基于隔代映射算子的差分进化算法
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摘要
提出一种基于隔代映射算子的差分进化算法以求解优化问题,该方法在保证解的精度的同时具有较快的收敛速度。在经典的差分进化算法基础上,采用反向学习策略产生初始种群,并采用两种差分变异策略产生变异个体,以增加种群的多样性;利用隔代映射算子产生三个新个体替换当前进化种群中最差的三个个体,以实现精英策略提升算法的收敛性;为了保持种群的多样性和避免获得局部解,利用探测算子策略产生新个体加入进化种群。采用11个单峰、多峰测试函数和两个工程实例验证了该方法的有效性。
A DE based on intergeneration projection operator with good optimum and fast convergence performance was proposed to solve optimization problems.The proposed method based on the classical differential evolution mainly included the following characteristics.Firstly,for improving the diversity of population,opposition learning was employed to generate initial population and two different strategies were randomly selected to generate new mutant individuals.Secondly,an intergeneration projection operator was designed to generate three offsprings to substitute for the three worst individuals into the next generation.Thirdly,the exploratory operator was introduced to generate the new individuals into the next generation for keeping the diversity of evolutionary population and avoiding to obtain local solution.Finally,the performances of IPDE algorithm were verified by the eleven single-and multi-modal benchmark tests and two practical engineering problems.
A DE based on intergeneration projection operator with good optimum and fast convergence performance was proposed to solve optimization problems.The proposed method based on the classical differential evolution mainly included the following characteristics.Firstly,for improving the diversity of population,opposition learning was employed to generate initial population and two different strategies were randomly selected to generate new mutant individuals.Secondly,an intergeneration projection operator was designed to generate three offsprings to substitute for the three worst individuals into the next generation.Thirdly,the exploratory operator was introduced to generate the new individuals into the next generation for keeping the diversity of evolutionary population and avoiding to obtain local solution.Finally,the performances of IPDE algorithm were verified by the eleven single-and multi-modal benchmark tests and two practical engineering problems.
引文
[1]Storn R,Price K.Differential Evolution-a Simple and Efficient Heuristic for Global Optimization over Continuous Spaces[J].Journal of Global Optimization,1997,11(4):341-359.
[2]Mezura-Montes E,Coello C A C,Vel Zquez-Reyes J,et al.Multiple Trial Vectors in Differential Evolution for Engineering Design[J].Engineering Optimization,2007,39(5):567-589.
[3]陈勇,吴云翔,王亚良,等.订单不确定下双资源约束多装配线鲁棒调度[J].中国机械工程,2014,25(12):1567-1573.Chen Yong,Wu Yunxiang,Wang Yaliang,et al.Multi-assembly Line Robust Scheduling of Double Resource Constrains under Uncertain Orders[J].Journal of Mechanical Engineering,2014,25(12):1567-1573.
[4]赵燕伟,张立萍,张景玲,等.加工装配式流水车间节能调度建模与优化[J].中国机械工程,2014,25(16):2196-2203.Zhao Yanwei,Zhang Liping,Zhang Jingling,et al.Modeling and Optimization of Process-assemblytype Flow-shop Scheduling Problem with Energy Saving[J].Journal of Mechanical Engineering,2014,25(16):2196-2203.
[5]Fan H Y,Lampinen J.A Trigonometric Mutation Operation to Differential Evolution[J].Journal of Global Optimization,2003,27(1):105-129.
[6]Zhang J,Sanderson A C.JADE:Adaptive Differential Evolution with Optional External Archive[J].IEEE Transactions on Evolutionary Computation,2009,13(5):945-958.
[7]Das S,Abraham A,Chakraborty U K,et al.Differential Evolution Using a Neighborhood-based Mutation Operator[J].IEEE Transactions on Evolutionary Computation,2009,13(3):526-553.
[8]Wang Y,Cai Z,Zhang Q.Enhancing the Search Ability of Differential Evolution through Orthogonal Crossover[J].Information Sciences,2012,185(1):153-177.
[9]Ronkkonen J,Kukkonen S,Price K V.Real-parameter Optimization with Differential Evolution[C]//Proceedings of the IEEE Congress on Evolutionary Computation(CEC'2005),Piscataway,NJ:IEEE Press,2005:506-513.
[10]Zhu W,Tang Y,Fang J A,et al.Adaptive Population Tuning Scheme for Differential Evolution[J].Information Sciences,2013,223:164-191.
[11]Brest J,Greiner S,Boskovic B,et al.Self-adapting Control Parameters in Differential Evolution:a Comparative Study on Numerical Benchmark Problems[J].IEEE Transactions on Evolutionary Computation,2006,10(6):646-657.
[12]Wang Y,Cai Z,Zhang Q.Differential Evolution with Composite Trial Vector Generation Strategies and Control Parameters[J].IEEE Transactions on Evolutionary Computation,2011,15(1):55-66.
