how can I solve an error of a different number of elements in GA multiobjective optimization?

Hello all,

here is my code.

fitness =@levulinicAcid;
nvars = 2;
[x,fval] = gamultiobj(fitness, nvars, [],[],[],[],[0.2 10],[0.3 100]);

%%Check the results
x(1) = 10:10:100;
x(2) = 0.2:0.01:0.3;
f1 = -(-4.398907104 + 69.627287709*x(1) - 73.88575606*x(2));
f2 = 5.5828360656 + 0.0697243039*x(1) - 0.052863409*x(2);    %FEDI
f3 = 119.81506557 + 1291.2552396*x(1) - 249.4926284*x(2);    %GWP
figure; hold on
plot(x(1),x(2),f1);
plot(x(1),x(2),f2);
plot(x(1),x(2),f3);
grid;
xlabel('x');
ylabel('f');

[Stephan]

What error do you get? Provide the complete red text. Also provide the fitness function and data if needed to run the code. Why do you overwrite the reults of gamultiobj after determining them?

[Rendra Hakim hafyan]

As I have two variables in my optimization. I have got the error of different elements in my lower bound and upper bound. this below part:

x(1) = 10:10:100;

x(2) = 0.2:0.01:0.3;

actually the fitness function contains the objective function only.

function y = levulinicAcid(x)

y(1) = -(-4.398907104 + 69.627287709*x(1) - 73.88575606*x(2)); %NPV

y(2) = 5.5828360656 + 0.0697243039*x(1) - 0.052863409*x(2); %FEDI

y(3) = 119.81506557 + 1291.2552396*x(1) - 249.4926284*x(2); %GWP

end

My objective is to maximize NPV then minimize both GWP and FEDI.

Answer 1

[Stephan]

Hi,

try:

% Optimize with gamultiobj
fitness =@levulinicAcid;
nvars = 2;
[x,fval] = gamultiobj(fitness, nvars, [],[],[],[],[0.2 10],[0.3 100]);

% Plot results
subplot(3,1,1)
scatter3(x(:,1),x(:,2),fval(:,1),'or')
xlabel('x(1)')
ylabel('x(2)')
title('y1')

subplot(3,1,2)
scatter3(x(:,1),x(:,2),fval(:,2),'og')
xlabel('x(1)')
ylabel('x(2)')
title('y2')

subplot(3,1,3)
scatter3(x(:,1),x(:,2),fval(:,3),'ob')
xlabel('x(1)')
ylabel('x(2)')
title('y3')

% Objective function
function y = levulinicAcid(x)
y(1) = -(-4.398907104 + 69.627287709*x(1) - 73.88575606*x(2)); %NPV
y(2) = 5.5828360656 + 0.0697243039*x(1) - 0.052863409*x(2);    %FEDI
y(3) = 119.81506557 + 1291.2552396*x(1) - 249.4926284*x(2);    %GWP
end

This runs for me on R2018b and gives a result:

Best regards

Stephan

[Rendra Hakim hafyan]

Thank you so much sir. what if I'd like to show my result in pareto front for three objective?

Actually I make this on as well. Unfortunately, I am still confused to set my lower bound and upper bound. I take how to make this code in one of video in youtube.

fitness =@levulinicAcid;

nvar = 2;

Lb = zeros(size(1,nvar)); *** still confuse about this one as my lower bound is 0.2 and 10

Ub = ones(size(1,nvar)); *** upper bound is 0.3 and 100

options = optimoptions('gamultiobj','Display','iter',...

'MaxGeneration',1000,...

'PopulationSize',50,...

'PlotFcn',@gaplotpareto);

[xf,fval] = gamultiobj(fitness,nvar,[],[],[],[],Lb,Ub,options);

[Stephan]

for your case the lower and upper bounds are setted correct. i would do exactly like you. for larger problems with more x(i) or for problems with the same bounds on all variables it is useful to use zeros and ones functions. regarding the pareto plot i would expect that this does it:

scatter3(fval(:,1), fval(:,2), fval(:,3))

[Rendra Hakim hafyan]

Thank you so much sir.

how about with my second code :

fitness =@levulinicAcid;

nvar = 2;

Lb = zeros(size(1,nvar)); *** still confuse about this one as my lower bound is 0.2 and 10

Ub = ones(size(1,nvar)); *** upper bound is 0.3 and 100

options = optimoptions('gamultiobj','Display','iter',...

'MaxGeneration',1000,...

'PopulationSize',50,...

'PlotFcn',@gaplotpareto);

[xf,fval] = gamultiobj(fitness,nvar,[],[],[],[],Lb,Ub,options);

I would like to know how many generation can be formed?

am I doing right?

what result am I supposed to show from Genetic Algorithm? pareto front only?

[Stephan]

"I would like to know how many generation can be formed?"

I do not know that there is a limit other than the time and resources you have available. The default is 100 * nvars. But look at your iterations - the algorithm converges after about 100...120 generations for your problem. So why do you want to change that?

"what result am I supposed to show from Genetic Algorithm? pareto front only?"

I can not tell you which plot is the most useful for you. For the given problem the pareto front is a straight line in the 3D-space of your objectives. Does it help you to interpret the results? Do you have more insight to the problem by looking how the y(i) depends from x(1) and x(2)? I can not say - it is just the question of what helps you most to interprete your results and work with them.

A possible way to get an idea of what could be the most helpful plot is to try it out with some different plots and with a quiet big population:

% Optimize with gamultiobj
options = optimoptions('gamultiobj','Display','iter',...
          'MaxGeneration',200,...
          'PopulationSize',2500,...
          'PlotFcn',@gaplotpareto);
fitness =@levulinicAcid;
nvars = 2;
[x,fval] = gamultiobj(fitness, nvars, [],[],[],[],[0.2 10],[0.3 100],options);
% Plot results
figure(2)
subplot(2,2,1)
scatter3(fval(:,1),fval(:,2),fval(:,3),'or')
xlabel('y(1)')
ylabel('y(2)')
zlabel('y(3)')
title('Pareto Front')
subplot(2,2,2)
scatter3(x(:,1),x(:,2),fval(:,1),'or')
xlabel('x(1)')
ylabel('x(2)')
title('y1')
subplot(2,2,3)
scatter3(x(:,1),x(:,2),fval(:,2),'og')
xlabel('x(1)')
ylabel('x(2)')
title('y2')
subplot(2,2,4)
scatter3(x(:,1),x(:,2),fval(:,3),'ob')
xlabel('x(1)')
ylabel('x(2)')
title('y3')
% Objective function
function y = levulinicAcid(x)
y(1) = -(-4.398907104 + 69.627287709*x(1) - 73.88575606*x(2)); %NPV
y(2) = 5.5828360656 + 0.0697243039*x(1) - 0.052863409*x(2);    %FEDI
y(3) = 119.81506557 + 1291.2552396*x(1) - 249.4926284*x(2);    %GWP
end

Using this code you get this result:

[Rendra Hakim hafyan]

After I tried to change the number of population, the generation stopped at around 100 - 120 as you did as well. I'd like to see the effect of number population to the solution I get anyway.

so, it can conclude that my result shows a trade-off. what if I would like to combine three objective into single objective. Should I use weighted factor? how could I do a weighted objective?

y(1) = -(-4.398907104 + 69.627287709*x(1) - 73.88575606*x(2)); %NPV

y(2) = 5.5828360656 + 0.0697243039*x(1) - 0.052863409*x(2); %FEDI

y(3) = 119.81506557 + 1291.2552396*x(1) - 249.4926284*x(2); %GWP

I want to compared the multi-objective result with single objective.