NSGA-II with Clustering Results

Clustering appears to be capable of helping NSGA-II converge faster, but it does not appear to do so reliably. For the two easier problems (Schaffer and Fonseca), the clustering version converges in significantly fewer generations than the baseline version. For the harder problems (Kursawe and Tanaka), it appears to have had little impact.

The clustering appears to have no impact on the variance in convergence.

The following are graphs of the convergences of the two NSGA-II versions on the four problems. The left column shows the median performance, and the right shows the 25th and 75th percentile performances.









The following are graphs of the running times for solving the previous problems. The clustering version is linearly slower than the baseline version.





There are some odd blips in some of the running times that seem to be noise. I tested the Tanaka problem with a population size of 2000 for 2000 generations, and I got a very linear result:



The only thing that can determine whether clustering truly helps NSGA-II perform better is a distribution metric. If clustering helps distribute solutions across the Pareto frontier in fewer generations than the baseline, it may be a viable technique even when it provides no benefit for the convergence.