Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Markowitz, H.M.: Portfolio selection: Efficient diversification of investments. Yale University Press, New York (1959)
Steuer, R.E., Qi, Y., Hirschberger, M.: Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection. Annals of Operations Research 152(1), 297–317 (2007)
Stein, M., Branke, J., Schmeck, H.: Efficient implementation of an active set algorithm for large-scale portfolio selection. Computers & Operations Research 35(12), 3945–3961 (2008)
Zhang, W.-G., Chen, W., Wang, Y.-L.: The adaptive genetic algorithms for portfolio selection problem. IJCSNS International Journal of Computer Science and Network Security 6(1), 196–200 (2006)
Lin, D., Li, X., Li, M.: A genetic algorithm for solving portfolio optimization problems with transaction costs and minimum transaction lots. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3612, pp. 808–811. Springer, Heidelberg (2005)
Lin, C.-M., Gen, M.: An effective decision-based genetic algorithm approach to multiobjective portfolio optimization problem. Applied Mathematical Sciences 1(5), 201–210 (2007)
Branke, J., Scheckenbach, B., Stein, M., Deb, K., Schmeck, H.: Portfolio optimization and an envelope-based multi-objective evolutionary algorithm. European Journal of Operational Research 199(3), 684–693 (2009)
Chang, T.-J., Meade, N., Beasley, J.B., Sharaiha, Y.: Heuristics for cardinality constrained portfolio optimisation. Comput. & Op. Res. 27, 1271–1302 (2000)
Crama, Y., Schyns, M.: Simulated annealing for complex portfolio selection problems. European Journal of Operational Research 150, 546–571 (2003)
Krink, T., Paterlini, S.: Differential evolution for multiobjective portfolio optimization. Center for Economic Research (RECent) 021, University of Modena and Reggio E., Dept. of Economics (2008)
Streichert, F., Tanaka-Yamawaki, M.: A memetic algorithm on the constrained portfolio selection problem. Institute of Statistical Mathematics 187, 140–149 (2006)
Streichert, F., Tanaka-Yamawaki, M.: The effect of local search on the constrained portfolio selection problem. In: IEEE International Congress on Evolutionary Computing (CEC 2006), pp. 2368–2374. IEEE Press, Piscatway (2006)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Systems 9(2), 115–148 (1995)
Deb, K.: Multi-objective optimization using evolutionary algorithms. Wiley, Chichester (2001)
Wierzbicki, A.P.: The use of reference objectives in multiobjective optimization. In: Fandel, G., Gal, T. (eds.) Multiple Criteria Decision Making Theory and Applications, pp. 468–486. Springer, Heidelberg (1980)
Hirschberger, M., Qi, Y., Steuer, R.E.: Randomly generating portfolio-selection covariance matrices with specified distributional characteristics. European Journal of Operational Research 177(3), 1610–1625 (2007)
Fonseca, C.M., da Fonseca, V.G., Paquete, L.: Exploring the performance of stochastic multiobjective optimisers with the second-order attainment function. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 250–264. Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Deb, K., Steuer, R.E., Tewari, R., Tewari, R. (2011). Bi-objective Portfolio Optimization Using a Customized Hybrid NSGA-II Procedure. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds) Evolutionary Multi-Criterion Optimization. EMO 2011. Lecture Notes in Computer Science, vol 6576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19893-9_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-19893-9_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19892-2
Online ISBN: 978-3-642-19893-9
eBook Packages: Computer ScienceComputer Science (R0)