how can i change Pareto front axis in genetic algorithm?

how can i change the axis in Pareto front plot in genetic algorithm? is there a way to plot the two objective functions on the y axis and indicate the optimal solution since there is an axis. Thank you

Answer 1

[Elizabeth Reese]

I am not exactly sure how you would like to "indicate the optimal solution" using the Pareto front, but here are a few ways to visualize the information about a Pareto front. I am elaborating on the example found at the link below which uses two fitness functions of one bounded variable.

https://www.mathworks.com/help/gads/gamultiobj.html#bvg28g2-1

The two fitness functions are cos(x) and sin(x) for 0 <= x <= 2*pi. If we want to visualize the two functions on the y-axis, we can execute the following code. This will plot black lines at each x on the Pareto front.

>> xs = linspace(lb,ub,500)';
>> figure
>> plot(xs,fitnessfcn(xs))
>> xlabel('x');
>> hold on;
>> plot([x';x'],fitnessfcn(x)','k')
>> legend('sin(x)','cos(x)','Pareto front')

Another way to visualize the Pareto front is to plot the parametric curve of the two objective functions over the input variable. This will look like the following.

>> fEvals = fitnessfcn(xs);
>> fEvalsPareto = fitnessfcn(x);
>> figure
>> plot(fEvals(:,1),fEvals(:,2))
>> hold on
>> plot(fEvalsPareto(:,1),fEvalsPareto(:,2),'*')
>> xlabel('sin(x)')
>> ylabel('cos(x)')
>> legend('fitness function','Pareto front')

[Gali Musa]

Thank you for the reply. The two objective function has different scale one with 10^8 and the other one with 10^6 so when i plot the two objective function it combined the objective function on the same axis. i want the two objective function to be on separate axis. this is the sample of the plot.

figure plot(xf,fval,'r') %%%,xf,fval hold on plot(xf,fval,'g') % % % plot(xf,fval,'r',xf,fval,'g'); % hold on; xlabel('Pd (hrs)') ylabel('Cost of Electricity ($)') hold on; xlabel('Pd (hrs)') ylabel('Loss of Revenue ($)')

[Elizabeth Reese]

If you want them on separate axis altogether, take a look at the " subplot" function. This will let you have two separate axis in the same figure.

https://www.mathworks.com/help/matlab/ref/subplot.html

If you want the plots to be on the same graph, just with different axis, you can try " yyaxis". This will take the two independent axis and display them on top of one another.

https://www.mathworks.com/help/matlab/ref/yyaxis.html

[Gali Musa]

Thank you so much for the useful information.

[Gali Musa]

how can i get an optimal solution from Pareto front graph. i noticed the Pareto front gives many solutions. Is it normal that i got a linear Pareto front rather than convex or non-convex front.