基于混合粒子群算法的随机混流装配线平衡问题研究
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摘要
装配线平衡问题是制造行业里的一个十分重要的研究课题,研究成果可以为企业带来显著的经济效益。随着社会经济的不断发展,市场竞争日益激烈。混流装配线由于能满足客户的多样化、个性化需求,增强企业对市场的反应能力,在制造企业中得到了广泛的应用。实际生产过程中,存在很多的随机因素,如操作人员、机器设备、工作环境等,装配线上的作业时间具有很大的随机性。但是目前的研究大多集中于作业时间为常量的装配线,这并不完全符合生产实际。本文以随机混流装配线为研究对象,具有一定的理论价值和现实意义。主要研究内容如下：
1)系统研究了装配线平衡问题的相关理论知识,并对装配线平衡问题的计算复杂性、平衡的影响因素、平衡的改善思路做了细致的分析,同时给出了相应的改进措施。在考虑影响装配线上作业时间随机因素的基础上,明确提出了随机混流装配线平衡问题,并根据其特征,建立了相应的数学模型。
2)针对粒子群算法容易出现“早熟”现象,提出了一种求解第1类装配线平衡问题的改进粒子群算法,该算法通过增强粒子的多样性来克服粒子群算法易陷入局部最优的缺陷,并通过设置优先权重来提高算法的搜索性能。并编制了相关程序,大量的测试问题计算结果验证了算法的有效性。
3)为求解本文提出的随机混流装配线平衡问题,提出了一种模拟退火算法与粒子群算法融合的混合算法,该算法通过模拟退火抽样过程使粒子及时跳出局部最优,实现了并行搜索,扩大搜索空间的同时增强了粒子在解空间的探索和开发能力,使算法的全局搜索能力、优化效率以及鲁棒性得到了很大的提高。大量的测试问题计算结果验证了算法的有效性。
4)考虑到作业时间的随机性能导致整个工作站作业时间具有随机性,操作者只能以一定的概率在规定的节拍时间内完成所有任务。为此,提出通过改变预设超限概率来改变完成工作站任务的概率,实例研究表明此种方法的可行性和有效性,从而实现对随机混流装配线平衡问题的研究。
5)应用所提出的PSO-SA算法,对某企业的发动机总装线进行了平衡优化改善,原总装线的效率明显提高,各工作站负荷更加均衡。结果表明,改善效果明显。
The assembly line balancing problem (ALBP) is an important issue in the manufacturing field; minor improvements can lead to significant gains in the economy. In the era of rapid change, the society economic activity is complicated changeful; the market competition is gradually fierce. The mixed model assembly line has got broad application in making enterprise, because it can meet customers'diversify and individuation needs, and also it has strengthened the enterprise adaptability to the marketplace. In the actual production process, operating time on the assembly line is with a lot of randomness. But in the current study, a variety of assembly line balancing design based on seting assembly work time as constant, which does not fully conform to actual production. In this paper, author take stochastic mixed-model assembly line as object of study, which have a certain amount of theoretical and practical significance. The thesis is organized as follows.
1) The thesis studys the theoretical knowledge of ALBP systematically, analyzes the computational complexity of ALBP and the faxtors which can affect the balance, then gives the improvements how to improve the balance efficiency. The stochastic mixed-model assembly line balancing problem (SMMALBP) is proposed based on considering the stochastic factors which can influce the assembly operation time, and a corresponding mathematical model is established according to its characteristics.
2) In this paper, an improved particle swarm optimization for ALBP of type-1according to is proposed to solve particle swrm optimization(PSO)'s premature phenomenon. The improved algorithm enhances the diversity of particles and improves the search performance by setting the priority weight. The paper also developes procedures by using Matlab, numerous calculations of rhe test problems to verify the effectiveness of the improved algorithm.
3) A hybrid particle swarm optimization algorithms base on simulated annealing (SA) mechanism for solving SMMALBP. The hybrid algorithms can make the particles escape from local optima in time and achieve parallel search which can expand the search space, enhance particles'exploration and development capabilities in the solution space. So the hybrid algotithms improve the global search capability, optimize efficiency and rubustness. A large number of examples demonstrate the effectiveness of the hybrid algorithms.
