Survey of Particle Swarm Optimization Algorithm for Association Rule Mining

doi:10.3778/j.issn.1673-9418.2010048

Abstract

Abstract:

Association rule mining is an important area in data mining, considering the large scale, high dimen-sionality, modal diversity and type complexity of current data, traditional association rule mining algorithms cannot meet the needs of big data. The particle swarm optimization algorithm, as an efficient intelligent algorithm, provides a new solution and has been widely used in association rule mining field in recent years. This paper introduces the basic principle of swarm optimization algorithm and the basic concept of association rules, and reviews the research progress of the swarm optimization algorithm itself. Then, this paper further summarizes the researches of the swarm optimization algorithm in association rule mining problem, including common data conversion methods, coding methods, and evaluation indexes. These improved algorithms from related researches are compared with other algorithms widely used in association rule mining, and their advantages, disadvantages, and application scenarios are discussed. After that, the existing improvement algorithms are systematically classified according to its methods, such as parameter, variation, and hybrid algorithm improvements, and the application areas of particle swarm optimization algorithms in association rule mining are also summarized, such as shopping baskets, finances, medical, industrial productions and risk assessments. At last, based on the introduction of the latest research pro-gress in this field, further research directions are discussed by analyzing the existing problems.

Key words: association rule mining, particle swarm optimization algorithm, intelligent algorithm

摘要：

关联规则挖掘是数据挖掘中的重要领域，考虑到当前数据的大规模、高维度、模态多样及类型复杂等特性，传统关联规则挖掘算法已无法适应大数据的需求，粒子群优化算法作为一种高效的智能优化算法，为其提供了一种全新的解决方案，近年来被广泛应用于该领域。首先对粒子群优化算法的基本原理及关联规则的基本概念进行了详细介绍，回顾了粒子群优化算法的研究进展，分析了粒子群优化算法在关联规则挖掘中的研究, 包括常用的数据转换方法、编码方式及评估指标，并与其他在关联规则挖掘中被广泛应用的算法进行了对比，总结了各自的优缺点及适用场景。然后对已有改进方法进行了较为系统的分类，即分为基于参数、基于变异机制和混合其他算法的改进。接着梳理归纳了粒子群优化算法在关联规则挖掘中的应用领域，阐述了该算法在购物篮、金融、医疗、工业生产及风险评估领域中的应用优势。最后在介绍这一领域的最新研究进展的基础上，通过对现存问题进行分析，讨论了进一步的研究方向。

关键词: 关联规则挖掘, 粒子群优化算法, 智能算法

ZHONG Qianyi, QIAN Qian, FU Yunfa, FENG Yong. Survey of Particle Swarm Optimization Algorithm for Association Rule Mining[J]. Journal of Frontiers of Computer Science and Technology, 2021, 15(5): 777-793.

钟倩漪, 钱谦, 伏云发, 冯勇. 粒子群优化算法在关联规则挖掘中的研究综述[J]. 计算机科学与探索, 2021, 15(5): 777-793.

References

[1] ZHU T S, GAO W, LING C X. Perspective of knowledge discovery in database process model[J]. Computer Science, 1999, 26(2): 44-47.
朱廷劭, 高文, LING C X. 数据库中知识发现的处理过程模型的研究[J]. 计算机科学, 1999, 26(2): 44-47.
[2] ZHAO X J, SUN Z X, YUAN Y. An efficient association rule mining algorithm based on prejudgment and screening[J]. Journal of Electronics and Information Technology, 2016, 38(7): 1654-1659.
赵学健, 孙知信, 袁源. 基于预判筛选的高效关联规则挖掘算法[J]. 电子与信息学报, 2016, 38(7): 1654-1659.
[3] AGRAWAL R, IMIELINSKI T, SWAMI A. Mining associa-tion rules between sets of items in large databases[C]//Proceedings of the 1993 ACM SIGMOD International Con-ference on Management of Data, Washington, May 26-28, 1993. New York: ACM, 1993: 207-216.
