Choosing a stock portfolio is one of the important topics in the field of investment management, which discusses how to allocate an investor's capital to different assets and form an efficient portfolio, which depends on the assumptions and modeling conditions for selecting and optimizing the investment portfolio. It is closer to real world conditions, the results will be more reliable. Considering a single period horizon for investment is not very realistic and most investors invest for more than one period so that the investor can review his position over time .Various patterns and methods have been presented since Markowitz's initial work to choose the optimal investment portfolio. However, finding the most useful pattern in choosing this portfolio has always been a concern of investors. In this research, a number of stock portfolio optimization algorithms such as ant algorithm, genetic algorithm, cultural algorithm, particle swarm algorithm, and firefly algorithm are given. Which is briefly explained about each.