Maximum Entropy Bi-Objective Model and its Evolutionary Algorithm for Portfolio Optimization

Diversification of investment is a well-established practice for reducing the total risk of investing. Portfolio optimization is an effective way for investors to disperse investment risk and increase portfolio return. Under the assumption of no short selling, a bi-objective minimizing portfolio optimization model, in which the first objective is a semi-absolute deviation mean function used to measure the portfolio risk, and the second objective is a maximum entropy smooth function used to measure the portfolio return, is given in this paper. Also, a maximum entropy multi-objective evolutionary algorithm is designed to solve the bi-objective portfolio optimization model. In order to obtain a sufficient number of uniformly distributed portfolio Pareto optimal solutions located on the true Pareto frontier and fully exploit the useful asset combination modes which can lead the search process toward the frontier direction quickly in the objective space, a subspace multi-parent uniform crossover operator and a subspace decomposition mutation operator are given. Furthermore, a normalization method to deal with the tight constraint and the convergence analysis of the proposed algorithm are also discussed. Finally, the performance of the proposed algorithm is verified by five benchmark investment optimization problems. The performance evaluations and results analyses illustrate that the proposed algorithm is capable of identifying good Pareto solutions and maintaining adequate diversity of the evolution population. Also, the proposed algorithm can obtain faster and better convergence to the true portfolio Pareto frontier compared with the three state-of-the-art multi-objective evolutionary algorithms. The result can also provide optimal portfolio plan and investment strategy for investors to allocate and manage asset effectively.