[4] HAN J W, PEI J, YIN Y W, et al. Mining frequent patterns without candidate generation: a frequent-pattern tree app-roach[J]. Data Mining & Knowledge Discovery, 2004, 8(1): 53-87.
[5] ZAKI M J, PARTHASARATHY S, OGIHARA M, et al. New algorithms for fast discovery of association rules[C]//Pro-ceedings of the 3rd International Conference on Knowledge Discovery and Data Mining, Newport Beach, Aug 14-17, 1997. Palo Alto: AAAI, 1997: 283-286．
[6] MAHBOUBI H, MOEZZI K, AGHDAM A G, et al. Distri-buted deployment algorithms for improved coverage in a network of wireless mobile sensors[J]. IEEE Transactions on Industrial Informatics, 2014, 10(1): 163-174.
[7] MINAEI-BIDGOLI B, BARMAKI R, NASIRI M. Mining numerical association rules via multi-objective genetic algorithms[J]. Information Sciences, 2013, 233: 15-24.
[8] THANGAVEL K, JAGANATHAN P. Rule mining algorithm with a new ant colony optimization algorithm[C]//Proceed-ings of the 2007 International Conference on Comput-ational Intelligence and Multimedia Applications, Sivakasi, Dec 13-15, 2007. Piscataway: IEEE, 2007: 135-140.
[9] WANG Z Q, SUN X, ZHANG D X. Classification rule min-ing based on particle swarm optimization[C]//LNCS 4062: Proceedings of the International Conference on Rough Sets and Knowledge Technology, Chongqing, Jul 24-26, 2006. Berlin, Heidelberg: Springer, 2006: 436-441.
[10] KENNEDY J, EBERHART R C. Particle swarm optimization[C]//Proceedings of the 1995 IEEE International Joint Con-ference on Neural Networks, Perth, Nov 27-Dec 1, 1995. Piscataway: IEEE, 1995: 1942-1948.
[11] SHI Y, EBERHART R. A modified particle swarm optimizer[C]//Proceedings of the 1998 IEEE World Congress on Com-putational Intelligence, Anchorage, May 4-9, 1998. Piscat-away: IEEE, 1998: 69-73.
[12] CLERC M, KENNEDY J. The particle swarm-explosion, stability, and convergence in a multidimensional complex space[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(1): 58-73.
[13] HIGASHI N, IBA H. Particle swarm optimization with Gaus-sian mutation[C]//Proceedings of the 2003 IEEE Swarm Intelligence Symposium, Indianapolis, Apr 26, 2003. Piscat-away: IEEE, 2003: 72-79.
[14] RATNAWEERA A, HALGAMUGE S K, WATSON H C. Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients[J]. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 240-255.
[15] JUANG C F. A hybrid of genetic algorithm and particle swarm optimization for recurrent network design[J]. IEEE Transac-tions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2004, 34(2): 997-1006.
[16] SUN J, XU W B, FENG B. A global search strategy of quantum-behaved particle swarm optimization[C]//Proceed-ings of the 2004 IEEE Conference on Cybernetics and Intel-ligent Systems, Singapore, Dec 1-3, 2004. Piscataway: IEEE, 2004: 111-116.
[17] GAO Y, XIE S L. Chaos particle swarm optimization algorithm[J]. Computer Science, 2004, 31(8): 13-15.
高鹰, 谢胜利. 混沌粒子群优化算法[J]. 计算机科学, 2004, 31(8): 13-15.
[18] KENNEDY J, MENDES R. Population structure and particle swarm performance[C]//Proceedings of the 2002 Congress on Evolutionary Computation, Honolulu, May 12-17, 2002. Piscataway: IEEE, 2002: 1671-1676.
[19] BLACKWELL T, KENNEDY J. Impact of communication topology in particle swarm optimization[J]. IEEE Transactions on Evolutionary Computation, 2018, 23: 689-702.
[20] JANSON S, MIDDENDORF M. A hierarchical particle swarm optimizer and its adaptive variant[J]. IEEE Transactions on Systems, Man, and Cybernetics, 2005, 35(6): 1272-1282.