4) Bacause of the randomness of assembly task's working time can lead to the workstation time become a random variable, the operator can complete all the assembly tasks in the given cycle time with a certain probability. So in this paper, a method to change the probability of completing all the workstation tasks by changing the default overrun paobability is proposed. Many examples show the feasibilityand effectiveness of this method to solve SMMALBP.
5) Using the proposed PSO-SA algorithm to improve a company's engine assembly line, which improve the original assembly line efficiency significantly and make the workstation load more balanced. The results show that the improvements are obvious.
1)系统研究了装配线平衡问题的相关理论知识,并对装配线平衡问题的计算复杂性、平衡的影响因素、平衡的改善思路做了细致的分析,同时给出了相应的改进措施。在考虑影响装配线上作业时间随机因素的基础上,明确提出了随机混流装配线平衡问题,并根据其特征,建立了相应的数学模型。
2)针对粒子群算法容易出现“早熟”现象,提出了一种求解第1类装配线平衡问题的改进粒子群算法,该算法通过增强粒子的多样性来克服粒子群算法易陷入局部最优的缺陷,并通过设置优先权重来提高算法的搜索性能。并编制了相关程序,大量的测试问题计算结果验证了算法的有效性。
3)为求解本文提出的随机混流装配线平衡问题,提出了一种模拟退火算法与粒子群算法融合的混合算法,该算法通过模拟退火抽样过程使粒子及时跳出局部最优,实现了并行搜索,扩大搜索空间的同时增强了粒子在解空间的探索和开发能力,使算法的全局搜索能力、优化效率以及鲁棒性得到了很大的提高。大量的测试问题计算结果验证了算法的有效性。
4)考虑到作业时间的随机性能导致整个工作站作业时间具有随机性,操作者只能以一定的概率在规定的节拍时间内完成所有任务。为此,提出通过改变预设超限概率来改变完成工作站任务的概率,实例研究表明此种方法的可行性和有效性,从而实现对随机混流装配线平衡问题的研究。
5)应用所提出的PSO-SA算法,对某企业的发动机总装线进行了平衡优化改善,原总装线的效率明显提高,各工作站负荷更加均衡。结果表明,改善效果明显。
The assembly line balancing problem (ALBP) is an important issue in the manufacturing field; minor improvements can lead to significant gains in the economy. In the era of rapid change, the society economic activity is complicated changeful; the market competition is gradually fierce. The mixed model assembly line has got broad application in making enterprise, because it can meet customers'diversify and individuation needs, and also it has strengthened the enterprise adaptability to the marketplace. In the actual production process, operating time on the assembly line is with a lot of randomness. But in the current study, a variety of assembly line balancing design based on seting assembly work time as constant, which does not fully conform to actual production. In this paper, author take stochastic mixed-model assembly line as object of study, which have a certain amount of theoretical and practical significance. The thesis is organized as follows.
1) The thesis studys the theoretical knowledge of ALBP systematically, analyzes the computational complexity of ALBP and the faxtors which can affect the balance, then gives the improvements how to improve the balance efficiency. The stochastic mixed-model assembly line balancing problem (SMMALBP) is proposed based on considering the stochastic factors which can influce the assembly operation time, and a corresponding mathematical model is established according to its characteristics.
2) In this paper, an improved particle swarm optimization for ALBP of type-1according to is proposed to solve particle swrm optimization(PSO)'s premature phenomenon. The improved algorithm enhances the diversity of particles and improves the search performance by setting the priority weight. The paper also developes procedures by using Matlab, numerous calculations of rhe test problems to verify the effectiveness of the improved algorithm.
3) A hybrid particle swarm optimization algorithms base on simulated annealing (SA) mechanism for solving SMMALBP. The hybrid algorithms can make the particles escape from local optima in time and achieve parallel search which can expand the search space, enhance particles'exploration and development capabilities in the solution space. So the hybrid algotithms improve the global search capability, optimize efficiency and rubustness. A large number of examples demonstrate the effectiveness of the hybrid algorithms.
