Abstract: Multi-objective portfolio optimization is decides the percentage of the overall portfolio value allocated to each portfolio component with specified risk and return and exchanging expense characteristics to make total investment risk and exchanging expense least,at the same time,make total investment return most and so on.The problem of multi-objective portfolio optimization is a problem of NP_hard.Ordinary methods are hard to be at the holistic best point.In this paper the authors study how to use Quantum-Behaved Partical Swarm Optimization(QPSO)combined Simulated Annealing(SA)algorithm to solve the problem of multiobjective portfolio optimization,and also compare performance of single QPSO with performance of QPSO-SA.Many experiments that optimize the allocation of various stocks in the market of USA using QPSO-SA algorithm and the analyse of experiment result indicate that the QPSO-SA is a kind of efficient and reliable optimization algorithm and it has determinate applied value in the field of multi-objective portfolio optimization.

Key words: multi-objective, portfolio, optimization, quantum, simulated annealing

摘要： 多目标投资组合优化就是决定每个具有特定风险、回报、交易费用等特征的资产在总投资价值中的投资比例，即选择那些资产投资以及寻找每个投资资产的最佳投资比例，使得总投资的风险最小、交易费用最小、回报最大等等。该问题是典型的NP难解问题，通常方法很难达到全局最优。研究如何把基于量子行为的微粒群优化算法（QPSO算法）和模拟退火算法(SA算法)结合起来解决多目标投资组合优化问题。利用美国标准普尔指数100的股票历史数据进行验证，纯QPSO算法与QPSO-SA混合算法的运行结果比较表明在解决多目标投资组优化问题中，QPSO-SA混合算法是一种高效的、可靠的优化算法，具有一定的实用价值。

关键词: 多目标, 投资组合, 最优化, 量子, 模拟退火