具有限额约束的投资组合优化问题的量子进化算法

A quantum evolutionary algorithm for portfolio optimization problems with constraints of investment limit

将量子进化算法应用到投资组合优化问题中,设计了一种具有限额约束的投资组合优化问题的量子进化算法.首先,考虑收益与风险的均衡性,提出了一种新的收益风险评判准则,并以该准则为目标优化投资配置;其次,改进了初始种群生成方式,给出了量子染色体的编码、解码技巧及自适应量子门旋转策略;设计检查修复算子将染色体简单解码得到的解修复为问题的可行解.实证分析检验了量子进化算法的可行性和有效性,结果显示,量子进化算法能够有效消除算法早熟问题;设置的风险水平越低,收益率增长越明显;收益率随着风险水平的上升而增大,最后逐渐趋于稳定;算法具有较好的稳定性和可靠性.

The quantum evolutionary algorithm is applied to the portfolio optimization problem,a quantum evolutionary algorithm is designed to solve portfolio optimization problem with constraints of investment limit.Firstly,considering the balance between return and risk for an investment portfolio,a new return-risk evaluation criterion is proposed,and the criterion is selected as the target to optimize the investment allocation.Secondly,the generation style of initial quantum population is improved,and the coding and decoding techniques of quantum chromosome,as well as an adaptive rotation strategy for quantum gate are given.Finally,a check repair operator is designed to repair a solution obtained by simple chromosome decoding to a feasible solution.The feasibility and effectiveness of the quantum evolutionary algorithm are verified by empirical analysis,the results show that the algorithm can effectively remove premature convergence of algorithm;the lower the risk level,the greater the increase of return rate;with the increase of risk level,the return rate increases gradually and tends to be stable,the algorithm has stronger stability and reliability.