),x(2)),nvars,[],[],[],[],lb,ub,[],options);
optimal_solution = x;
objective_functions = fval;
figure(1)
hold on
box on
plot3(fval(:,1),fval(:,2),fval(:,3),'mo')
figure(2)
[X,Y]=meshgrid(x,fval);
surf(X,Y,length(Z),'FaceAlpha',0.5) 
hold off

[sogol bandekian]

@Walter Roberson can you look at this

Answer 1

[Walter Roberson]

Your question is not clear.

nvars = 2;
lb = [-3 -3];
ub = [3 3];

%initial population
%crossover and mutation
options = optimoptions("gamultiobj",  ...
    'InitialPopulationRange', [1;100], ...
    "PopulationSize", 50, ...
    "MaxGenerations", 500, ...
    "MaxStallGenerations", 100, ...
    "FunctionTolerance", 1e-4, ...
    "MutationFcn", {@mutationadaptfeasible,2}, ...
    "CrossoverFcn", {@crossoverintermediate, 2}, ...
    "PlotFcn", {@gaplotpareto ,@gaplotselection ,@gaplotbestf});

if isunix()
    options.PlotFcn = {};
end

[x,fval,exitflag,output,population,score] = gamultiobj(@(x) tripleobjectivefunction(x(1),x(2)),nvars,[],[],[],[],lb,ub,[],options);

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

optimal_solution = x;
objective_functions = fval;
figure(1)
hold on
box on
plot3(fval(:,1),fval(:,2),fval(:,3),'mo')
hold off

figure(2)
[X, Y] = meshgrid(linspace(lb(1),ub(1)), linspace(lb(2), ub(2)));
Z3c = arrayfun(@(x,y) tripleobjectivefunction(x,y), X, Y, 'uniform', 0);
Z3d = cell2mat(cellfun(@(z3) reshape(z3, 1, 1, []), Z3c, 'uniform', 0));

s1 = surf(X, Y, Z3d(:,:,1), 'FaceAlpha', 0.5, 'edgecolor', 'none', 'DisplayName', 'First Objective');
hold on
scatter3(x(:,1), x(:,2), fval(:,1), 'rx');
hold off
legend(s1);

figure(3)
s2 = surf(X, Y, Z3d(:,:,2), 'FaceAlpha', 0.5, 'edgecolor', 'none', 'DisplayName', 'Second Objective');
hold on
scatter3(x(:,1), x(:,2), fval(:,2), 'rx');
hold off
legend(s2);

figure(4)
s3 = surf(X, Y, Z3d(:,:,3), 'FaceAlpha', 0.5, 'edgecolor', 'none', 'DisplayName', 'Third Objective');
hold on
scatter3(x(:,1), x(:,2), fval(:,3), 'rx');
hold off
legend(s3)

%%%%%multiobjective(triple) optimization problems
function Z= tripleobjectivefunction(x,y)

f1 = 0.5.*(x.^2+y.^2) +sin(x.^2+y.^2);
f2 =((3.*x-2.*y+4).^2./8)+((x-y+1).^2)/27+15;
f3 =1/(x.^2+y.^2+1)-1.1.*exp(-(x.^2+y.^2));
Z=[f1,f2,f3];
end