Monday, November 14, 2011
Clustering Accelerates NSGA-II
Using a natural clustering method, and replacing poor solutions with solutions bred within "interesting" clusters, appears to accelerate how quickly NSGA-II converges upon the Pareto frontier with little impact on the diversity of the solutions or the speed of the algorithm.
Clusters are divided by heuristically and recursively dividing space along a natural axis for the individuals. The FastMap heuristic is used to pick individuals that are very distant from each other by their independent attributes. All the other individuals are placed in the coordinate space by the magnitude of their orthogonal projections onto the line between the two extreme individuals. A division point is chosen along this axis that minimizes the weighted variance of the individuals' ranks. The splitting continues on each half of the split down to "sqrt(individuals)".
An "interesting" cluster is one that has at least one first-rank individual within it and a low ratio of first-rank individuals to total individuals in the cluster. A "boring" cluster is either completely saturated with first-rank individuals or lower-ranked individuals.