[21] ZHANG C, YI Z. Scale-free fully informed particle swarm optimization algorithm[J]. Information Sciences, 2011, 181(20): 4550-4568.
[22] JIANG B, WANG N, WANG L P. Particle swarm optimiza-tion with age-group topology for multimodal functions and data clustering[J]. Communications in Nonlinear Science and Numerical Simulation, 2013, 18(11): 3134-3145.
[23] WUR S Y, LEU Y. An effective Boolean algorithm for mining association rules in large databases[C]//Proceedings of the 6th International Conference on Advanced Systems for Ad-vanced Applications, Hsinchu, Apr 19-21, 1999. Washington: IEEE Computer Society, 1999: 179-186.
[24] KENNEDY J, EBERHART R C. A discrete binary version of the particle swarm algorithm[C]//Proceedings of the 1997 IEEE International Conference on Systems, Man, and Cybernetics, Orlando, Oct 12-15, 1997. Piscataway: IEEE,1997: 4104-4108.
[25] CHEN M, LUDWIG S A. A fuzzy discrete particle swarm optimization classifier for rule classification[J]. International Journal of Hybrid Intelligent Systems, 2014, 11(3): 145-156.
[26] NASIRI M, TAGHAVI L S, MINAEE B. Multi-objective rule mining using simulated annealing algorithm[J]. Journal of Convergence Information Technology, 2010, 5(1): 60-68.
[27] MUKHOPADHYAY A, MAULIK U, BANDYOPADHYAY S, et al. A survey of multiobjective evolutionary algorithms for data mining: part I[J]. IEEE Transactions on Evolutionary Computation, 2014, 18(1): 4-19.
[28] MERCERON A, YACEF K. Interestingness measures for association rules in educational data[C]//Proceedings of the 1st International Conference on Educational Data Mining, Montreal, Jun 20-21, 2008. International Educational Data Mining Society, 2008: 57-66.
[29] LI C L, CHEN S L. PSO-based weighted items association rules mining algorithm[J]. Journal of Jimei University (Natural Science), 2007, 12(1): 52-58.
李呈林, 陈水利. 基于PSO的加权关联规则挖掘算法[J]. 集美大学学报(自然科学版), 2007, 12(1): 52-58.
[30] GHOSH A, NATH B. Multi-objective rule mining using genetic algorithms[J]. Information Sciences, 2004, 163: 123-133.
[31] BEIRANVAND V, MOBASHER-KASHANI M, BAKAR A A. Multi-objective PSO algorithm for mining numerical association rules without a priori discretization[J]. Expert Systems with Applications, 2014, 41(9): 4259-4273.
[32] TAHYUDIN I, NAMBO H. The rules determination of num-erical association rule mining optimization by using combina-tion of PSO and Cauchy distribution[C]//Proceedings of the 2018 International Conference on Management Science and Engineering Management, Melbourne, Aug 1-4, 2018. Berlin, Heidelberg: Springer, 2018: 151-164.
[33] YAN D F, ZHAO X, LIN R H, et al. PPQAR: parallel PSO for quantitative association rule mining[C]//Proceedings of the 2018 IEEE International Conference on Big Data and Smart Computing, Shanghai, Jan 15-17, 2018. Piscataway: IEEE, 2018: 163-169.
[34] MOSLEHI F, HAERI A, MARTíNEZ-áLVAREZ F. A novel hybrid GA-PSO framework for mining quantitative associa-tion rules[J]. Soft Computing, 2020, 24(6): 4645-4666.
[35] FIDELIS M V, LOPES H S, FREITAS A A. Discovering comprehensible classification rules with a genetic algorithm[C]//Proceedings of the 2000 Congress on Evolutionary Com-putation, La Jolla, Jul 16-19, 2000. Piscataway: IEEE, 2000:805-810.
[36] KOU Z C, XI L F. Binary particle swarm optimization-based association rule mining for discovering relationships between machine capabilities and product features[J]. Mathe-matical Problems in Engineering, 2018, 2018(4): 1-16.
