An analysis of the Hypervolume Sharpe-Ratio Indicator

Hypervolume Sharpe-Ratio Indicator: Formalization and First Theoretical Results

Set-quality indicators have been used in Evolutionary Multiobjective Optimization Algorithms (EMOAs) to guide the search process. A new class of set-quality indicators, the Sharpe-Ratio Indicator, combining the selection of solutions with fitness assignment has been recently proposed. This class is based on a formulation of fitness assignment as a Portfolio Selection Problem which sees solution...

Tight Bounds for the Approximation Ratio of the Hypervolume Indicator

The hypervolume indicator is widely used to guide the search and to evaluate the performance of evolutionary multi-objective optimization algorithms. It measures the volume of the dominated portion of the objective space which is considered to give a good approximation of the Pareto front. There is surprisingly little theoretically known about the quality of this approximation. We examine the m...

The Sharpe Ratio Efficient Frontier

We evaluate the probability that an estimated Sharpe ratio exceeds a given threshold in presence of non-Normal returns. We show that this new uncertainty-adjusted investment skill metric (called Probabilistic Sharpe ratio, or PSR) has a number of important applications: First, it allows us to establish the track record length needed for rejecting the hypothesis that a measured Sharpe ratio is b...

Approximation quality of the hypervolume indicator

In order to allow a comparison of (otherwise incomparable) sets, many evolutionary multiobjective optimizers use indicator functions to guide the search and to evaluate the performance of search algorithms. The most widely used indicator is the hypervolume indicator. It measures the volume of the dominated portion of the objective space bounded from below by a reference point. Though the hyperv...

The Sharpe Ratio Indifference Curve