Abstract: The research on portfolio selection provides a quantifiable way and scientific basis for investment decision and risk management. In this paper, we introduce a typical nonconcave and nonconvex transaction cost function, and establish a mean-variance lower-semi-variance portfolio model with transaction cost. Considering that different investors have different degrees of risk aversion, the risk aversion coefficient is introduced and the double objective portfolio optimization model is transformed into single objective portfolio optimization model. The model is solved by using Teaching and Learning algorithm, and the optimal portfolio under different returns is obtained. At the same time, the effective boundary of portfolio is given. Finally, the advantage of the algorithm is analyzed, and a good simulation result is presented.

Key words: portfolio, mean-variance, lower semi-variance, transaction cost, teaching-learning-based optimization