Portfolio optimization using multi-objective genetic algorithms

Abstract

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 2ndversion (SPEA2) and Non-Dominated Sorting Genetic Algorithm 2nd version (NSGA2). The results show that using fuzzy logic to combine optimization objectives of VEGA (in VEGA_Fuz1) 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. © 2007 IEEE.