改进的粒子群优化算法及其应用研究
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摘要
一直以来,优化技术作为一种广泛应用于求解各种工程技术问题优化解的技术,受到了相关领域专家学者的高度重视,而且获得了快速发展。随着应用领域的不断拓宽,被优化问题的日益复杂,使得求其优化解越来越难,一些传统的优化技术已经不能满足求解的需要。智能优化算法的出现,不仅为优化技术提供了新的思路和手段,并且广泛应用于经济、科学研究和工程技术问题中。粒子群优化算法(Particle Swarm Optimization, PSO算法)是一种基于群体搜索策略的随机优化算法,来源于对鸟群和鱼群群体运动行为的研究。作为一种新的智能优化算法,它在求解复杂问题的优化解过程中,显示出了很强的优势。
粒子群优化算法本身也存在一些固有的缺陷,如在算法运行后期种群多样性丧失和搜索速度迅速减小,导致算法停滞,出现早熟收敛。因此本文将惯性权重自适应调节机制引入到算法中,提出了一种动态自适应粒子群算法。在定义群体多样性度量函数的基础上,采用动态自适应调节策略,使得粒子的惯性权重随群体聚集程度而适时变化,从而调整粒子群搜索的速度和方向以跳出局部最优。
对本文提出的改进粒子群优化算法的性能,在4个具有代表性的多峰测试函数上进行实验,并与其他经典算法比较,分析本文算法的搜索能力。实验结果表明,本文提出的改进算法在改善粒子群算法容易出现的早熟收敛和算法运行后期局部开发能力不足等问题是有效的。
通过研究基于PSO算法的神经网络学习算法的原理和实现步骤,本文还将提出的改进算法用来优化RBF神经网络的关键参数,并将训练后的网络算法应用于时间序列预测问题。预测结果表明,经过改进算法训练的RBF神经网络,不仅具有收敛速度快的优点,而且具有很好的泛化能力。在时间序列预测的问题上,预测精度高,是一种有效的时间序列预测方法。
Optimization technique is concerned by the relevant experts and scholars, and has developed rapidly as a technique that has been widely used to solve technical optimal solution of various engineering problems. With the application areas are continuously expanding and the problems to be optimized are more complex, it becomes more difficult to seek the optimal solution, and some traditional optimization techniques can not meet the needs of the solution. The appear of intelligent optimization algorithm not only provides new ideas and means for optimize technology, and is widely used in economic, scientific and engineering problems. Particle Swarm Optimization is a population-based random optimization algorithm, comes from the study on the movement behavior of birds and fish populations. It as a new intelligent optimization algorithm, which is used to seek the optimal solution of complex problems, shows a strong advantage.
There are some inherent flaws in PSO algorithm. For example, the loss of population diversity and search speed decreasing rapidly in the late running lead to stagnation and premature convergence. Therefore the adaptive inertia weight adjustment mechanism is introduced to the algorithm, and a dynamic adaptive particle swarm algorithm is presented. Using the dynamic adaptive regulation strategy inertia weight makes the inertia weight change with the group level timely based on the definition of population diversity measure, for adjusting the particle swarm search speed and direction to jump out of local optimum.
In order to analyze the improved PSO algorithm performance, we carry out the experiments on the four representative testing functions, and compared with other classical algorithms. From the experimental result, we can see that the improved algorithm is effective for the premature convergence and insufficient local development.
The improved algorithm proposed in this paper is used to optimize the key parameters of RBF neural network through studying the principles and steps of neural network based on PSO algorithm, and the network training algorithm is applied to time series forecasting problems. Through the prediction results we can conclude that RBF neural network trained by the improved PSO algorithm not only has fast convergence speed, but also has good generalization ability. In time series prediction problem, it has prediction accuracy, and is an effective method of time series prediction.
粒子群优化算法本身也存在一些固有的缺陷,如在算法运行后期种群多样性丧失和搜索速度迅速减小,导致算法停滞,出现早熟收敛。因此本文将惯性权重自适应调节机制引入到算法中,提出了一种动态自适应粒子群算法。在定义群体多样性度量函数的基础上,采用动态自适应调节策略,使得粒子的惯性权重随群体聚集程度而适时变化,从而调整粒子群搜索的速度和方向以跳出局部最优。
对本文提出的改进粒子群优化算法的性能,在4个具有代表性的多峰测试函数上进行实验,并与其他经典算法比较,分析本文算法的搜索能力。实验结果表明,本文提出的改进算法在改善粒子群算法容易出现的早熟收敛和算法运行后期局部开发能力不足等问题是有效的。
通过研究基于PSO算法的神经网络学习算法的原理和实现步骤,本文还将提出的改进算法用来优化RBF神经网络的关键参数,并将训练后的网络算法应用于时间序列预测问题。预测结果表明,经过改进算法训练的RBF神经网络,不仅具有收敛速度快的优点,而且具有很好的泛化能力。在时间序列预测的问题上,预测精度高,是一种有效的时间序列预测方法。
Optimization technique is concerned by the relevant experts and scholars, and has developed rapidly as a technique that has been widely used to solve technical optimal solution of various engineering problems. With the application areas are continuously expanding and the problems to be optimized are more complex, it becomes more difficult to seek the optimal solution, and some traditional optimization techniques can not meet the needs of the solution. The appear of intelligent optimization algorithm not only provides new ideas and means for optimize technology, and is widely used in economic, scientific and engineering problems. Particle Swarm Optimization is a population-based random optimization algorithm, comes from the study on the movement behavior of birds and fish populations. It as a new intelligent optimization algorithm, which is used to seek the optimal solution of complex problems, shows a strong advantage.
