利用动态降维差分进化算法解决多约束的投资组合优化问题  

Dimension-decreasing Differential Evolution Method for Portfolio Optimization

作　　者：王佳彬[1,2] 沈洁[1,2] 陈伟能[1,2] 张军[1,2] 

机构地区：[1]中山大学超级计算学院,广州510006 [2]中山大学机器智能与先进计算教育部重点实验室,广州510006

出　　处：《小型微型计算机系统》2016年第7期1526-1530,共5页Journal of Chinese Computer Systems

基　　金：国家自然科学基金面上项目(61379061)资助;博士点基金项目(20130171120016)资助;广东省自然科学基金项目(S2013040014949;2015A030306024)资助

摘　　要：投资者在实际投资过程中会有各种各样的偏好,因此在投资组合优化问题的数学模型中,会含有多种约束条件.在这些约束条件下,投资组合问题的复杂程度会随投资规模的增大而急剧增加.采用一种可动态降维的差分进化算法,用于解决含有基本约束、边界约束以及基数约束的多约束投资组合优化问题.这种差分进化算法具有两大优势,由于该算法可以在求解过程中通过逐渐降维来降低求解复杂性,因此能够处理较大规模的投资组合优化问题;此外,通过动态降维的方法,可以处理投资组合优化问题中的基数约束.实验结果表明,动态降维差分进化算法的性能优于粒子群优化算法,同时在处理基数约束方面优于k-means聚类分析算法.Investors have various preferences when they make investments. Therefore,many constraints are included in the mathematical model of the portfolio optimization problem. These constraints may render the problem much more complex when the number of assets grows. This paper develops a dimension-decreasing differential evolution algorithm for solving the portfolio optimization problem with basic,bounding and cardinality constraints. The dimension-decreasing differential evolution algorithm has two remarkable advantages. On the one hand,the dimension-decreasing differential evolution algorithm can handle relatively large-scale problems,as it can cut dimensions gradually and reduce the complexity of these problems. On the other hand,this algorithm can easily handle the cardinality constraint by dynamically decreasing the number of selected assets from the total assets. The experimental results showthat the dimension-decreasing differential evolution algorithm performs better than the particle swarm optimization algorithm,and it also do better than the k-means cluster analysis method in terms of cardinality constraint.

关 键 词：投资组合优化 差分进化算法 基数约束 动态降维 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]