4) Bacause of the randomness of assembly task's working time can lead to the workstation time become a random variable, the operator can complete all the assembly tasks in the given cycle time with a certain probability. So in this paper, a method to change the probability of completing all the workstation tasks by changing the default overrun paobability is proposed. Many examples show the feasibilityand effectiveness of this method to solve SMMALBP.
5) Using the proposed PSO-SA algorithm to improve a company's engine assembly line, which improve the original assembly line efficiency significantly and make the workstation load more balanced. The results show that the improvements are obvious.
引文
[1]阚树林.基础工业工程[M].北京：高等教育出版社,2005.
[2]Rekiek B, De Lit P, Delchambre A. Designing mixed-product assembly lines[J]. IEEE Transactions on Robotics and Automation,2000,16(3):268-280.
[3]贾大龙,韩玉启等.应用工业工程[M].北京：北京兵器工业出版社,1993.
[4]陈诚和.基于仿真优化的制造企业生产线平衡问题研究[D]：[硕士学位论文].合肥工业大学,2007.
[5]Byrton B. Balancing of a Continuous Production Line[D]. Evanston, Illinois:North-West University 1954.
[6]Scholl A. Balancing and sequencing of assembly lines[M].2nd ed. Heidelberg: Physica-Verlga, 1999.
[7]张则强.基于仿生的数字物流平衡问题理论与应用研究[D]：[博士学位论文].西南交通大学,2007.
[8]刘晋浩,侯东亮.装配线平衡问题的求解方法浅析[J].森林工程,2005,22(4)：21-23.
[9]余庆良,张则强,宋林.某减速器装配线平衡的精益改造研究[J].价值工程, 2010,29(16)：148-150.
[10]Wester L, Kilbridge M D. Heuristic Line Balancing-A case[J]. Journal of Industrial Engineering, 1962.
[11]Thomopoulos N T. Mixed Model Assembly Line Balancing with smoothed station assignments[J]. Management Science, 1970, 16(9):593-603.
[12]Uddin M K, Soto M C, Lastra J L M. An integrated approach to mixed-model assembly line balancing and sequencing[J]. Assembly Automation, 2010, 30(2):164-172.
[13]Oumlzcan U, Ccedilerccediliogbrevelu H, Goumlkccedilen H, Toklu B. Balancing and sequencing of parallel mixed-model assembly lines[J]. International Journal of Production Research, 2010, 48(17): 5089-5113.
[14]胡罗克,陈勇,唐任仲.混流装配线平衡分析与算法设计[J].现代制造工程,2011,(9)：1-5.
[15]卫东,金烨.给定序列的混合品种装配生产线平衡算法[J].机械工程学报,2004,40(4)：135-138.
[16]Noorul Haq A, Jayaprakash J, Rengarajan K. A hybrid genetic algorithm approach to mixed-model assembly line balancing[J]. International Journal of Advanced Manufacturing Technology, 2006, 28(3-4):337-341.
[17]于兆勤,苏平.基于遗传算法和仿真分析的混合装配线平衡问题研究[J].计算机集成制造系统,2008,14(6)：1120-1129.
[18]张则强,程文明,钟斌等.混合品种装配线平衡问题的一种混合搜索机制的蚁群算法[J].机械工程学报,2009,45(5)：96-100.
[19]Betul Y. Mixed-model assembly line balancing using a multi-objective ant colony optimization approach[J]. Expert Systems with Applications, 2011,38(10):12453-12461.
[20]Parames C, Palida C. Multi-objective two-sided mixed-model assembly line balancing using particle swarm optimization with negative knowledge[J], Computers& Industrial Engineering, 2012, 62(1): 39-55.
[21]刘炜琪,刘琼,张超勇,邵新宇.基于混合粒子群算法求解多目标混流装配线排序[J].计算机集成制造系统,2011,17(12)：2590-2598.
[22]董巧英,阚树林,桂元坤,蔡纯之.基于改进离散微粒群优化算法的混流装配线多目标排序[J].系统仿真学报,2009,21(22)：7103-7108.