There are some inherent flaws in PSO algorithm. For example, the loss of population diversity and search speed decreasing rapidly in the late running lead to stagnation and premature convergence. Therefore the adaptive inertia weight adjustment mechanism is introduced to the algorithm, and a dynamic adaptive particle swarm algorithm is presented. Using the dynamic adaptive regulation strategy inertia weight makes the inertia weight change with the group level timely based on the definition of population diversity measure, for adjusting the particle swarm search speed and direction to jump out of local optimum.
In order to analyze the improved PSO algorithm performance, we carry out the experiments on the four representative testing functions, and compared with other classical algorithms. From the experimental result, we can see that the improved algorithm is effective for the premature convergence and insufficient local development.
The improved algorithm proposed in this paper is used to optimize the key parameters of RBF neural network through studying the principles and steps of neural network based on PSO algorithm, and the network training algorithm is applied to time series forecasting problems. Through the prediction results we can conclude that RBF neural network trained by the improved PSO algorithm not only has fast convergence speed, but also has good generalization ability. In time series prediction problem, it has prediction accuracy, and is an effective method of time series prediction.
引文
[1]Kennedy J, Eberhart R.C.. Particle swarm optimization[C]. Proceeding of IEEE international conference on neutral networks, Perth, Australia,1995,1942-1948.
[2]王凌.智能优化算法及其应用.北京：清华大学出版社,2001.
[3]Eberhart R.C, Shi Y, particle swarm optimization:developments, applications and resources. Proceeding of IEEE Congress on Evolutionary Computation,2001:81-86.
[4]Kennedy J, Eberhart R.C. A Discrete Binary Version of the Particle Swarm Algorithm. In:Proc.1997 Conf. on Systems, Man, and Cybernetics. Piscataway, NJ: IEEE Service Center,1997,4104-4109.
[5]Shi Y, Eberhart R., Fuzzy adaptive particle swarm optimization. The IEEE Congress on Evolutionary Computation, San Francisco, USA,2001:101-106.
[6]Shi Y, Eberhart R C.A Modified Particle Swarm Optimizer. In:Proceedings of the IEEE International Conference on Evolutionary Computation. Piscataway, NJ:IEEE Press,1998,69-73.
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[10]Trelea I C. The particle swarm optimization algorithm:convergence analysis and parameter selection[J]. Information Processing Letters,2003,85(6):317-325.
[11]Angeline P J. Using Selection to Improve Particle Swarm Optimization [A]. IEEE International Conference on Evolutionary Computation[C], Anchorage, Alaska, 1998.
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[23]刘华蓥,林玉娥,王淑云.粒子群算法改进及其在求解约束优化问题中的应用[J],吉林大学学报理学版,2005(4)：472-476.
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[2]王凌.智能优化算法及其应用.北京：清华大学出版社,2001.
[3]Eberhart R.C, Shi Y, particle swarm optimization:developments, applications and resources. Proceeding of IEEE Congress on Evolutionary Computation,2001:81-86.
[4]Kennedy J, Eberhart R.C. A Discrete Binary Version of the Particle Swarm Algorithm. In:Proc.1997 Conf. on Systems, Man, and Cybernetics. Piscataway, NJ: IEEE Service Center,1997,4104-4109.
[5]Shi Y, Eberhart R., Fuzzy adaptive particle swarm optimization. The IEEE Congress on Evolutionary Computation, San Francisco, USA,2001:101-106.
[6]Shi Y, Eberhart R C.A Modified Particle Swarm Optimizer. In:Proceedings of the IEEE International Conference on Evolutionary Computation. Piscataway, NJ:IEEE Press,1998,69-73.
[7]Clerc M, Kennedy J. The particle swarm-explosion, stability, and convergence in a multidimension complex space[J]. IEEE Trans. on Evolutionary Computation,2002, 6(1):58-73.
[8]Ozcan, E. and Mohan, C. K. Particle swarm optimization:surfing the waves[A]. Proceedings of the IEEE Congress on Evolutionary Computation[C], Picataway, NJ,1999,1939-1944.
[9]Ozcan, E. and Mohan, C. K. Analysis of a simple particle optimization system[J]. Intelligent Engineering Systems Through Artificial Neural Networks,1998,8: 253-258.
[10]Trelea I C. The particle swarm optimization algorithm:convergence analysis and parameter selection[J]. Information Processing Letters,2003,85(6):317-325.
