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• A portfolio selection problem with higher-order moments is considered. • Machine learning algorithms are applied for data analysis and prediction in the stock market. • Genetic algorithm is used to solve the multi-objective optimization problem. • The out-of-sample performance of our model is significantly better than those of traditional ones. • Robustness is checked, compared with another two existing methods. Skewness and kurtosis, the third and fourth order moments, are statistics to summarize the shape of a distribution function. Recent studies show that investors would take these higher-order moments into consideration to make a profitable investment decision. Unfortunately, due to the difficulties in solving the multi-objective problem with higher-order moments, the literature on portfolio selection problem with higher-order moments is few. This paper proposes a new hybrid approach to solve the portfolio selection problem with skewness and kurtosis, which includes not only the multi-objective optimization but also the data-driven asset selection and return prediction, where the techniques of two-stage clustering, radial basis function neural network and genetic algorithm are employed. With the historical data from Shanghai stock exchange, we find that the out-of-sample performance of our model with higher-order moments is significantly better than that of traditional mean-variance model and verify the robustness of our hybrid algorithm. [ABSTRACT FROM AUTHOR]