Portfolio optimization using multi-obj ective genetic algorithms

A portfolio optimisation problem involves allocation of investment to a number of different assets to maximize yield and minimize risk in a given investment period. The selected assets in a portfolio not only collectively contribute to its yield but also interactively define its risk as usually measured by a portfolio variance. In this paper we apply various techniques of multiobjective genetic algorithms to solve portfolio optimization with some realistic constraints, namely cardinality constraints, floor constraints and round-lot constraints. The algorithms experimented in this paper are Vector Evaluated Genetic Algorithm (VEGA), Fuzzy VEGA, Multiobjective Optimization Genetic Algorithm (MOGA) , Strength Pareto Evolutionary Algorithm 2nd version (SPEA2) and Non-Dominated Sorting Genetic Algorithm 2nd version (NSGA2). The results show that using fuzzy logic to combine optimization objectives of VEGA (in VEGAFuzl) for this problem does improve performances measured by Generation Distance (GD) defined by average distances of the last generation of population to the nearest members of the true Pareto front but its solutions tend to cluster around a few points. MOGA and SPEA2 use some diversification algorithms and they perform better in terms of finding diverse solutions around Pareto front. SPEA2 performs the best even for comparatively small number of generations. NSGA2 performs closed to that of SPEA2 in GD but poor in distribution.

[1]  F. Black,et al.  The Capital Asset Pricing Model: Some Empirical Tests , 2006 .

[2]  Andreas Zell,et al.  Hybrid Representations for Composition Optimization and Parallelizing MOEAs , 2005, Practical Approaches to Multi-Objective Optimization.

[3]  Franco Raoul Busetti,et al.  Metaheuristic Approaches to Realistic Portfolio Optimization , 2005, cond-mat/0501057.

[4]  Andrea G. B. Tettamanzi,et al.  A genetic approach to portfolio selection , 1993 .

[5]  Piero P. Bonissone,et al.  Multiobjective financial portfolio design: a hybrid evolutionary approach , 2005, 2005 IEEE Congress on Evolutionary Computation.

[6]  Andreas Zell,et al.  Evaluating a hybrid encoding and three crossover operators on the constrained portfolio selection problem , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[7]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[8]  Marco Laumanns,et al.  A Tutorial on Evolutionary Multiobjective Optimization , 2004, Metaheuristics for Multiobjective Optimisation.

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

[10]  Marco Tomassini,et al.  Distributed Genetic Algorithms with an Application to Portfolio Selection Problems , 1995, ICANNGA.

[11]  D. Maringer.  Heuristic Optimization for Portfolio Management [Application Notes] , 2008, IEEE Computational Intelligence Magazine.

[12]  Christian Blum,et al.  Metaheuristics in combinatorial optimization: Overview and conceptual comparison , 2003, CSUR.

[13]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

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

[15]  E. Elton,et al.  Modern Portfolio Theory, 1950 to Date , 1997 .