具有自适应弹射机制的粒子群算法
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摘要
针对粒子群算法容易陷入局部最优和停滞的问题,提出自适应弹射机制的粒子群算法.为了保持粒子群的活力,在算法内引入弹射操作.当粒子满足条件,当前位置赋予很大的速度,使其飞到很远的区域.弹射方式可以选择全维弹射和概率弹射.为了配合弹射操作,提出粒子优劣的判断机制,使粒子可以被弹射飞出可行域.在算法中设定自适应判别函数,当粒子满足该判别函数,对粒子实施弹射.数值实验表明,文中算法具有较强的全局搜索能力和较快的搜索速度.
Particle swarm optimization(PSO) is easily trapped in local optimum and stagnation, and therefore a self-adaptive ejector particle swarm optimization algorithm(SAEPSO) is proposed. To keep the vitality of the particle swarm, the ejector operation is introduced into the algorithm. While the satisfying the condition, the particle is given a high speed at the current position to fly to a faraway area. Full-dimensional ejection and probabilistic ejection can be selected for the ejection mode. To cope with the ejector operation, a new quality judgment for particles is proposed, so particles can be ejected out of the feasible region. A self-adaptive discrimination function is introduced in the proposed algorithm to judge whether the particle should be ejected. While satisfying the function, the particles are ejected. Numerical experiments show that the proposed algorithm possesses relatively strong global search ability and fast search speed.
Particle swarm optimization(PSO) is easily trapped in local optimum and stagnation, and therefore a self-adaptive ejector particle swarm optimization algorithm(SAEPSO) is proposed. To keep the vitality of the particle swarm, the ejector operation is introduced into the algorithm. While the satisfying the condition, the particle is given a high speed at the current position to fly to a faraway area. Full-dimensional ejection and probabilistic ejection can be selected for the ejection mode. To cope with the ejector operation, a new quality judgment for particles is proposed, so particles can be ejected out of the feasible region. A self-adaptive discrimination function is introduced in the proposed algorithm to judge whether the particle should be ejected. While satisfying the function, the particles are ejected. Numerical experiments show that the proposed algorithm possesses relatively strong global search ability and fast search speed.
引文
[1] KENNEDY J, EBERHART R C. Particle Swarm Optimization // Proc of the IEEE International Conference on Neural Networks. Washington, USA: IEEE, 1995: 1942-1948.
[2] 王小巧,刘明周,葛茂根,等.基于混合粒子群算法的复杂机械产品装配质量控制阈优化方法.机械工程学报, 2016, 52(1): 130-138.(WANG X Q, LIU M Z, GE M G, et al. Online Control Threshold Optimization for Complex Mechanical Products Assembly Process Based on Hybrid Genetic Particle Swarm Optimization. Journal of Mechanical Engineering, 2016, 52(1): 130-138.)
[3] 高红民,李臣明,王艳,等.混合编码差分进化粒子群算法及多示例学习的高光谱影像降维与分类.中国图象图形学报, 2015, 20(12): 1689-1698.(GAO H M, LI C M, WANG Y, et al. Dimension Reduction and Classification for Hyperspectral Image Based on Particle Swarm Optimization and Differential Evolution Algorithm with Hybrid Encoding and Multiple Instance Learning. Journal of Image and Graphics, 2015, 20(12): 1689-1698.)
[4] 张晔嘉,孙正兴,李晨曦,等.三维模型最优视角选择的粒子群优化方法.计算机辅助设计与图形学学报, 2014 , 26(12): 2126-2135.(ZHANG Y J, SUN Z X, LI C X, et al. A Method of Best View Selection of 3D Shapes Based on PSO. Journal of Computer-Aided Design and Computer Graphics, 2014, 26(12): 2126-2135.)
[5] 邱云飞,杨倩,唐晓亮.基于粒子群优化的软子空间聚类算法.模式识别与人工智能, 2015, 28(10): 903-912.(QIU Y F, YANG Q, TANG X L. Soft Subspace Clustering Based on Particle Swarm Optimization. Pattern Recognition and Artificial Intelligence, 2015, 28(10): 903-912.)