[13]车林仙,何兵,程志红.6-CRS并联机器人机构及其位置分析[J].中国机械工程,2010,21(14):1669-1675.Che Linxian,He Bing,Cheng Zhihong.A 6-CRSParallel Manipulator and Its Positional Analysis[J].Journal of Mechanical Engineering,2010,21(14):1669-1675.
[14]杨晓明,邱清盈,冯培恩,等.盘式制动器的全性能优化设计[J].中国机械工程,2005,16(7):630-633.Yang Xiaoming,Qiu Qingying,Feng Pei’en,et al.Optimal Design for Overall Performance of Disk Brake[J].Journal of Mechanical Engineering,2005,16(7):630-633.
[15]王前,杨志坚,丁康.基于新自适应差分进化算法的Magic Formula轮胎模型参数辨识方法[J].机械工程学报,2014,50(6):120-128.Wang Qian,Yang Zhijian,Ding Kang.Method in Identifying the Parameters of Magic Formula Tire Model Based on New Self-adaptive Differential Evolution[J].Journal of Mechanical Engineering,2014,50(6):120-128.
[16]Rahnamayan S,Tizhoosh H R,Salama M M.Opposition-based Differential Evolution[J].IEEETransactions on Evolutionary Computation,2008,12(1):64-79.
[17]Xu Y,Li G,Wu Z.A Novel Hybrid Genetic Algorithm Using Local Optimizer Based on Heuristic Pattern Move[J].Applied Artificial Intelligence,2001,15(7):601-631.
[18]刘桂萍.基于微型遗传算法的多目标优化方法及应用研究[D].长沙:湖南大学,2007.
[19]Suganthan P N,Hansen N,Liang J J,et al.Problem Definitions and Evaluation Criteria for the CEC 2005Special Session on Real-parameter Optimization[R].Singapore:Nanyang Technological University,2005.
[20]Qin A K,Huang V L,Suganthan P N.Differential Evolution Algorithm with Strategy Adaptation for Global Numerical Optimization[J].IEEETransactions on Evolutionary Computation,2009,13(2):398-417.
[21]Mallipeddi R,Suganthan P N,Pan Q K,et al.Differential Evolution Algorithm with Ensemble of Parameters and Mutation Strategies[J].Applied Soft Computing,2011,11(2):1679-1696.
[22]Liang J J,Qin A K,Suganthan P N,et al.Comprehensive Learning Particle Swarm Optimizer for Global Optimization of Multimodal Functions[J].IEEE Transactions on Evolutionary Computation,2006,10(3):281-295.
[23]Garcia-Martnez C,Lozano M,Herrera F,et al.Global and Local Real-coded Genetic Algorithms Based on Parent-centric Crossover Operators[J].European Journal of Operational Research,2008,185(3):1088-1113.
[24]陈光宋,钱林方,徐亚栋,等.身管横向固有振动的半解析解法[J].兵工学报,2012,33(10):1168-1172.Chen Guangsong,Qian Linfang,Xu Yadong,et al.Semi-analysis Solution of Nature Frequency of Transverse Vibration of a Barrel[J].Acta Armamentarii,2012,33(10):1168-1172.
[25]Jiang C,Han X,Lu G Y,et al.Correlation Analysis of Non-probabilistic Convex Model and Corresponding Structural Reliability Technique[J].Computer Methods in Applied Mechanics and Engineering,2011,200(33):2528-2546.
[2]Mezura-Montes E,Coello C A C,Vel Zquez-Reyes J,et al.Multiple Trial Vectors in Differential Evolution for Engineering Design[J].Engineering Optimization,2007,39(5):567-589.
[3]陈勇,吴云翔,王亚良,等.订单不确定下双资源约束多装配线鲁棒调度[J].中国机械工程,2014,25(12):1567-1573.Chen Yong,Wu Yunxiang,Wang Yaliang,et al.Multi-assembly Line Robust Scheduling of Double Resource Constrains under Uncertain Orders[J].Journal of Mechanical Engineering,2014,25(12):1567-1573.
[4]赵燕伟,张立萍,张景玲,等.加工装配式流水车间节能调度建模与优化[J].中国机械工程,2014,25(16):2196-2203.Zhao Yanwei,Zhang Liping,Zhang Jingling,et al.Modeling and Optimization of Process-assemblytype Flow-shop Scheduling Problem with Energy Saving[J].Journal of Mechanical Engineering,2014,25(16):2196-2203.
[5]Fan H Y,Lampinen J.A Trigonometric Mutation Operation to Differential Evolution[J].Journal of Global Optimization,2003,27(1):105-129.
