An important feature of industrialized and developed countries is the existence of a dynamic and active money and capital market. Therefore, investment plays a decisive role in economic growth. One of the main objectives of the countries is to achieve sustainable economic growth and development. Nowadays a considerable amount of works of investment managers and investors, is building a portfolio of assets that effectively meet demand goal. Portfolio optimization and diversification concepts have become a tool for developing and understanding financial markets and financial decision making. The introduction of Harry Markowitz's portfolio selection theory was the main and most important success in this direction. In this study, we use the mean-variance Markowitz model with cardinality constraints and also a new innovative approach called the Big Bang-Big Crunch algorithm to create a portfolio of assets. The proposed algorithm in this study compares with other algorithms such as simulated annealing, genetic, etc. Using datasets are taken from the stock exchange indices in Hong Kong, Iran and Japan and the results show that this algorithm is competitive to solve the portfolio optimization problem efficiently.