[23]郑永前,王永生.免疫粒子群算法在混流装配线排序中的应用[J].工业工程与管理,2011,16(4)：16-20.
[24]C.L.Moodie and H.H.Young. A heuristic method of assembly line balancing for assumptions constant or variable work element times[J]. Journal Industrial Engineering, 1965. 16(1):23-29.
[25]Erel E, Sabuncuoglu I, Sekerci H. Stochastic assembly line balancing using beam search[J]. International Journal of Production Research,2005,43(7): 1411-1426.
[26]Liu S B, Ong H L, Huang H C. A bidirectional heuristic for stochastic assembly line balancing Type II problem[J]. International Journal of Advanced Manufacturing Technology, 2005,25(1-2):71-77.
[27]Agpak K, Gokcen H. A chance-constrained approach to stochastic line balancing problem[J]. European Journal of Operational Research, 2007, 180(3):1098-1115.
[28]Ana Maria, Gonzalez-Garces. Development of a Methodology to Solve the Line Balancing Problem with Parallel Workstations [D]:[Master thesis]. University of Puerto Rico, 2006.
[29]Ozbakir L, Baykasoqlu A. Stochastic U-line-balancing using genetic algorithms[J]. International Journal of Advanced Manufacturing Technology, 2007, 32(04):139-147.
[30]Gebennini E, Grassi A, Regattieri A. A multiple single-pass heuristic algorithm solving the stochastic assembly line rebalancing problem[J]. International Journal of Production Research, 2009,47(01): 2141-2164.
[31]Bagher M, Zandieh M, Farsijani H. Balancing of stochastic U-type assembly lines:an imperialist competitive algorithm[J]. The International Journal of Advanced Manufacturing Technology, 2011, 54(1):271-285.
[32]Ozcan U, Kelleg Z T, Toklu B. A genetic algorithm for the stochastic mixed-model U-line balancing and sequencing problem[J]. International Journal of Production Research, 2011,49(6):1605-1626.
[33]周亮,宋华明.韩玉启.基于遗传算法的随机型生产线负荷平衡[J].机械制造,2003,41(463)：23-25.
[34]宋林.随机型双边装配线问题的平衡与仿真分析[D]：[硕士学位论文].西南交通大学,2011.
[35]于兆勤.混合型装配线平衡问题的不确定性仿真研究[J].中国机械工程,2008,19(11)：1297-1302.
[36]张斌杰,阐树林等.随机混合装配线的启发式平衡设计方法[J].工业工程与管理,2008(01)：8-11.
[37]李怀祖.生产计划与控制[M].北京：中国科学技术出版社,2005,171-172.
[38]吴君华,夏世谌,曹山河.ALB问题的数学模型及优化算法的研究[J].系统仿真学报,1999,11(5)： 358-361.
[39]赵建辉.发动机装配生产线平衡问题[D]：[硕士学位论文].北京机械工业学院,2007.
[40]张则强,程文明,钟斌等.求解装配线平衡问题的一种改进蚁群算法[J].计算机集成制造系统,2007,13(8)：1632-1638.
[41]卫东.大规模定制生产装配生产线平衡技术的研究[D]：[博士学位论文].上海交通大学,2005.
[42]朱振杰.机械产品装配线平衡问题优化研究[D]：[硕士学位论文].山东大学,2010.
[43]杨召凯,刘德忠,李志强.发动机装配生产线平衡问题研究[J].机械设计与制造,2008(1)：215-217.
[44]王立勇,徐克林.装配线平衡中统计波动问题仿真研究[J].工业工程,2007,10(2)：125-129.
[45]宋华明,韩玉启,杨慧.多品种混合型装配流水线的平衡设计[J].中国机械工程,2003,14(6)：475-477.
[46]Su P, Lu Y. Combining Genetic Algorithm and Simulation for Mixed-model Assembly Line Balancing Problem[C]. Proceedings of the Third International Conference on Natural Computation, ICNC. Piscataway: IEEE Computer Society,2007:314-328.
[47]康立山等著.非数值并行算法：模拟退火算法[M].北京：科学技术出版社,1994.