[6]Zhang J,Sanderson A C.JADE:Adaptive Differential Evolution with Optional External Archive[J].IEEE Transactions on Evolutionary Computation,2009,13(5):945-958.
[7]Das S,Abraham A,Chakraborty U K,et al.Differential Evolution Using a Neighborhood-based Mutation Operator[J].IEEE Transactions on Evolutionary Computation,2009,13(3):526-553.
[8]Wang Y,Cai Z,Zhang Q.Enhancing the Search Ability of Differential Evolution through Orthogonal Crossover[J].Information Sciences,2012,185(1):153-177.
[9]Ronkkonen J,Kukkonen S,Price K V.Real-parameter Optimization with Differential Evolution[C]//Proceedings of the IEEE Congress on Evolutionary Computation(CEC'2005),Piscataway,NJ:IEEE Press,2005:506-513.
[10]Zhu W,Tang Y,Fang J A,et al.Adaptive Population Tuning Scheme for Differential Evolution[J].Information Sciences,2013,223:164-191.
[11]Brest J,Greiner S,Boskovic B,et al.Self-adapting Control Parameters in Differential Evolution:a Comparative Study on Numerical Benchmark Problems[J].IEEE Transactions on Evolutionary Computation,2006,10(6):646-657.
[12]Wang Y,Cai Z,Zhang Q.Differential Evolution with Composite Trial Vector Generation Strategies and Control Parameters[J].IEEE Transactions on Evolutionary Computation,2011,15(1):55-66.
[13]车林仙,何兵,程志红.6-CRS并联机器人机构及其位置分析[J].中国机械工程,2010,21(14):1669-1675.Che Linxian,He Bing,Cheng Zhihong.A 6-CRSParallel Manipulator and Its Positional Analysis[J].Journal of Mechanical Engineering,2010,21(14):1669-1675.
[14]杨晓明,邱清盈,冯培恩,等.盘式制动器的全性能优化设计[J].中国机械工程,2005,16(7):630-633.Yang Xiaoming,Qiu Qingying,Feng Pei’en,et al.Optimal Design for Overall Performance of Disk Brake[J].Journal of Mechanical Engineering,2005,16(7):630-633.
[15]王前,杨志坚,丁康.基于新自适应差分进化算法的Magic Formula轮胎模型参数辨识方法[J].机械工程学报,2014,50(6):120-128.Wang Qian,Yang Zhijian,Ding Kang.Method in Identifying the Parameters of Magic Formula Tire Model Based on New Self-adaptive Differential Evolution[J].Journal of Mechanical Engineering,2014,50(6):120-128.
[16]Rahnamayan S,Tizhoosh H R,Salama M M.Opposition-based Differential Evolution[J].IEEETransactions on Evolutionary Computation,2008,12(1):64-79.
[17]Xu Y,Li G,Wu Z.A Novel Hybrid Genetic Algorithm Using Local Optimizer Based on Heuristic Pattern Move[J].Applied Artificial Intelligence,2001,15(7):601-631.
[18]刘桂萍.基于微型遗传算法的多目标优化方法及应用研究[D].长沙:湖南大学,2007.
[19]Suganthan P N,Hansen N,Liang J J,et al.Problem Definitions and Evaluation Criteria for the CEC 2005Special Session on Real-parameter Optimization[R].Singapore:Nanyang Technological University,2005.
[20]Qin A K,Huang V L,Suganthan P N.Differential Evolution Algorithm with Strategy Adaptation for Global Numerical Optimization[J].IEEETransactions on Evolutionary Computation,2009,13(2):398-417.
[21]Mallipeddi R,Suganthan P N,Pan Q K,et al.Differential Evolution Algorithm with Ensemble of Parameters and Mutation Strategies[J].Applied Soft Computing,2011,11(2):1679-1696.
[22]Liang J J,Qin A K,Suganthan P N,et al.Comprehensive Learning Particle Swarm Optimizer for Global Optimization of Multimodal Functions[J].IEEE Transactions on Evolutionary Computation,2006,10(3):281-295.
[23]Garcia-Martnez C,Lozano M,Herrera F,et al.Global and Local Real-coded Genetic Algorithms Based on Parent-centric Crossover Operators[J].European Journal of Operational Research,2008,185(3):1088-1113.
[24]陈光宋,钱林方,徐亚栋,等.身管横向固有振动的半解析解法[J].兵工学报,2012,33(10):1168-1172.Chen Guangsong,Qian Linfang,Xu Yadong,et al.Semi-analysis Solution of Nature Frequency of Transverse Vibration of a Barrel[J].Acta Armamentarii,2012,33(10):1168-1172.
[25]Jiang C,Han X,Lu G Y,et al.Correlation Analysis of Non-probabilistic Convex Model and Corresponding Structural Reliability Technique[J].Computer Methods in Applied Mechanics and Engineering,2011,200(33):2528-2546.