An Evolutionary Algorithm with a New Coding Scheme for Multi-objective Portfolio Optimization

  • Yi Chen
  • Aimin Zhou
  • Rongfang Zhou
  • Peng He
  • Yong Zhao
  • Lihua Dong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10593)

Abstract

A portfolio optimization problem involves optimal allocation of finite capital to a series of assets to achieve an acceptable trade-off between profit and risk in a given investment period. In the paper, the extended Markowitz’s mean-variance portfolio optimization model is studied. A major challenge with this model is that it contains both discrete and continuous decision variables, which represent the assignment and allocation of assets respectively. To deal with this hard problem, this paper proposes an evolutionary algorithm with a new coding scheme that converts discrete variables into continuous ones. By this way, the mixed variables can be handled, and some of the constraints are naturally satisfied. The new approach is empirically studied and the experiment results indicate its efficiency.

Keywords

Multi-objective portfolio Constraints handling Mixed variables 

Notes

Acknowledgement

This work is supported by the Shanghai Clearing House under the project of ‘artificial intelligence methods for complex 0-1 financial optimization’, the National Natural Science Foundation of China under Grant No. 61673180, and the Science and Technology Commission of Shanghai Municipality under Grant No. 14DZ2260800.

References

  1. 1.
    Bean, J.C.: Genetic algorithms and random keys for sequencing and optimization. ORSA J. Comput. 6(2), 154–160 (1994)CrossRefMATHGoogle Scholar
  2. 2.
    Bienstock, D.: Computational study of a family of mixed-integer quadratic programming problems. Math. Program. 74(2), 121–140 (1996)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Chang, T.-J., Meade, N., Beasley, J.E., Sharaiha, Y.M.: Heuristics for cardinality constrained portfolio optimisation. Comput. Oper. Res. 27(13), 1271–1302 (2000)CrossRefMATHGoogle Scholar
  4. 4.
    Coello, C.A.C.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput. Methods Appl. Mech. Eng. 191(11), 1245–1287 (2002)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Elton, E.J., Gruber, M.J.: Investments and Portfolio Performance. World Scientific, Singapore (2011)Google Scholar
  6. 6.
    Grinblatt, M., Titman, S., Wermers, R.: Momentum investment strategies, portfolio performance, and herding: a study of mutual fund behavior. Am. Econ. Rev. 1088–1105 (1995)Google Scholar
  7. 7.
    Gulpinar, N., An, L.T.H., Moeini, M.: Robust investment strategies with discrete asset choice constraints using DC programming. Optimization 59(1), 45–62 (2010)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Lwin, K., Rong, Q., Kendall, G.: A learning-guided multi-objective evolutionary algorithm for constrained portfolio optimization. Appl. Soft Comput. 24, 757–772 (2014)CrossRefGoogle Scholar
  9. 9.
    Mansini, R., Speranza, M.G.: Heuristic algorithms for the portfolio selection problem with minimum transaction lots. Eur. J. Oper. Res. 114(2), 219–233 (1999)CrossRefMATHGoogle Scholar
  10. 10.
    Markowitz, H.: Portfolio selection. J. Finance 7(1), 77–91 (1952)Google Scholar
  11. 11.
    Newman, A.M., Weiss, M.: A survey of linear and mixed-integer optimization tutorials. INFORMS Trans. Educ. 14(1), 26–38 (2013)CrossRefGoogle Scholar
  12. 12.
    Robič, T., Filipič, B.: DEMO: differential evolution for multiobjective optimization. In: Coello, C.A.C., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 520–533. Springer, Heidelberg (2005). doi:10.1007/978-3-540-31880-4_36 CrossRefGoogle Scholar
  13. 13.
    Shaw, D.X., Liu, S., Kopman, L.: Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optim. Methods Softw. 23(3), 411–420 (2008)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Sierra, M.R., Coello, C.A.C.: Improving PSO-based multi-objective optimization using crowding, mutation and \(\epsilon \)-dominance. In: Coello, C.A.C., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 505–519. Springer, Heidelberg (2005). doi:10.1007/978-3-540-31880-4_35 CrossRefGoogle Scholar
  15. 15.
    Skolpadungket, P., Dahal, K., Harnpornchai, N.: Portfolio optimization using multi-objective genetic algorithms. In: 2007 IEEE Congress on Evolutionary Computation, pp. 516–523. IEEE (2007)Google Scholar
  16. 16.
    Steuer, R.E., Hirschberger, M., Deb, K.: Extracting from the relaxed for large-scale semi-continuous variable nondominated frontiers. J. Glob. Optim. 64(1), 33–48 (2016)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Streichert, F., Ulmer, H., Zell, A.: Evolutionary algorithms and the cardinality constrained portfolio optimization problem. In: Ahr, D., Fahrion, R., Oswald, M., Reinelt, G. (eds.) ORP 2003. Operations Research Proceedings, vol. 2003, pp. 253–260. Springer, Heidelberg (2004). doi:10.1007/978-3-642-17022-5_33 CrossRefGoogle Scholar
  19. 19.
    Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Yi Chen
    • 1
  • Aimin Zhou
    • 1
  • Rongfang Zhou
    • 2
  • Peng He
    • 2
  • Yong Zhao
    • 2
  • Lihua Dong
    • 2
  1. 1.Shanghai Key Laboratory of Multidimensional Information Processing, Department of Computer Science and TechnologyEast China Normal UniversityShanghaiChina
  2. 2.Shanghai Clearing HouseShanghaiChina

Personalised recommendations