求解自融资投资组合模型的量子行为的粒子群优化算法  

Quantum-Behaved Particle Swarm Optimization Algorithm for Solving Self-Financing Portfolio Model

作　　者：卢小丽 何光 李高西 LU Xiaoli;HE Guang;LI Gaoxi(Research Center for Economy of Upper Reaches of the Yangtze River,Chongqing Technology and Business University,Chongqing 400067,China;College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学长江上游经济研究中心,重庆400067 [2]重庆工商大学数学与统计学院,重庆400067

出　　处：《武汉大学学报（理学版）》2021年第2期136-142,共7页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金(11901068);重庆市基础与前沿研究计划项目(cstc2016jcyjA0564);重庆工商大学博士科研启动项目(2015-56-08);重庆工商大学青年项目(1552004);长江上游研究中心科研项目(17540003)。

摘　　要：为有效求解自融资投资组合模型,基于粒子群优化(particle swarm optimization,PSO)算法,提出了一种改进的量子行为的粒子群优化算法(LDQPSO)。在算法的设计中,借助Levy飞行策略对粒子位置的迭代公式进行更新,用于提高算法的局部收敛精度和全局探索能力;针对迭代后期的早熟问题,引入了多样性的判定和增强的操作。算法性能测试结果表明,LDQPSO算法在收敛精度和鲁棒性上比已有的3种PSO改进算法有更好的表现。应用改进算法对自融资投资组合模型进行了求解。与传统的遗传算法、差分进化、粒子群优化算法和量子行为的粒子群优化算法相比,LDQPSO算法在实际应用中拥有更好的寻优能力。In order to solve self-financing portfolio model effectively, an improved QPSO(quantum-behaved particle swarm optimization)algorithm—LDQPSO is proposed based on PSO(particle swarm optimization)algorithms. To enhance local convergence precision and global exploration capability of the algorithm, Levy flight strategy is used to renew the iterative formula of particle position in the algorithm design. Meanwhile, the identification and improvement of diversity are considered against premature in the later stage of iteration. And performance test results indicate that LDQPSO algorithm achieves better convergence accuracy and robustness than three modified PSO algorithms. Finally, the improved algorithm is applied to solve self-financing portfolio model. Compared with traditional genetic algorithm, differential evolution, particle swarm optimization algorithm and quantum-behaved particle swarm optimization algorithm, LDQPSO algorithm has better search ability in practical application.

关 键 词：自融资投资组合 量子行为的粒子群优化算法 Levy飞行 收敛精度 多样性 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]