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 solutions as assets whose returns are random variables, and fitness as the investment in such assets/solutions. An instance of this class based on the Hypervolume Indicator has shown promising results when integrated in an EMOA called POSEA. The aim of this paper is to formalize the class of Sharpe-Ratio Indicators and to demonstrate some of the properties of that particular Sharpe-Ratio Indicator instance concerning monotonicity, sensitivity to scaling and parameter independence.
KeywordsSharpe Ratio Portfolio selection Evolutionary algorithms Multiobjective optimization
This work was supported by national funds through the Portuguese Foundation for Science and Technology (FCT), by the European Regional Development Fund (FEDER) through COMPETE 2020 – Operational Program for Competitiveness and Internationalization (POCI). A. P. Guerreiro acknowledges FCT for Ph.D. studentship SFHR/BD/77725/2011, co-funded by the European Social Fund and by the State Budget of the Portuguese Ministry of Education and Science in the scope of NSRF–HPOP–Type 4.1–Advanced Training.
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