[6] 李坤,黎明,陈昊.基于探索与利用平衡理论的灾变粒子群算法.模式识别与人工智能, 2015, 28(7): 603-612.(LI K, LI M, CHEN H. Particle Swarm Optimization with Exhaustive Disturbance Based on Exploration-Exploitation Balance Theory. Pattern Recognition and Artificial Intelligence, 2015, 28(7): 603-612.)
[7] 李胜, 何明辉,李建林,等.嵌入层叠混沌策略的随机粒子群算法.模式识别与人工智能, 2015, 28(10): 953-960.(LI S, HE M H, LI J L, et al. Stochastic Particle Swarm Optimization Algorithm with Embedded Cascading Chaotic Strategy. Pattern Recognition and Artificial Intelligence, 2015, 28(10): 953-960.)
[8] 夏学文,刘经南,高柯夫,等.具备反向学习和局部学习能力的粒子群算法.计算机学报, 2015, 38(7): 1397-1407.(XIA X W, LIU J N, GAO K F, et al. Particle Swarm Optimization Algorithm with Reverse-Learning and Local-Learning Behavior. Chinese Journal of Computers, 2015, 38(7): 1397-1407.)
[9] CHAUHAN P, PANT M, DEEP K. Parameter Optimization of Multipass Turning Using Chaotic PSO. International Journal of Machine Learning and Cybernetics, 2015, 6(2): 319-337.
[10] ZHAO F Q, TANG J X, WANG J B, et al. An Improved Particle Swarm Optimisation with a Linearly Decreasing Disturbance Term for Flow Shop Scheduling with Limited Buffers. International Journal of Computer Integrated Manufacturing, 2014, 27(5): 488-499.
[11] 赵新超,刘国莅,刘虎球,等.基于非均匀变异和多阶段扰动的粒子群优化算法.计算机学报, 2014, 37(9): 2058-2070.(ZHAO X C, LIU G L, LIU H Q, et al. Particle Swarm Optimization Algorithm Based on Non-uniform Mutation and Multiple Stages Perturbation. Chinese Journal of Computers, 2014, 37(9): 2058-2070.)
[12] XIA X W, LIU J N, HU Z B. An Improved Particle Swarm Optimizer Based on Tabu Detecting and Local Learning Strategy in a Shrunk Search Space. Applied Soft Computing, 2014, 23: 76-90.
[13] CHEN W N, ZHANG J, LIN Y, et al. Particle Swarm Optimization with an Aging Leader and Challengers. IEEE Transactions on Evolutionary Computation, 2013, 17(2): 241-258.
[14] PARSOPOULOS K E. Parallel Cooperative Micro-particle Swarm Optimization: A Master-Slave Model. Applied Soft Computing, 2012, 12(11): 3552-3579.
[15] ZHAO Z H, ZHANG J, LI Y, et al. Orthogonal Learning Particle Swarm Optimization. IEEE Transactions on Evolutionary Computation, 2011, 15(6): 832-847.
[16] LI C H, YANG S X, NGUYEN T T. A Self-learning Particle Swarm Optimizer for Global Optimization Problems. IEEE Transactions on Systems, Man, and Cybernetics(Cybernetics), 2012, 42(3): 627-646.
[17] 王东风,孟丽,赵文杰.基于自适应搜索中心的骨干粒子群算法.计算机学报, 2016, 39(12): 2652-2667.(WANG D F, MENG L, ZHAO W J. Improved Bare Bones Particle Swarm Optimization with Adaptive Search Center. Chinese Journal of Computers, 2016, 39(12): 2652-2667.)
[18] 吕柏权,张静静,李占培,等.基于变换函数与填充函数的模糊粒子群优化算法.自动化学报, 2018, 44(1): 74-86. (Lü B Q, ZHANG J J, LI Z P, et al. Fuzzy Particle Swarm Optimization Based on Filled Function and Transformation Function. Acta Automatica Sinica, 2018, 44(1): 74-86.)
[19] TAN Y, XIAO Z M. Clonal Particle Swarm Optimization and Its Applications // Proc of the IEEE Congress on Evolutionary Computation. Washington, USA: IEEE, 2007: 2303-2309.
[20] SUGANTHAN P N, HANSEN N, LIANG J J, et al. Problem Definitions and Evaluation criteria for the CEC 2005 Special Session on Real-Parameter Optimization. Technical Report. Singapore, Singapore: Nanyang Technological University, 2005.
