An Efficient Algorithm for Computing Hypervolume Contributions

The hypervolume indicator serves as a sorting criterion in many recent multi-objective evolutionary algorithms (MOEAs). Typical algorithms remove the solution with the smallest loss with respect to the dominated hypervolume from the population. We present a new algorithm which determines for a population of size n with d objectives, a solution with minimal hypervolume contribution in time O(nd/2 log n) for d > 2. This improves all previously published algorithms by a factor of n for all d > 3 and by a factor of n for d = 3. We also analyze hypervolume indicator based optimization algorithms which remove > 1 solutions from a population of size n =

• Type: Journal
• Year: 2010
• Where: EC
• Authors: Karl Bringmann, Tobias Friedrich
• Keywords: Algorithms, EC 2010, ECommerce, Hypervolume, Solutions