[37] DJENOURI Y, GHERAIBIA Y, MEHDI M, et al. An efficient measure for evaluating association rules[C]//Proceedings of the 2014 6th International Conference of Soft Computing and Pattern Recognition, Tunis, Aug 11-14, 2014. Piscataway: IEEE, 2015: 406-410.
[38] YKHLEF M. A quantum swarm evolutionary algorithm for mining association rules in large databases[J]. Journal of King Saud University-Computer and Information Sciences, 2011, 23: 1-6.
[39] GOU J, WANG F, LUO W. Mining fuzzy association rules based on parallel particle swarm optimization algorithm[J]. Intelligent Automation & Soft Computing, 2015, 21(2): 147-162.
[40] HOLLAND J H. Genetic algorithms and the optimal alloca-tion of trials[J]. SIAM Journal on Computing, 1973, 2(2): 88-105.
[41] LI H Y, PENG Y Z, DENG C Y, et al. Review of hybrids of GA and PSO[J]. Computer Engineering and Applications, 2018, 54(2): 20-28.
李红亚, 彭昱忠, 邓楚燕, 等. GA与PSO的混合研究综述[J]. 计算机工程与应用, 2018, 54(2): 20-28.
[42] Dorigo M, Gambardella L M. Ant colony system: a coopera-tive learning approach to the traveling salesman problem[J]. IEEE Transactions on Evolutionary Computation, 1997, 1(1): 53-66.
[43] TELIKANI A, GANDOMI A H, SHAHBAHRAMI A. A survey of evolutionary computation for association rule mining[J]. Information Sciences, 2020, 524: 318-352.
[44] INDIRA K, KANMANI S, PRASHANTH P, et al. Popula-tion based search methods in mining association rules[C]//Proceedings of the Advances in Communication, Network, and Computing, Istanbul, Aug 26-29, 2012. Berlin, Heidel-berg: Springer, 2012: 255-261.
[45] EIBEN A E, HINTERDING R, MICHALEWICZ Z. Para-meter control in evolutionary algorithms[J]. IEEE Transac-tions on Evolutionary Computation, 1999, 3(2): 124-141.
[46] MANGAT V, VIG R. Novel associative classifier based on dynamic adaptive PSO: application to determining candi-dates for thoracic surgery[J]. Expert Systems with Applica-tions, 2014, 41(18): 8234-8244.
[47] INDIRA K, KANMANI S. Association rule mining through adaptive parameter control in particle swarm optimization[J]. Computational Statistics, 2015, 30(1): 251-277.
[48] ALATAS B, AKIN E. Multi-objective rule mining using a chaotic particle swarm optimization algorithm[J]. Know-ledge Based Systems, 2009, 22(6): 455-460.
[49] ZHANG Y D, HUANG S B. A novel multiobjective particle swarm optimization for buoys-arrangement design[C]//Pro-ceedings of the 2004 IEEE/WIC/ACM International Con-ference on Intelligent Agent Technology, Beijing, Sep 20-24, 2004. Washington: IEEE Computer Society, 2004: 24-30.
[50] AGRAWAL M, MISHRA M, KUSHWAH S P S. Associa-tion rules optimization using improved PSO algorithm[C]//Proceedings of the 2015 International Conference on Com-munication Networks, Gwalior, Nov 19-21, 2015. Piscat-away: IEEE, 2015: 395-398.
[51] CAI Z Q, HUANG H. Comprehensive learning particle swarm optimization algorithm with adaptive mutation[J]. Computer Engineering, 2009, 35(7): 170-171.
蔡昭权, 黄翰. 自适应变异综合学习粒子群优化算法[J]. 计算机工程, 2009, 35(7): 170-171.
[52] WANG F, GOU J. Mining fuzzy association rules based on multi-mutation particle swarm optimization algorithm[J]. Com-puter Science, 2013, 40(5): 217-223.
王飞, 缑锦. 基于多变异粒子群优化算法的模糊关联规则挖掘[J]. 计算机科学, 2013, 40(5): 217-223.
