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A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem

  • Multiple Objective Optimization
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Abstract

This paper proposes a novel multiobjective evolutionary Algorithm (MOEA) for the solution of the cardinality constrained portfolio optimization problem (CCPOP). The proposed algorithm introduces an efficient encoding scheme specially designed for dealing with the difficulties of the CCPOP. Also, the proposed algorithm incorporates a new mutation and recombination operator tailor-made to work well with the new encoding scheme. Datasets from seven different stock markets are utilized for testing the efficiency of the proposed approach. In particular, the performance of the proposed efficiently encoded multiobjective portfolio optimization solver (EEMPOS) is assessed in comparison with two well-known MOEAs, namely NSGAII and MOEA/D. The experimental results indicate that the proposed EEMPOS outperforms the two other MOEAs for all examined performance metrics when is applied to the solution of the CCPOP for a fraction of time required by the other techniques.

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Abbreviations

\(\Omega \) :

The search space

\(\hbox {f}_{\mathrm{i}}\) :

Objective function i

\(\hbox {R}^{\mathrm{N}} \) :

Set of all N-tuples of real numbers (N-dimentional space of the decision variables)

\(\rho _{ij} \) :

Correlation

N :

Number of assets available

\(w_i\) :

Decision variable denoting the proportion of asset i in the portfolio

\(\sigma _i \) :

Standard deviation of stock returns

\(K_{min}\) :

Minimum number of assets that a portfolio can hold

\(K_{max} \) :

Maximum number of assets that a portfolio can hold

\(l_i\) :

Floor constraint

\(u_i \) :

Ceiling constraint

\(P_{c}\) :

Crossover probability

\(P_{m}\) :

Mutation probability

\(\eta _{c}\) :

Distribution index for the crossover operator

\(\eta _{m}\) :

Distribution index for the mutation operators

F:

Real constant factor, \(\hbox {F}~\in ~[0, 2]\) which controls the amplification of the differential variation

CR:

Crossover constant \(\hbox {CR}~\in ~[0, 1]\)

\(\hbox {N}^{\mathrm{pop}}\) :

Population size

HV:

Hypervolume indicator

IGD:

Inverted Generational distance

\(\hbox {I}_{\upvarepsilon }\) :

Epsilon indicator

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  1. Decision Support Systems Laboratory, Department of Informatics, University of Piraeus, 80, Karaoli & Dimitriou Str., 18534, Piraeus, Greece

    K. Liagkouras & K. Metaxiotis

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  1. K. Liagkouras
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Liagkouras, K., Metaxiotis, K. A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem. Ann Oper Res 267, 281–319 (2018). https://doi.org/10.1007/s10479-016-2377-z

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