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

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sogol bandekian on 26 May 2022
Answered: Walter Roberson on 27 May 2022
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
[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 on 27 May 2022
@Walter Roberson can you look at this

Walter Roberson on 27 May 2022
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, ...
"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