MOEA/D with An Improved Multi-Dimensional Mapping Coding Scheme for Constrained Multi-Objective Portfolio Optimization

Abstract

Portfolio optimization is an important financial problem, which involves an optimal allocation of finite capital to a series of assets to achieve an acceptable trade-off between profit and risk in a given investment period. In this paper, an extended Markowitz’s mean-variance portfolio optimization model, which is converted as a constrained multi-objective problem, is studied. Since this model involves both discrete and continuous variables, a multi-dimensional mapping coding scheme (MDM) has been adopted to convert discrete variables to continuous ones. Although the basic MDM is effective for dealing with the constrained multi-objective portfolio optimization problems, it sometimes prefers to choose some balanced investments, in which the allocation of funds for each selected asset is very similar. This may result in a focus on the low-risk and low-yield solutions. To solve this problem, an improved multi-dimensional mapping coding scheme is proposed in this paper. This new coding scheme is integrated into the decomposition based multi-objective evolutionary algorithm (MOEA/D). The algorithm is then applied to some test data, with the asset size ranging from 31 to 255, and the experimental results have indicated that the improved MDM coding scheme can significantly improve the performance comparing to the basic MDM coding scheme.