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An analysis of the Hypervolume Sharpe-Ratio Indicator

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  • Guerreiro, Andreia P.
  • Fonseca, Carlos M.

Abstract

Set-quality indicators have been used in Evolutionary Multiobjective Optimization Algorithms (EMOAs) to guide the search process. Recently, a new class of set-quality indicators combining the selection of solutions with fitness assignment has been proposed. This class is based on a formulation of fitness assignment as a Portfolio Selection Problem, where solutions are seen as assets whose returns are random variables, and fitness represents the investment in such assets/solutions. The Hypervolume Sharpe Ratio (HSR) Indicator is an instance of this class of indicators which has led to promising results as part of an EMOA denominated the Portfolio Optimization Selection Evolutionary Algorithm (POSEA). In this paper, the class of Sharpe-Ratio Indicators is formalized, and the HSR indicator is studied in regard to monotonicity, sensitivity to objective scaling, and dependence on its parameters. In addition, optimal μ-distributions on two-objective linear fronts, and the corresponding fitness assignments, are characterized. Such optimal μ-distributions turn out to be identical to those of the Hypervolume Indicator on the same fronts. Experimental results complement the analysis.

Suggested Citation

  • Guerreiro, Andreia P. & Fonseca, Carlos M., 2020. "An analysis of the Hypervolume Sharpe-Ratio Indicator," European Journal of Operational Research, Elsevier, vol. 283(2), pages 614-629.
    • Handle: RePEc:eee:ejores:v:283:y:2020:i:2:p:614-629
    DOI: 10.1016/j.ejor.2019.11.023
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    References listed on IDEAS

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    1. Miłosz Kadziński & Michał K. Tomczyk, 2017. "Interactive Evolutionary Multiple Objective Optimization for Group Decision Incorporating Value-based Preference Disaggregation Methods," Group Decision and Negotiation, Springer, vol. 26(4), pages 693-728, July.
    2. Günter Rudolph & Oliver Schütze & Christian Grimme & Christian Domínguez-Medina & Heike Trautmann, 2016. "Optimal averaged Hausdorff archives for bi-objective problems: theoretical and numerical results," Computational Optimization and Applications, Springer, vol. 64(2), pages 589-618, June.
    3. Beume, Nicola & Naujoks, Boris & Emmerich, Michael, 2007. "SMS-EMOA: Multiobjective selection based on dominated hypervolume," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1653-1669, September.
    4. Branke, Juergen & Corrente, Salvatore & Greco, Salvatore & Słowiński, Roman & Zielniewicz, Piotr, 2016. "Using Choquet integral as preference model in interactive evolutionary multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 250(3), pages 884-901.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
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    Cited by:

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    2. Audet, Charles & Bigeon, Jean & Cartier, Dominique & Le Digabel, Sébastien & Salomon, Ludovic, 2021. "Performance indicators in multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 292(2), pages 397-422.
    3. Chakrabarti, Deepayan, 2021. "Parameter-free robust optimization for the maximum-Sharpe portfolio problem," European Journal of Operational Research, Elsevier, vol. 293(1), pages 388-399.
    4. Lu, Shuai & Li, Shouwei & Chen, Ning, 2022. "Robust return efficiency and herding behavior of fund managers," Finance Research Letters, Elsevier, vol. 46(PA).

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