I_(ϵ+)LGEA:A Learning-Guided Evolutionary Algorithm Based on I_(ϵ+) Indicator for Portfolio Optimization

Portfolio optimization is a classical and important problem in the field of asset management,which aims to achieve a trade-off between profit and risk.Previous portfolio optimization models use traditional risk measurements such as variance,which symmetrically delineate both positive and negative sides and are not practical and stable.In this paper,a new model with cardinality constraints is first proposed,in which the idiosyncratic volatility factor is used to replace traditional risk measurements and can capture the risks of the portfolio in a more accurate way.The new model has practical constraints which involve the sparsity and irregularity of variables and make it challenging to be solved by traditional Multi-Objective Evolutionary Algorithms(MOEAs).To solve the model,a Learning-Guided Evolutionary Algorithm based on I_(ϵ+)indicator(I_(ϵ+)LGEA)is developed.In I_(ϵ+)LGEA,the I_(ϵ+)indicator is incorporated into the initialization and genetic operators to guarantee the sparsity of solutions and can help improve the convergence of the algorithm.And a new constraint-handling method based on I_(ϵ+)indicator is also adopted to ensure the feasibility of solutions.The experimental results on five portfolio trading datasets including up to 1226 assets show that I_(ϵ+)LGEA outperforms some state-of-the-art MOEAs in most cases.