• Login
  • Register
  • Search

Portfolio Optimization with Metaheuristics

Georgios Mamanis


Portfolio optimization is the problem ofsearching foran optimal allocation of wealth to put in the available assets. Since the seminalworkdoneby Markowitz, the problem is codifiedas a two-objective mean-risk optimization problem where the best trade-off solutions (portfolios) between risk (measured by variance) and mean are hunted. Complex measures of risk (e.g., value-at-risk, expected shortfall, semivariance), addedobjective functions (e.g., maximization of skewness, liquidity, dividends) and pragmatic, real-worldconstraints (e.g., cardinality constraints, quantity constraints, minimum transaction lots, class constraints) that are included in recent portfolio selection models, provide many optimization challenges. The resulting portfolio optimizationproblem becomes very hard to be tackledwith exact techniquesas it displaysnonlinearities, discontinuities and high dimensional efficient frontiers. These characteristics prompteda lot ofresearchers to explorethe use of metaheuristics, which are powerful techniquesfor discoveringnear optimal solutions (sometimes the real optimum) for hard optimization problems in acceptable computationaltime. This report provides a briefnoteon the field of portfolio optimization with metaheuristics and concludes that especially Multiobjectivemetaheuristics (MOMHs) provide a natural background for dealing with portfolio selection problems with complex measures of risk (which define non-convex, non-differential objective functions), discrete constraints and multiple objectives.


Metaheuristics; Multiobjective optimization; Portfolio selection

Full Text:



Anagnostopoulos, K. P., &Mamanis, G. (2010).A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research, 37, 1285–1297.

Anagnostopoulos, K. P., &Mamanis, G. (2011). The mean–variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms. Expert Systems with Applications, 38, 14208–14217

Bienstock, D. (1995). Computational study of a family of mixed integer quadratic programming problems. Mathematical Programming, 74, 121–140.

Chang, T. J., Meade, N., & Beasley, J. E. (2000). Heuristics for cardinality constrained portfolio optimization. Computers & Operations Research, 27, 1271–1302.

Crama, Y., &Schyns, M. (2003).Simulated annealing for complex portfolio selection problems.European Journal of Operational Research, 150, 546–571.

Cura, T. (2009). Particle swarm optimization approach to portfolio optimization. Nonlinear Analysis: Real World Applications, 10, 2396–2406.

Elton, E. J., Gruber, M. J., Brown, S. J., &Goetzmann, W. N. (2014). Modern portfolio theory and investment analysis (9th ed.). Wiley.

Fernandez, A., & Gomez, S. (2007). Portfolio selection using neural networks. Computers & Operations Research, 34, 1177–1191.

Gilli, M., Maringer, D., & Winker, P. (2008). Applications of Heuristics in Finance, in: D. Seese, C. Weinhardt, F. Schlottmann (Eds), Handbook of Information Technology in Finance, Springer, pp. 635–653.

Hirschberger, M., Qi, Y., &Steuer, R. E. (2010).Large-scale MV efficient frontier computation via a procedure of parametric quadratic programming. European Journal of Operational Research, 204, 581–588.

Jobst, N. J., Horniman, M. D., Lucas, C. A., &Mitra, G. (2001).Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints. Quantitative Finance, 1, 489–501.

Kumar, D., & Mishra, K. K. (2017). Portfolio optimization using novel co-variance guided Artificial Bee Colony algorithm. Swarm and Evolutionary Computation, 33, 119–130.

Macedo, L. L., Godinho, P., &Alves, M. J. (2017).Mean-semivariance portfolio optimization with multiobjective evolutionary algorithms and technical analysis rules. Expert Systems with Applications, 79, 33–43.

Maringer, D. (2005).Portfolio Management with Heuristic Optimization.Springer, New York.

Maringer, D. G., &Kellerer, H. (2003). Optimization of cardinality constrained portfolios with a hybrid local search algorithm. OR Spectrum, 25, 481–495.

Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7, 77–91.

Markowitz, H. M. (1990). Portfolio selection, efficient diversification of investments. Cambridge MA and Oxford UK: Blackwell.

Mitra, G., Kyriakis, T., Lucas, C., &Pirbhai, M. (2003). A review of portfolio planning: Models and systems. In S. Satchell, & A. Scowcroft (Eds.), Advances in portfolio construction and implementation (pp. 1–39).

Righi, M., B., &Borenstein, D. (2017). A simulation comparison of risk measures for portfolio optimization. Finance Research Letters, in press doi: https://doi.org/10.1016/j.frl.2017.07.013.

Qi, Y., Hirschberger, M., Steuer, R.E. (2009).Dotted Representations of Mean-Variance Efficient Frontiers and their Computation, INFOR, 47, 15–21.

Roman, D., Darby-Dowman, K.,&Mitra, G. (2007).Mean-risk models using two risk measures: A multi-objective approach. Quantitative Finance, 7, 443–458.

Schaerf, A. (2002). Local search techniques for constrained portfolio selection problems. Computational Economics, 20, 177–190.

Schlottmann, F., Seese, D. (2004). Financial applications of multi-objective evolutionary algorithms: recent development and future research directions, in: C.A.C. Coello, G. Lamont, (Eds.), Applications of Multi-Objective Evolutionary Algorithms, World Scientific, pp. 627–652.

Shaw, D. X., Liu, S., &Kopman, L. (2008).Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optimization Methods and Software, 23, 411–420.

Soleimani, H., Golmakani, H. R., &Salimi, M. H. (2009).Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm. Expert Systems with Applications, 36, 5058–5063.

DOI: http://dx.doi.org/10.18686/fm.v2i2.1048