Hybrid Enhanced Binary Honey Badger Algorithm with Quadratic Programming for Cardinality Constrained Portfolio Optimization

A portfolio selection problem with cardinality constraints has been proved to be an NP-hard problem, and it is difficult to solve by the traditional optimization methods. This study considers it to be a hybrid of a classical feature selection problem and a standard mean-variance (MV) portfolio selection model. In particular, we propose a new hybrid meta-heuristic algorithm that combines an enhanced binary honey badger algorithm (EBHBA) with quadratic programming to address this issue. First, we employ the proposed EBHBA algorithm to select a portfolio of K stocks from N candidate stocks. Second, based on its choice we transform the problem into a mean-variance model, whose objective function could be defined as the fitness function of EBHBA. Finally, the optimal solution to the model could be found with the quadratic programming method. We also test our approach using the benchmark data sets available at the OR-Library involving real capital markets, where indices are derived from major stock markets around the world. Computational results demonstrate that the proposed method can achieve a satisfactory result for portfolio selection with cardinality constraints and perform well in searching non-dominated portfolios with high expected returns.