[48]Kennedy J, Eberhart R C. Particle swarm optimization[C]. Proceedings of IEEE International Conference on Neural Networks,1995,1942-1948.
[49]Martinez J L, Gonzalo E G. The Generalized PSO: A New Door to PSO Evolution[J]. Journal of Artificial Evolution and Applications, 2008, 8(6):12-17.
[50]Zhang J, Zhang J, Lok T and Lyu M R. A hybrid particle swarm optimization-back-propagation algorithm for feedforward neural network training[J]. Applied Mathematics and Computation, 2007, 185(2):1026-1037.
[51]Abido M A. Optimal design of power-system stabilizers using paticle swarm optimization[J]. IEEE Trans, Energy Conversion, 2002, 17(3):406-413.
[52]Clerc M. Discrete particle swarm optimization illustratrd by the traveling saleman problems. http://www.maurieeclerc.net, 2000.
[53]Wu H, Sun F, Sun Z and Wu L. Optimal trajectory planning of a flexible dual-arm space robot with vibration reduction[J]. Intelligent and Robotic Systems, 2004, 400(2):147-163.
[54]Rasmussen T K, Krink T. Improved hidden markov model training for multiple sequence alignment by a particle swarm optimization---evolutionary algorithm hybrid[J]. Biosystems, 2003,72(1-2):5017.
[55]李静,王京.一类求解复杂优化问题的改进粒子群算法[J].控制工程,2010,18(6)：841-844.
[56]纪震,廖惠连,吴青华.粒子群算法及应用[M].北京：科学出版社,2009.
[57]Shi Y, Eberhart R C. A modified particle swarm optimization[C]. IEEE Int. Conf. on Evolutionary Computation, Piscataway, NJ, IEEE Service Center, 1998:69-73.
[58]Wolpert D H, Macready W G. No free lunch theorems for optimization[C]. IEEE Transaction on Evolutional Computation, 1997, 1(1):67-82.
[59]鲁建厦,蒋玲玲等.基于混合粒子群算法求解装配线第二类平衡问题[J].中国机械工程,2010,21(4)：420-423.
[60]Nearchou A C. Maximizing Production Rate and Workload Smoothing in Assembly Lines using Particle Swarm Optimization [J]. International Journal of Production Economics, 2011, 129(2): 242-250.
[61]张朋俊.发动机混流装配生产线规划与仿真[D]：[硕士学位论文].河南科技大学,2009.
[2]Rekiek B, De Lit P, Delchambre A. Designing mixed-product assembly lines[J]. IEEE Transactions on Robotics and Automation,2000,16(3):268-280.
[3]贾大龙,韩玉启等.应用工业工程[M].北京：北京兵器工业出版社,1993.
[4]陈诚和.基于仿真优化的制造企业生产线平衡问题研究[D]：[硕士学位论文].合肥工业大学,2007.
[5]Byrton B. Balancing of a Continuous Production Line[D]. Evanston, Illinois:North-West University 1954.
[6]Scholl A. Balancing and sequencing of assembly lines[M].2nd ed. Heidelberg: Physica-Verlga, 1999.
[7]张则强.基于仿生的数字物流平衡问题理论与应用研究[D]：[博士学位论文].西南交通大学,2007.
[8]刘晋浩,侯东亮.装配线平衡问题的求解方法浅析[J].森林工程,2005,22(4)：21-23.
[9]余庆良,张则强,宋林.某减速器装配线平衡的精益改造研究[J].价值工程, 2010,29(16)：148-150.
[10]Wester L, Kilbridge M D. Heuristic Line Balancing-A case[J]. Journal of Industrial Engineering, 1962.
[11]Thomopoulos N T. Mixed Model Assembly Line Balancing with smoothed station assignments[J]. Management Science, 1970, 16(9):593-603.
[12]Uddin M K, Soto M C, Lastra J L M. An integrated approach to mixed-model assembly line balancing and sequencing[J]. Assembly Automation, 2010, 30(2):164-172.
[13]Oumlzcan U, Ccedilerccediliogbrevelu H, Goumlkccedilen H, Toklu B. Balancing and sequencing of parallel mixed-model assembly lines[J]. International Journal of Production Research, 2010, 48(17): 5089-5113.
