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Algorithms 2017, 10(4), 130; https://doi.org/10.3390/a10040130

2-Phase NSGA II: An Optimized Reward and Risk Measurements Algorithm in Portfolio Optimization

1
Department of Financial Engineering, Raja University of Qazvin, Qazvin 341451177, Iran
2
Department of Information Engineering, Electronics and Telecommunications, University of Rome Sapienza, Via Eudossiana 18, 00184 Rome, Italy
3
Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam
4
Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam
*
Authors to whom correspondence should be addressed.
Received: 17 October 2017 / Revised: 17 November 2017 / Accepted: 23 November 2017 / Published: 28 November 2017
(This article belongs to the Special Issue Evolutionary Computation for Multiobjective Optimization)
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Abstract

Portfolio optimization is a serious challenge for financial engineering and has pulled down special attention among investors. It has two objectives: to maximize the reward that is calculated by expected return and to minimize the risk. Variance has been considered as a risk measure. There are many constraints in the world that ultimately lead to a non–convex search space such as cardinality constraint. In conclusion, parametric quadratic programming could not be applied and it seems essential to apply multi-objective evolutionary algorithm (MOEA). In this paper, a new efficient multi-objective portfolio optimization algorithm called 2-phase NSGA II algorithm is developed and the results of this algorithm are compared with the NSGA II algorithm. It was found that 2-phase NSGA II significantly outperformed NSGA II algorithm. View Full-Text
Keywords: multi-objective optimization; portfolio selection; Evolutionary Algorithm; NSGA II; 2-phase NSGA II multi-objective optimization; portfolio selection; Evolutionary Algorithm; NSGA II; 2-phase NSGA II
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Eftekharian, S.E.; Shojafar, M.; Shamshirband, S. 2-Phase NSGA II: An Optimized Reward and Risk Measurements Algorithm in Portfolio Optimization. Algorithms 2017, 10, 130.

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