[11]Angeline P J. Using Selection to Improve Particle Swarm Optimization [A]. IEEE International Conference on Evolutionary Computation[C], Anchorage, Alaska, 1998.
[12]Lovbjerg M, Rasmussen T K, et al. Hybrid Particle Swarm Optimization with Breeding and Subpopulation[A]. IEEE International Conference on Evolutionary Computation[C], San Dieego,2000.
[13]Higashi N, Iba H. Particle swarm optimization with Gaussian mutation[J]. In:Proc. of the IEEE Swarm Intelligence Symp. Indianapolis:IEEE Inc.,2003,72-79.
[14]Kennedy J. Bare bones particle swarms[J]. In:Proc. of the IEEE Swarm Intelligence
Symp. Indianapolis:IEEE Press,2003,53-57.
[15]Zhang W J, Xie XF. DEPSO:Hybrid particle swarm with differential evolution operator[A]. In:Proc. of the IEEE Int'l Conf. on Systems, Man and Cybernetics[C]. Washington:IEEE Inc.,2003,3816-3821.
[16]Hong-Ji Meng, Peng Zhang, Rong-Yang Wu. A hybrid particle swarm algorithm with embedded chaotic search[A]. IEEE Conference on Cybernetics and Intelligent Systems[C].2004,367-371.
[17]高鹰,谢胜利.免疫粒子群优化算法[J],计算机工程与应用,2004(6)：4-7.
[18]高鹰,谢胜利.基于模拟退火的粒子群优化算法[J],计算机工程与应用,2004(1)：47-50.
[19]Parsopoulos K E, Vrahatis M N. Initializing the particle swarm optimizer using the nonlinear simplex Method[J]. In Grmela, A. and Mastorakis, N.E.(eds.). Advances in Intelligent Systems, Fuzzy Systems, Evolutionary Computation, WSEAS Press,2002, 216-221.
[20]Juang C F. A hybrid of genetic algorithm and particle warm optimization for recurrent network design[J]. IEEE Transactions on Systems, Man, and Cubernetics Part B:Cybernetics,2004,34(2):997-1006.
[21]Victoire, T.A.A. and Jeyakumar, A.E. Hybrid PSO-SQP for economic dispatch with valve-point effect[J]. Electric Power Systems Research,2004,71(1):51-59.
[22]李宁,邹彤,孙德宝,秦元庆.基于粒子群的多目标优化算法[J],计算机工程与应用,2005(23)：43-46.
[23]刘华蓥,林玉娥,王淑云.粒子群算法改进及其在求解约束优化问题中的应用[J],吉林大学学报理学版,2005(4)：472-476.
[24]赵辉,刘鲁源,张更新.基于复合适应度微粒群算法神经网络训练[J],控制与决策,2005(8)：958-960.
[25]李方方,赵英凯,贾玉莹.基于粒子群优化算法的神经网络在油品质量预测中的应用[J],计算机应用,2006(5)：1122-1124.
[26]潘昊,侯清兰.基于粒子群优化算法的BP网络学习研究[J],计算机工程与应用,2006(16)：41-43.
[27]高立群,任苹,李楠.基于混沌粒子群算法的告诉旅客列车优化调度[J],东北大学学报(自然科学版),2007(2)：176-179.
[28]李桂芝,何万里.基于改进粒子群算法优化电梯群控系统[J],渤海大学学报(自然科学版),2007(1)：42-45.
[29]韩璞,王学厚,李剑波,王东风.粒子群优化的模糊控制器设计[J],动力工程,
2005(5)：663-667.
[30]郝万君,强文义,柴庆宣.基于粒子群优化的一类模糊控制器设计[J],控制与决策,2007(5)：585-588.
[31]Wachowiak M P, Smolfkova R, Zheng Y, et al. An approach to Multimodal Biomedical Image Registration Utilizing Particle Swarm Optimization[J]. IEEE Transactions On Evolutionary Computation,2004,8(3):289-301.
[32]吕振肃,侯志荣.自适应变异的粒子群优化算法[J].电子学报,2004,32(3)：416-420.
[33]Van den Bergh F., An analysis of particle swarm optimizers, [PhD thesis]. South Africa:Department of Computer Science, University of Pretoria,2002.
[34]李娟,邵春福.基于BP神经网络的交通事故预测模型[J].交通与计算机,2006,24(2)：34-37.
[35]朱文兴,龙艳萍.基于RBF神经网络的交通流量预测算法[J].山东大学学报,2007,37(4)：24-25.
[36]TAN S H, HAO J B. Efficient identification of RBF neural net models for nonlinear discrete time multivariable dynamical systems[J]. Neurocompution,1995,9(1): 11-26.
[37]姜鹏飞,蔡之华.基于遗传算法和梯度下降的RBF神经网络组合训练方法[J].计算机应用,2007,27(2)：366-368.
[38]张铃,张钹.人工神经网络理论及应用[M].杭州：浙江科学技术出版社,1997：51-53.
[39]Zhang D X, Liu X Z, Guan Z H. Radial basis function neural network algorithm and its application[J]. Journal of Petrochemical Universities,2007,20(3):86-88.
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