The gaining returns in line with risks is always a major concern for market play-ers. This study compared the selection of stock portfolios based on the strategy of buying and retaining winning stocks and the purchase strategy based on the level of investment risks. In this study, the two-step optimization algorithms NSGA-II and SPEA-II were used to optimize the stock portfolios. In order to determine the winning algorithm, the performance indexes, Set coverage and the Mean Ideal Distance were used. Finally, the active shares of 50 Tehran Stock Exchange com-panies were analysed (2007-2016). The results indicate that the SPEA-II algo-rithm can perform optimization and achieve a better performance than the NSGA-II. This algorithm could achieve better outcomes than the winning strategy during the selection period based on the risk-taking strategies in different months
