Abstract: To the rational investors, besides giving attention to asset return and risk, the assets number of the portfolio is also an important aspect of their concerns. In certain return and risk level, the number of assets under fewer is easier to manage. This paper optimizes the Markowitz extension multi-objective optimization model using the NSGA-II algorithm and verifies the result through empirical analysis. The analysis result is that the assets number of the portfolio can reduce in certain return and risk levels, and it can greatly reduce the portfolio management cost for the investors.

Key words: portfolio, multi-objective optimization, Genetic Algorithm（GA）

摘要： 对理性的投资者而言，除了关注投资收益和风险外，资产组合中数目的多少也是其关注的重要方面。在一定的收益和风险水平下，资产的数目越少越容易管理。利用NSGA-II算法对Markowitz的扩展模型进行多目标优化，通过实证分析进行验证。由分析结果可知，在一定的收益和风险水平下，资产组合中的数目是可以降低的，对投资者来说可以大大降低其资产组合的管理成本。

关键词: 投资组合, 多目标优化, 遗传算法