针对PSO算法搜索精度较低,并且在复杂多模态函数优化中,容易陷入局部极值的问题,提出了一种改进的量子行为粒子群优化算法。研究了该算法的基本原理、给出了算法流程并采用正交试验的方式获得了一套通用性较强的算法参数。并以CEC’13的28个测试函数作为测试集,采用Wilcoxon符号秩检验将NM-QPSO算法分别与PSO算法和QPSO算法的误差进行比较试验。试验表明:NM-QPSO算法在统计意义上优于传统的PSO算法和QPSO算法,并且在高维函数优化中,具有显著优势。
PSO algorithm is poor in search accuracy and prone to fall into the local extremum when solving complex multimodal function optimization problem. So, we propose an improved quantum behaved particle swarm optimization algorithm. This paper studies the fundamentals and basic procedure of that algorithm, An orthogonal test for parameter selection is designed to select a set of reasonable control parameters. We use a suite of 28 test functions from CEC’13 as test set. NM-QPSO is compared with both of traditional PSO and QPSO by using the Wilcoxon Signed Ranks Test respectively. Tests show that the NM-QPSO algorithm has better performance than the traditional PSO and QPSO algorithms in statistical sense, and it has obvious advantages in the high-dimensional function optimization.
[1] Millonas M M. Swarms, phase transitions, and collective intelligence[C]//Marks R J, Palaniswami M, Fogel D B. Computational Intelligence: A Dynamic System Perspective. Richmond, TX, USA: Institute of Electrical & Electronics Engineers(IEEE).1994: 137-151.
[2] Kennedy J. Particle swarm optimization[C]//International Conference on Neural Networks. Western Austalia, 1995: 1942-1948.
[3] 冯奇峰,李言.改进粒子群优化算法在工程优化问题中的应用研究[J].仪器仪表学报,2006,26(9): 984-987.
Feng Qi Feng,Li Yan. Application of improved particle swarm optimization algorithm in engineering optimization problems[J].Chinese Journal of Scientific Instrument, 2006, 26(9):984-987.
[4] Gülcü S, Kodaz H. A novel parallel multi-swarm algorithm based on comprehensive learning particle swarm optimization[J].Engineering Applications of Artificial Intelligence, 2015, 45: 33-45.
[5] 张勇,巩敦卫,张婉秋.一种基于单纯形法的改进微粒群优化算法及其收敛性分析,自动化学报,2009,35(3):289-298.
Zhang Yong, Gong Dun Wei, Zhang Wan Qiu.A simplex method based improved particle swarm optimization and analysis on its global convergence[J].Acta Automatica Sinica,2009,35(3):289-298.
[6] Meng A, Li Z, Yin H, et al. Accelerating particle swarm optimization using crisscross search[J].Information Sciences, 2016, 329: 52-72.
[7] Sun J, Feng B, Xu W B. Particle swarm optimization with particles having quantum behavior[C]//IEEE Proceedings of Congress on Evolutionary Computation, Portland, USA. 2004: 325-331.
[8] Sun J, Xu W B, Feng B, A global search strategy of quantum-behaved particle swarm optimization[C]//IEEE Proceedings of Cybernetics and Intelligent Systems, Singapore.2004: 111-116.
[9] Liu F, Zhou Z. An improved QPSO algorithm and its application in the high-dimensional complex problems[J].Chemometrics and Intelligent Laboratory Systems, 2014, 132: 82-90.
[10] Nelder J A, Mead R. A simplex method for function minimization[J].The computer journal, 1965, 7(4): 308-313.
[11] Shi Y, Eberhart R C. A modified particle swarm optimizer[C]//Proceedings of the IEEE Congress on Evolutionary Computation, Piscataway, N J. 1998: 69-73.
[12] Ma G, Zhou W, Chang X L. A novel particle swarm global optimization algorithm based on particle migration[J].Applied Mathematics and Computation, 2012, 218(11): 6620-6626.
[13] 孙俊.量子行为粒子群优化算法研究[D].无锡:江南大学,2009.
Sun Jun. Research on quantum behaved particle swarm optimization algorithm[D].Wuxi: Jiangnan University,2009.
[14] Derrac J, García S, Molina D, et al. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms[J].Swarm and Evolutionary Computation, 2011, 1(1): 3-18.
[15] Liang J J, Qu B Y, Suganthan P N, et al. Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization[R].Singapore: Nanyang Technological University,2013.
[16] Pant M, Thangaraj R, Abraham A. A new quantum behaved particle swarm optimization[C]//The 10th annual conference on Genetic and evolutionary computation. Atlanta, GA, USA, 2008: 87-94.
