In multi-objective optimization, how to calculate the average inverted generational distance (IGD) value of each generation over N independent runs? I need to get something similar to the attached picture.
You need to calculate IGD values for the pareto solutions acheived in each iteration I w.r.t. to the refrence point (optimal pareto) considered. Store it in a matrix/variable.
You should do the same for N independent runs. Find the average of the values, ultimately you will get a separate column for the average of IGD for each iterations. Now you can use the results of average values to plot the graph.
For an example, see in attached image. For I=10 and N=3 , you can obtain "Avergae IGD" values to plot.
Have you thought to apply some K-NN at number of generation. Some regression
@Amit Rauniyar thank you for your answer. Could you please explain why the Average IGD1 = 1/3(x1+y1+z1) and not
Average IGD1 = (x1+y1+z1)/3
@Amit Rauniyar
Could you tell me, how can I calculate or get the reference points?