Although there has been an increasing number of studies investigate portfolio optimization from different perspectives, few attempts could be found that focus on the development trend and hotspots of this research area. Therefore, it motivates us to comprehensively investigate the development of portfolio optimization research and give some deep insights into this knowledge domain. In this paper, some bibliometric methods are utilized to analyse the status quo and emerging trends of portfolio optimization research on various aspects such as authors, countries and journals. Besides, 'theories', 'models' and 'algorithms', especially heuristic algorithms are identified as the hotspots in the given periods. Furthermore, the evolutionary analysis tends to presents the dynamic changes of the cutting-edge concepts of this research area in the time dimension. It is found that more portfolio optimization studies were at an exploration stage from mean-variance analysis to consideration of multiple constraints. However, heuristic algorithms have become the driving force of portfolio optimization research in recent years. Multidisciplinary analyses and applications are also the main trends of portfolio optimization research. By analysing the dynamic changes and multi-dimensional evolution in recent decades, we contribute to presenting some deep insights of the portfolio optimization research directly, which assists researchers especially beginners to comprehensively learn this research field.