[53] WU R, ZHANG J L, LIU X L. An association rule mining algorithm based on mutation mechanism and QPSO[J]. Journal of Shandong University of Science and Technology (Natural Science), 2020, 39(2): 95-104.
吴嵘, 张姣玲, 刘小兰. 结合变异机制和量子PSO的关联规则挖掘算法[J]. 山东科技大学学报(自然科学版), 2020, 39(2): 95-104.
[54] SARATH K N V D, RAVI V. Association rule mining using binary particle swarm optimization[J]. Engineering Applica-tions of Artificial Intelligence, 2013, 26(8): 1832-1840.
[55] ZENG B C, WAN W G. Analysis of correlation features of terrorist organizations based on improved PSO-Apriori algo-rithm[J]. Electronic Measurement Technology, 2020, 43(1):46-51.
曾本冲, 万旺根. 基于改进PSO-Apriori算法的恐怖组织关联特征分析[J]. 电子测量技术, 2020, 43(1): 46-51.
[56] ZHOU F C, WANG Z J, YE F, et al. Research and improve-ment of Apriori algorithm for mining association rules[J]. Journal of Frontiers of Computer Science and Technology, 2015, 9(9): 1075-1083.
周发超, 王志坚, 叶枫, 等. 关联规则挖掘算法Apriori的研究改进[J]. 计算机科学与探索, 2015, 9(9): 1075-1083.
[57] CHEN J G. An availability measure of data mining on mass data[J]. Computer Engineering & Software, 2011, 32(5): 65-66.
陈建国. 一种海量数据挖掘的有效方法[J]. 软件, 2011, 32(5): 65-66.
[58] MISHRA S, MISHRA D, SATAPATHY K S. Particle swarm optimization based fuzzy frequent pattern mining from gene expression data[C]//Proceedings of the 2011 2nd Inter-national Conference on Computer and Communication Tech-nology, Allahabad, Sep 15-17, 2011. Piscataway: IEEE, 2011: 15-20.
[59] MISHRA S, SATAPATHY K S, MISHRA D. CLPSO-fuzzy frequent pattern mining from gene expression data[J]. Pro-cedia Technology, 2012, 4: 807-811.
[60] HAMIDI M, BORJI A. Color image segmentation with CLPSO based fuzzy[J]. International Journal of Computer Science and Network Security, 2007, 7(6): 215-221.
[61] SATHYA M, THANGADURAI D K. Implementation of optimization using Eclat and PSO for efficient association rule mining[J]. International Journal of Computer Engineering in Research Trends, 2017, 4(1): 4-8.
[62] KANG L L, DONG W Y, TIAN J S. Opposition-based particle swarm optimization with adaptive Cauchy mutation[J]. Com-puter Science, 2015, 42(10): 226-231.
康岚兰, 董文永, 田降森. 一种自适应柯西变异的反向学习粒子群优化算法[J]. 计算机科学, 2015, 42(10): 226-231.
[63] INDIRA K, KANMANI S. Mining association rules using hybrid genetic algorithm and particle swarm optimisation algorithm[J]. International Journal of Data Analysis Tech-niques and Strategies, 2015, 7(1): 59-76.
[64] AGARWAL A, NANAVATI N. Association rule mining using hybrid GA-PSO for multi-objective optimisation[C]//Proceedings of the 2016 IEEE International Conference on Computational Intelligence and Computing Research, Chennai, Dec 15-17, 2016. Piscataway: IEEE, 2017: 1-7.
[65] DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II[J]. IEEE Transac-tions on Evolutionary Computation, 2002, 6(2): 182-197.
[66] COELLO C A C, LECHUGA M S. MOPSO: a proposal for multiple objective particle swarm optimization[C]//Proceedings of the 2002 Congress on Evolutionary Computation, Honolulu, May 12-17, 2002. Piscataway: IEEE, 2002: 1051-1056.
