Stock portfolio optimization is both an attractive research topic and a complex problem due to the rapidly changing economy. Based on optimization techniques, many algorithms have been proposed to mine different portfolios. In the previous approach, a group stock portfolio (GSP) was derived based on the investors' objective and subjective requests by the grouping genetic algorithm. Stocks were divided into groups, with those in the same group being similar. The benefit of using a GSP is that investors can replace any stock that they do not like with substitute stocks in the same group. To increase the similarity of stocks in groups, stock price series are taken into consideration, and an enhanced approach is proposed to derive a series-based GSP that can be used to provide more actionable stock portfolios to investors making decisions. In chromosome representation, grouping, stock and stock portfolio parts are used to represent a GSP as did the previous approach. To increase the return and similarity of a GSP, the stability factor is designed based on cash dividends, and the unit and price balances are utilized as well. Because the dimension of stock price series is high, the symbolic aggregate approximation (SAX) and extended symbolic aggregate approximation (ESAX) are selected to transform data points into symbols. Then, the series distance factor is presented to evaluate the similarity of stock price series in groups of a GSP. By using the new factors and the existing factors in the previous approach, two new fitness functions are developed to evaluate the quality of chromosomes. Experiments on a real-world dataset were conducted to show the merits of the proposed approach using the two fitness functions with SAX and ESAX. The results show that the return on investment (ROI) of the proposed approach using the fitness functions with SAX is approximately 16% to 18% and better than the ROI obtained with ESAX. However, the proposed approach with ESAX achieves better group similarity than does SAX.
