Abstract
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.
Keywords
- Sharpe Ratio
- Portfolio selection
- Evolutionary algorithms
- Multiobjective optimization
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Auger, A., Bader, J., Brockhoff, D., Zitzler, E.: Theory of the hypervolume indicator: optimal \(\mu \)-distributions and the choice of the reference point. In: Foundations of Genetic Algorithms (FOGA 2009), pp. 87–102. ACM (2009)
Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: multiobjective selection based on dominated hypervolume. EJOR 181, 1653–1669 (2007)
Cornuejols, G., Tuntuncu, R.: Optimization Methods in Finance. Cambridge University Press, Cambridge (2007)
Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Heidelberg (2005)
Knowles, J.D.: Local-search and hybrid evolutionary algorithms for Pareto optimization. Ph.D. thesis, Department of Computer Science, University of Reading (2002)
Nocedal, J., Wright, S.J.: Numerical Optimization. Springer Series in Operations Research and Financial Engineering, 2nd edn. Springer, New York (2006)
Rudolph, G., Schütze, O., Trautmann, H.: On the closest averaged Hausdorff archive for a circularly convex Pareto front. In: Squillero, G., Burelli, P. (eds.) EvoApplications 2016. LNCS, vol. 9598, pp. 42–55. Springer, Heidelberg (2016). doi:10.1007/978-3-319-31153-1_4
Yevseyeva, I., Guerreiro, A.P., Emmerich, M.T.M., Fonseca, C.M.: A portfolio optimization approach to selection in multiobjective evolutionary algorithms. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds.) PPSN 2014. LNCS, vol. 8672, pp. 672–681. Springer, Heidelberg (2014)
Zitzler, E.: Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. thesis, ETH Zurich, Switzerland (1999)
Zitzler, E., Knowles, J.D., Thiele, L.: Quality assessment of pareto set approximations. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization. LNCS, vol. 5252, pp. 373–404. Springer, Heidelberg (2008)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)
Acknowledgments
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Guerreiro, A.P., Fonseca, C.M. (2016). Hypervolume Sharpe-Ratio Indicator: Formalization and First Theoretical Results. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_76
Download citation
DOI: https://doi.org/10.1007/978-3-319-45823-6_76
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45822-9
Online ISBN: 978-3-319-45823-6
eBook Packages: Computer ScienceComputer Science (R0)