[67] ZHOU Z P, ZHANG D W, SUN Z W, et al. An adaptive hybrid PSO and GSA algorithm for association rules mining[C]//LNCS 9483: Proceedings of the International Conference on Cloud Computing and Security, Nanjing, Aug 13-15, 2015. Berlin, Heidelberg: Springer, 2015: 469-479.
[68] ZHAN Z H, ZHANG J, LI Y, et al. Adaptive particle swarm optimization[J]. IEEE Transactions on Systems, Man, and Cybernetics, 2009, 39(6): 1362-1381.
[69] RASHEDI E, NEZAMABADI-POUR H, SARYAZDI S. GSA: a gravitational search algorithm[J]. Information Sciences, 2009, 179(13): 2232-2248.
[70] SHE Y L, ZHOU L. A hazard analysis algorithm based on mixed ant colony association rules mining[J]. Computer Tech-nology and Development, 2018, 28(11): 89-93.
佘雅莉, 周良. 基于混合蚁群关联规则挖掘的危险源分析算法[J]. 计算机技术与发展, 2018, 28(11): 89-93.
[71] DHANALAXMI B, NAIDU A G, ANURADHA K. Adaptive PSO based association rule mining technique for software defect classification using ANN[J]. Procedia Computer Science, 2015, 46: 432-442.
[72] MA M, ZHANG L B. Particle swarm optimization of weighted fuzzy neural network model[C]//Proceedings of the 2012 3rd Global Congress on Intelligent Systems, Wuhan, Nov 6-8, 2012. Piscataway: IEEE, 2012: 58-61.
[73] BOOMILINGAM T, SUBRAMANIAM M. An efficient retrieval using edge GLCM and association rule mining guided IPSO based artificial neural network[J]. Multimedia Tools and Applications, 2017, 76(20): 21729-21747.
[74] KUO R J, PAI C M, LIN R H, et al. The integration of association rule mining and artificial immune network for supplier selection and order quantity allocation[J]. Applied Mathematics and Computation, 2015, 250: 958-972.
[75] WANG K, LIU T, HAN J W, et al. Top down FP-growth for association rule mining[C]//LNCS 2336: Proceedings of the 6th Pacific-Asia Conference on Knowledge Discovery and Data Mining, Taipei, China, May 6-8, 2002: 334-340.
[76] PASTI R, CASTRO L N D. An immune and a gradient-based method to train multi-layer perceptron neural net-works[C]//Proceedings of the 2006 IEEE International Joint Conference on Neural Network Proceedings, Vancouver, Jul 16-21, 2006. Piscataway: IEEE, 2006: 2075-2082.
[77] GUO S W, MENG Y Y, CHEN S L. Application of improved PSOGM algorithm in dynamic association rule mining[J]. Computer Engineering and Applications, 2018, 54(8): 160-165.
郭世伟, 孟昱煜, 陈绍立. 改进的PSOGM算法在动态关联规则挖掘中的应用[J]. 计算机工程与应用, 2018, 54(8):160-165.
[78] WANG C W, YIN S L, LIU W Y, et al. High utility itemset mining algorithm based on improved particle swarm optimiza-tion[J]. Journal of Chinese Computer Systems, 2020, 41(5): 1084-1090.
王常武, 尹松林, 刘文远, 等. HUIM-IPSO:一个改进的粒子群优化高效用项集挖掘算法[J]. 小型微型计算机系统, 2020, 41(5): 1084-1090.
[79] AHMED C F, TANBEER S K, JEONG B, et al. Efficient tree structures for high utility pattern mining in incremental databases[J]. IEEE Transactions on Knowledge and Data Engineering, 2009, 21(12):1708-1721.
[80] YANG Z M, WANG W J, GUO X E. Stock data mining of association rules based on synergy of particle swarm[J]. Journal of Jilin Normal University (Natural Science Edition), 2012, 33(3): 31-34.
杨泽民, 王文军, 郭显娥. 基于协同微粒群的股票数据关联规则挖掘[J]. 吉林师范大学学报(自然科学版), 2012, 33(3): 31-34.
[81] KUO R J, CHAO C M, CHIU Y T. Application of particle swarm optimization to association rule mining[J]. Applied Soft Computing, 2011, 11(1): 326-336.