[14]胡罗克,陈勇,唐任仲.混流装配线平衡分析与算法设计[J].现代制造工程,2011,(9)：1-5.
[15]卫东,金烨.给定序列的混合品种装配生产线平衡算法[J].机械工程学报,2004,40(4)：135-138.
[16]Noorul Haq A, Jayaprakash J, Rengarajan K. A hybrid genetic algorithm approach to mixed-model assembly line balancing[J]. International Journal of Advanced Manufacturing Technology, 2006, 28(3-4):337-341.
[17]于兆勤,苏平.基于遗传算法和仿真分析的混合装配线平衡问题研究[J].计算机集成制造系统,2008,14(6)：1120-1129.
[18]张则强,程文明,钟斌等.混合品种装配线平衡问题的一种混合搜索机制的蚁群算法[J].机械工程学报,2009,45(5)：96-100.
[19]Betul Y. Mixed-model assembly line balancing using a multi-objective ant colony optimization approach[J]. Expert Systems with Applications, 2011,38(10):12453-12461.
[20]Parames C, Palida C. Multi-objective two-sided mixed-model assembly line balancing using particle swarm optimization with negative knowledge[J], Computers& Industrial Engineering, 2012, 62(1): 39-55.
[21]刘炜琪,刘琼,张超勇,邵新宇.基于混合粒子群算法求解多目标混流装配线排序[J].计算机集成制造系统,2011,17(12)：2590-2598.
[22]董巧英,阚树林,桂元坤,蔡纯之.基于改进离散微粒群优化算法的混流装配线多目标排序[J].系统仿真学报,2009,21(22)：7103-7108.
[23]郑永前,王永生.免疫粒子群算法在混流装配线排序中的应用[J].工业工程与管理,2011,16(4)：16-20.
[24]C.L.Moodie and H.H.Young. A heuristic method of assembly line balancing for assumptions constant or variable work element times[J]. Journal Industrial Engineering, 1965. 16(1):23-29.
[25]Erel E, Sabuncuoglu I, Sekerci H. Stochastic assembly line balancing using beam search[J]. International Journal of Production Research,2005,43(7): 1411-1426.
[26]Liu S B, Ong H L, Huang H C. A bidirectional heuristic for stochastic assembly line balancing Type II problem[J]. International Journal of Advanced Manufacturing Technology, 2005,25(1-2):71-77.
[27]Agpak K, Gokcen H. A chance-constrained approach to stochastic line balancing problem[J]. European Journal of Operational Research, 2007, 180(3):1098-1115.
[28]Ana Maria, Gonzalez-Garces. Development of a Methodology to Solve the Line Balancing Problem with Parallel Workstations [D]:[Master thesis]. University of Puerto Rico, 2006.
[29]Ozbakir L, Baykasoqlu A. Stochastic U-line-balancing using genetic algorithms[J]. International Journal of Advanced Manufacturing Technology, 2007, 32(04):139-147.
[30]Gebennini E, Grassi A, Regattieri A. A multiple single-pass heuristic algorithm solving the stochastic assembly line rebalancing problem[J]. International Journal of Production Research, 2009,47(01): 2141-2164.
[31]Bagher M, Zandieh M, Farsijani H. Balancing of stochastic U-type assembly lines:an imperialist competitive algorithm[J]. The International Journal of Advanced Manufacturing Technology, 2011, 54(1):271-285.
[32]Ozcan U, Kelleg Z T, Toklu B. A genetic algorithm for the stochastic mixed-model U-line balancing and sequencing problem[J]. International Journal of Production Research, 2011,49(6):1605-1626.
[33]周亮,宋华明.韩玉启.基于遗传算法的随机型生产线负荷平衡[J].机械制造,2003,41(463)：23-25.
[34]宋林.随机型双边装配线问题的平衡与仿真分析[D]：[硕士学位论文].西南交通大学,2011.
[35]于兆勤.混合型装配线平衡问题的不确定性仿真研究[J].中国机械工程,2008,19(11)：1297-1302.
