In the mean-variance-skewness-kurtosis framework, this study solve multiple conflicting and competing portfolio objectives such as maximizing expected return and skewness and minimizing risk and kurtosis simultaneously, by construction of a polynomial goal programming (PGP) model into which investor preferences over higher return moments are incorporated. To examine its practicality, the approach is tested on four major stock indices. Empirical results indicate that, for all examined investor preferences and stock indices, the PGP approach is significantly efficient way to solve multiple conflicting portfolio objectives in the mean-varianceskewness- kurtosis framework. In the meantime, we find that the different investors' preferences not only affect asset allocations of portfolio, but also affect the four moment statistics of return.