The portfolio selection problem has a venerable history. For example, Markowitz (1952), (1959), formulates the problem as a trade-off between the expected return and the expected risk of a portfolio. For his path breaking work that has revolutionized investment practice, he won the Nobel Prize in 1990. In this paper we proposed enhancement to the traditional portfolio selection problem. We enhance the formulation of the problem by introducing four additional constraints that take into account (a) the collinearity problem to decrease the portfolio risk, (b) the special preference of active stocks to control the systematic portfolio risk, (c) the special preference of stocks with outstanding performance to increase the unexpected return which it is special case of the non-efficient market, and (d) control the overall risk of the portfolio. Additionally, we propose enhancement method for GA (EGA). In the
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