[36]张斌杰,阐树林等.随机混合装配线的启发式平衡设计方法[J].工业工程与管理,2008(01)：8-11.
[37]李怀祖.生产计划与控制[M].北京：中国科学技术出版社,2005,171-172.
[38]吴君华,夏世谌,曹山河.ALB问题的数学模型及优化算法的研究[J].系统仿真学报,1999,11(5)： 358-361.
[39]赵建辉.发动机装配生产线平衡问题[D]：[硕士学位论文].北京机械工业学院,2007.
[40]张则强,程文明,钟斌等.求解装配线平衡问题的一种改进蚁群算法[J].计算机集成制造系统,2007,13(8)：1632-1638.
[41]卫东.大规模定制生产装配生产线平衡技术的研究[D]：[博士学位论文].上海交通大学,2005.
[42]朱振杰.机械产品装配线平衡问题优化研究[D]：[硕士学位论文].山东大学,2010.
[43]杨召凯,刘德忠,李志强.发动机装配生产线平衡问题研究[J].机械设计与制造,2008(1)：215-217.
[44]王立勇,徐克林.装配线平衡中统计波动问题仿真研究[J].工业工程,2007,10(2)：125-129.
[45]宋华明,韩玉启,杨慧.多品种混合型装配流水线的平衡设计[J].中国机械工程,2003,14(6)：475-477.
[46]Su P, Lu Y. Combining Genetic Algorithm and Simulation for Mixed-model Assembly Line Balancing Problem[C]. Proceedings of the Third International Conference on Natural Computation, ICNC. Piscataway: IEEE Computer Society,2007:314-328.
[47]康立山等著.非数值并行算法：模拟退火算法[M].北京：科学技术出版社,1994.
[48]Kennedy J, Eberhart R C. Particle swarm optimization[C]. Proceedings of IEEE International Conference on Neural Networks,1995,1942-1948.
[49]Martinez J L, Gonzalo E G. The Generalized PSO: A New Door to PSO Evolution[J]. Journal of Artificial Evolution and Applications, 2008, 8(6):12-17.
[50]Zhang J, Zhang J, Lok T and Lyu M R. A hybrid particle swarm optimization-back-propagation algorithm for feedforward neural network training[J]. Applied Mathematics and Computation, 2007, 185(2):1026-1037.
[51]Abido M A. Optimal design of power-system stabilizers using paticle swarm optimization[J]. IEEE Trans, Energy Conversion, 2002, 17(3):406-413.
[52]Clerc M. Discrete particle swarm optimization illustratrd by the traveling saleman problems. http://www.maurieeclerc.net, 2000.
[53]Wu H, Sun F, Sun Z and Wu L. Optimal trajectory planning of a flexible dual-arm space robot with vibration reduction[J]. Intelligent and Robotic Systems, 2004, 400(2):147-163.
[54]Rasmussen T K, Krink T. Improved hidden markov model training for multiple sequence alignment by a particle swarm optimization---evolutionary algorithm hybrid[J]. Biosystems, 2003,72(1-2):5017.
[55]李静,王京.一类求解复杂优化问题的改进粒子群算法[J].控制工程,2010,18(6)：841-844.
[56]纪震,廖惠连,吴青华.粒子群算法及应用[M].北京：科学出版社,2009.
[57]Shi Y, Eberhart R C. A modified particle swarm optimization[C]. IEEE Int. Conf. on Evolutionary Computation, Piscataway, NJ, IEEE Service Center, 1998:69-73.
[58]Wolpert D H, Macready W G. No free lunch theorems for optimization[C]. IEEE Transaction on Evolutional Computation, 1997, 1(1):67-82.
[59]鲁建厦,蒋玲玲等.基于混合粒子群算法求解装配线第二类平衡问题[J].中国机械工程,2010,21(4)：420-423.
[60]Nearchou A C. Maximizing Production Rate and Workload Smoothing in Assembly Lines using Particle Swarm Optimization [J]. International Journal of Production Economics, 2011, 129(2): 242-250.
[61]张朋俊.发动机混流装配生产线规划与仿真[D]：[硕士学位论文].河南科技大学,2009.