改进的粒子群算法及在CVaR模型中的应用  

Improved Particle Swarm Optimizer and Its Application for CvaR Model

作　　者：刘衍民[1] 赵庆祯[2] 牛奔[3] 

机构地区：[1]遵义师范学院数学系,贵州遵义563002 [2]山东师范大学管理与经济学院,山东济南250014 [3]深圳大学管理学院,深圳518060

出　　处：《数学的实践与认识》2011年第17期139-147,共9页Mathematics in Practice and Theory

基　　金：贵州教育厅社科项目(0705204;10ZC077);遵市科技局项目([2008]21)

摘　　要：为了求解带有条件风险价值(CVaR)约束的均值-方差模型,提出一种基于广义学习和柯西变异的粒子群算法(CCPSO).在CCPSO算法中,为了提升种群跳出局部最优解的能力,引入一种广义学习策略,提升粒子向最优解飞行的概率;并引入一种动态变异概率,对粒子自身最优位置进行柯西变异,更好地引导种群的飞行;最后,根据全局最优粒子的运行状况,每间隔若干代对其进行变异,以产生全局新的领导者.在基准函数测试中,结果显示CCPSO算法有较好的运行结果.在CVaR模型投资组合优化中,与其它算法相比,CCPSO算法所获结果是有效的,并且优于其它算法.In order to solve the mean-variance portfolio model with conditional value-at-risk （CVaR） constraint, a PSO algorithm based on comprehensive learning and Cauchy mutation is proposed. In CCPSO, to improve the ability to escape from local optima, a comprehensive learning strategy is adopted, which increase the probability of flying to the optimal solution. And a dynamic mutation is introduced to make the Cauchy mutation for each pbest. At last, in terms of the condition of the best performing particle （gbest） in the swarm, at each iteration, the mutation operation is employed to generate the new gbest. The experiments on benchmarks indicate that the proposed algorithm has good performance. In the CvaR model, the CCPSO algorithm is feasible and effective, and better results compared with other algorithms.

关 键 词：广义学习 粒子群算法 柯西变异 条件风险价值(CvaR) 

分 类 号：O212.1[理学—概率论与数理统计]