A knowledge-based constructive estimation of distribution algorithm for bi-objective portfolio optimization with cardinality constraints

Portfolio optimization is an essential and practical model for financial decision making. With the consideration of some real-world constraints, especially the cardinality constraints, the problem becomes much more challenging as it converts to a mixed-integer quadratic multi-objective optimization problem. To solve this problem, we propose a knowledge-based constructive estimation of distribution algorithm (KC-EDA) with the following three features. First, a hybrid design of Ant colony optimization (ACO) and Estimation distribution algorithm (EDA) is used to solve this mixed-variable optimization problem based on knowledge information. Second, a knowledge accumulation mechanism is designed to discover the internal relationship among the assets. The mechanism can not only guide the selection of assets effectively but also enable the use of historical information during evolution to direct the allocation of investment proportion. Third, a constructive approach is applied to construct portfolios under the constraints. This hybrid and constructive approach is incorporated into the multi-objective evolutionary framework and the experiment has been performed on the SZ50, SZ180, and SZ380 datasets (from January 2014 to December 2018). The experimental results demonstrate the effectiveness of KC-EDA in solving the portfolio optimization problem with cardinality constraints.