Bi-objective Portfolio Optimization Using a Customized Hybrid NSGA-II Procedure

Bi-objective portfolio optimization for minimizing risk and maximizing expected return has received considerable attention using evolutionary algorithms. Although the problem is a quadratic programming (QP) problem, the practicalities of investment often make the decision variables discontinuous and introduce other complexities. In such circumstances, usual QP solution methodologies can not always find acceptable solutions. In this paper, we modify a bi-objective evolutionary algorithm (NSGA-II) to develop a customized hybrid NSGA-II procedure for handling situations that are non-conventional for classical QP approaches. By considering large-scale problems, we demonstrate how evolutionary algorithms enable the proposed procedure to find fronts, or portions of fronts, that can be difficult for other methods to obtain.

[1]  Yew-Soon Ong,et al.  Advances in Natural Computation, First International Conference, ICNC 2005, Changsha, China, August 27-29, 2005, Proceedings, Part I , 2005, ICNC.

[2]  Kalyanmoy Deb,et al.  Portfolio optimization with an envelope-based multi-objective evolutionary algorithm , 2009, Eur. J. Oper. Res..

[3]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[4]  Felix Streichert,et al.  The Effect of Local Search on the Constrained Portfolio Selection Problem , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[5]  Yazid M. Sharaiha,et al.  Heuristics for cardinality constrained portfolio optimisation , 2000, Comput. Oper. Res..

[6]  Andrzej P. Wierzbicki,et al.  The Use of Reference Objectives in Multiobjective Optimization , 1979 .

[7]  Yves Crama,et al.  Simulated annealing for complex portfolio selection problems , 2003, Eur. J. Oper. Res..

[8]  Sandra Paterlini,et al.  Differential Evolution for Multiobjective Portfolio Optimization , 2008 .

[9]  Yue Qi,et al.  Randomly generating portfolio-selection covariance matrices with specified distributional characteristics , 2007, Eur. J. Oper. Res..

[10]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[11]  Wei Chen,et al.  The Adaptive Genetic Algorithms for Portfolio Selection Problem , 2006 .

[12]  Simon French,et al.  Multiple Criteria Decision Making: Theory and Application , 1981 .

[13]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[14]  Carlos M. Fonseca,et al.  Exploring the Performance of Stochastic Multiobjective Optimisers with the Second-Order Attainment Function , 2005, EMO.

[15]  Jürgen Branke,et al.  Efficient implementation of an active set algorithm for large-scale portfolio selection , 2008, Comput. Oper. Res..

[16]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[17]  Minqiang Li,et al.  A Genetic Algorithm for Solving Portfolio Optimization Problems with Transaction Costs and Minimum Transaction Lots , 2005, ICNC.

[18]  Yue Qi,et al.  Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection , 2007, Ann. Oper. Res..

[19]  Mitsuo Gen,et al.  An Effective Decision-Based Genetic Algorithm Approach to Multiobjective Portfolio Optimization Problem , 2007 .