HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization

Abstract—In the field of evolutionary multi-criterion optimization, the hypervolume indicator is the only single set quality measure that is known to be strictly monotonic with regard to Pareto dominance: whenever a Pareto set approximation entirely dominates another one, then also the indicator value of the former will be better. This property is of high interest and relevance for problems involving a large number of objective functions. However, the high computational effort required for hypervolume calculation has so far prevented to fully exploit the potential of this indicator; current hypervolume-based search algorithms are limited to problems with only a few objectives. This paper addresses this issue and proposes a fast search algorithm that uses Monte Carlo simulation to approximate the exact hypervolume values. The main idea is that not the actual indicator values are important, but rather the rankings of solutions induced by the hypervolume indicator. In detail, we presen...

• Type: Journal
• Year: 2011
• Where: EC
• Authors: Johannes Bader, Eckart Zitzler
• Keywords: EC 2011, ECommerce, Hypervolume Indicator, Indicator Values, Multiobjective Optimization