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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (4): 533-544.doi: 10.3969/j.issn.1005-3085.2022.04.003

• • 上一篇    下一篇

改进的 QPSO 算法在自融资投资组合中的应用

何  光1,2,  卢小丽3,  李高西1,2   

  1. 1. 重庆工商大学经济社会应用统计重庆市重点实验室，重庆 400067;
    2. 重庆工商大学数学与统计学院，重庆 400067;
    3. 重庆工商大学长江上游经济研究中心，重庆 400067
  • 出版日期:2022-08-15 发布日期:2022-10-15
  • 基金资助:
    国家自然科学基金 (11901068)；重庆市自然科学基金 (cstc2020jcyj-msxmX0328; cstc2020jcyj-msxmX0316)；重庆市教委人文社科基地项目 (18SKJD034)；重庆工商大学博士科研启动项目 (2015-56-08)；重庆工商大学校级项目 (KFJJ2016008; 1552004).

Application of Improved QPSO Algorithm in Self-financing Portfolio

HE Guang1,2,  LU Xiaoli3,  LI Gaoxi1,2   

  1. 1. Chongqing Key Laboratory of Social Economic and Applied Statistics, Chongqing Technology and Business University, Chongqing 400067; 
    2. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067; 
    3. Research Center for Economy of Upper Reaches of the Yangtze River, Chongqing Technology and Business University, Chongqing 400067
  • Online:2022-08-15 Published:2022-10-15
  • Supported by:
    The National Natural Science Foundation of China (11901068); the Natural Science Foundation of Chongqing Municipality (cstc2020jcyj-msxmX0328; cstc2020jcyj-msxmX0316); the Humanities and Social Sciences Base Project of Chongqing Municipal Education Commission (18SKJD034); the Doctoral Research Project of Chongqing Technology and Business University (2015-56-08); the Project of Chongqing Technology and Business University (KFJJ2016008; 1552004).

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摘要：

针对量子粒子群优化 (Quantum Particle Swarm Optimization, QPSO) 算法的缺陷，提出了一种基于 L$\acute{\rm e}$vy 飞行策略和混合概率分布的改进量子粒子群优化 (Hybrid Quantum Particle Swarm Optimization, HQPSO) 算法。在算法的设计中，借助 L$\acute{\rm e}$vy 飞行策略对粒子位置的迭代公式进行更新，用于改善算法的局部收敛精度，增强其全局探索能力。另外，考虑到迭代后期的早熟问题，在势阱模型中引入了指数分布和正态分布相结合的混合概率分布，帮助算法及时逃离局部最优。基于 16 个基准函数的测试结果表明，HQPSO 算法在收敛精度和鲁棒性上比其他几种算法表现更好。最后，将改进的 QPSO 算法应用到自融资投资组合模型的求解中，其数值结果与差分进化、粒子群优化算法和量子粒子群优化算法相比，HQPSO 算法展现出更好的可比性和优越性。

关键词: 量子粒子群优化算法, 自融资投资组合, L$\acute{\rm e}$vy 飞行, 混合概率分布, 收敛精度

Abstract:

Aiming at the shortcomings of quantum-behaved particle swarm optimization (QPSO) algorithm, an improved quantum-behaved particle swarm optimization (HQPSO) algorithm based on L$\acute{\rm e}$vy flight strategy and hybrid probability distribution is proposed. In the algorithm design aspect, L$\acute{\rm e}$vy flight strategy is used to renew the iterative formula of particle position, which enhances the local convergence precision and global exploration capability of the algorithm. Besides, considering premature in the later stage of iteration, a hybrid probability distribution combining normal distribution and exponential distribution is introduced into potential well model, which helps algorithm escape local optima in time. Furthermore, the experimental results on 16 benchmark functions show that HQPSO has better convergence and robustness than several other algorithms. Finally, when solving self-financing portfolio model, HQPSO provides comparable and superior numerical results compared with differential evolution, particle swarm optimization algorithm and quantum behaved particle swarm optimization algorithm.

Key words: quantum behaved particle swarm optimization algorithm, self-financing portfolio, L$\acute{\rm e}$vy flight;
hybrid probability distribution, convergence precision

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