[82] ABDI M J, GIVEKI D. Automatic detection of erythemato-squamous diseases using PSO-SVM based on association rules[J]. Engineering Applications of Artificial Intelligence, 2013, 26(1): 603-608.
[83] VAPNIK V N. The nature of statistical learning theory[M]. Berlin, Heidelberg: Springer, 1995.
[84] WANG L, ZHANG Y J, ZHONG S S, et al. Binary particle swarm optimization based process knowledge mining for typical parts of satellite[J]. Journal of Northeastern University (Natural Science), 2015, 36(1): 119-123.
王琳, 张永健, 钟诗胜, 等. 基于二进制粒子群优化的卫星典型件工艺知识挖掘[J]. 东北大学学报(自然科学版), 2015, 36(1): 119-123.
[85] TONG S, XU H T, ZHOU X W. Particle swarm optimiza-tion-based association rule mining in big data environment[J]. IEEE Access, 2019, 7: 161008-161016.
[86] SUN Z L, ZHU X F, PAN Y Z, et al. Flood risk analysis: progress, challenges and prospect[J]. Journal of Catastro-phology, 2017, 32(3): 125-130.
孙章丽, 朱秀芳, 潘耀忠, 等. 洪水灾害风险分析进展与展望[J]. 灾害学, 2017, 32(3): 125-130.
[87] WANG Z L, CHEN X H, LAI C G, et al. Flood risk assess-ment model based on particle swarm optimization rule mining algorithm[J]. System Engineering-Theory & Practice, 2013, 33(6): 1615-1621.
王兆礼, 陈晓宏, 赖成光, 等. 基于粒子群规则挖掘算法的洪灾风险评价模型[J]. 系统工程理论与实践, 2013, 33(6):1615-1621.
[88] SHE X Y, ZHANG L. Apriori parallel improved algorithm based on MapReduce distributed architecture[C]//Proceedings of the 2016 6th International Conference on Instrumentation & Measurement, Computer, Communication and Control, Har-bin, Jul 21-23, 2016. Piscataway: IEEE, 2016: 517-521.
[89] LI H Y, WANG Y, ZHANG D, et al. PFP: parallel FP-growth for query recommendation[C]//Proceedings of the 2008 ACM Conference on Recommender Systems, Lausanne, Oct 23-25, 2008. New York: ACM, 2018: 107-114.
[90] FENG X J, PAN X. Eclat algorithm based on Spark[J]. Application Research of Computers, 2019, 36(1): 18-21.
冯兴杰, 潘轩. 基于Spark的并行Eclat算法[J]. 计算机应用研究, 2019, 36(1): 18-21.
[91] HUANG F, FAN X P. Parallel particle swarm optimization algorithm with island population model[J]. Control and Decision, 2006, 21(2): 175-179.
黄芳, 樊晓平. 基于岛屿群体模型的并行粒子群优化算法[J]. 控制与决策, 2006, 21(2): 175-179.
[92] GAO S, YANG J Y. Research on chaos particle swarm optimi-zation algorithm[J]. Pattern Recognition and Artificial Intel-ligence, 2006, 19(2): 266-270.
高尚, 杨静宇. 混沌粒子群优化算法研究[J]. 模式识别与人工智能, 2006, 19(2): 266-270.
[93] HE D, CHANG H, CHANG Q, et al. Particle swarm optimi-zation based on the initial population of clustering[C]//Pro-ceedings of the 2010 International Conference on Natural Computation, Yantai, Aug 10-12, 2010. Piscataway: IEEE, 2010: 2664-2667.
[94] JIN Y X, CHENG H Z, YAN J Y, et al. Improved particle swarm optimization method and its application in power transmission network planning[J]. Proceedings of the Chinese Society for Electrical Engineering, 2005, 25(4): 46-50.
金义雄, 程浩忠, 严健勇, 等. 改进粒子群算法及其在输电网规划中的应用[J]. 中国电机工程学, 2005, 25(4): 46-50.