[21] MENDES R, KENNEDY J, NEVES J. The Fully Informed Particle Swarm: Simpler, Maybe Better. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 204-210.
[22] LIANG J J, QIN A K, SUGANTHAN P N, et al. Comprehensive Learning Particle Swarm Optimizer for Global Optimization of Multimodal Functions. IEEE Transactions on Evolutionary Computation, 2006, 10(3): 281-295.
[2] 王小巧,刘明周,葛茂根,等.基于混合粒子群算法的复杂机械产品装配质量控制阈优化方法.机械工程学报, 2016, 52(1): 130-138.(WANG X Q, LIU M Z, GE M G, et al. Online Control Threshold Optimization for Complex Mechanical Products Assembly Process Based on Hybrid Genetic Particle Swarm Optimization. Journal of Mechanical Engineering, 2016, 52(1): 130-138.)
[3] 高红民,李臣明,王艳,等.混合编码差分进化粒子群算法及多示例学习的高光谱影像降维与分类.中国图象图形学报, 2015, 20(12): 1689-1698.(GAO H M, LI C M, WANG Y, et al. Dimension Reduction and Classification for Hyperspectral Image Based on Particle Swarm Optimization and Differential Evolution Algorithm with Hybrid Encoding and Multiple Instance Learning. Journal of Image and Graphics, 2015, 20(12): 1689-1698.)
[4] 张晔嘉,孙正兴,李晨曦,等.三维模型最优视角选择的粒子群优化方法.计算机辅助设计与图形学学报, 2014 , 26(12): 2126-2135.(ZHANG Y J, SUN Z X, LI C X, et al. A Method of Best View Selection of 3D Shapes Based on PSO. Journal of Computer-Aided Design and Computer Graphics, 2014, 26(12): 2126-2135.)
[5] 邱云飞,杨倩,唐晓亮.基于粒子群优化的软子空间聚类算法.模式识别与人工智能, 2015, 28(10): 903-912.(QIU Y F, YANG Q, TANG X L. Soft Subspace Clustering Based on Particle Swarm Optimization. Pattern Recognition and Artificial Intelligence, 2015, 28(10): 903-912.)
[6] 李坤,黎明,陈昊.基于探索与利用平衡理论的灾变粒子群算法.模式识别与人工智能, 2015, 28(7): 603-612.(LI K, LI M, CHEN H. Particle Swarm Optimization with Exhaustive Disturbance Based on Exploration-Exploitation Balance Theory. Pattern Recognition and Artificial Intelligence, 2015, 28(7): 603-612.)
[7] 李胜, 何明辉,李建林,等.嵌入层叠混沌策略的随机粒子群算法.模式识别与人工智能, 2015, 28(10): 953-960.(LI S, HE M H, LI J L, et al. Stochastic Particle Swarm Optimization Algorithm with Embedded Cascading Chaotic Strategy. Pattern Recognition and Artificial Intelligence, 2015, 28(10): 953-960.)
[8] 夏学文,刘经南,高柯夫,等.具备反向学习和局部学习能力的粒子群算法.计算机学报, 2015, 38(7): 1397-1407.(XIA X W, LIU J N, GAO K F, et al. Particle Swarm Optimization Algorithm with Reverse-Learning and Local-Learning Behavior. Chinese Journal of Computers, 2015, 38(7): 1397-1407.)
[9] CHAUHAN P, PANT M, DEEP K. Parameter Optimization of Multipass Turning Using Chaotic PSO. International Journal of Machine Learning and Cybernetics, 2015, 6(2): 319-337.
[10] ZHAO F Q, TANG J X, WANG J B, et al. An Improved Particle Swarm Optimisation with a Linearly Decreasing Disturbance Term for Flow Shop Scheduling with Limited Buffers. International Journal of Computer Integrated Manufacturing, 2014, 27(5): 488-499.
[11] 赵新超,刘国莅,刘虎球,等.基于非均匀变异和多阶段扰动的粒子群优化算法.计算机学报, 2014, 37(9): 2058-2070.(ZHAO X C, LIU G L, LIU H Q, et al. Particle Swarm Optimization Algorithm Based on Non-uniform Mutation and Multiple Stages Perturbation. Chinese Journal of Computers, 2014, 37(9): 2058-2070.)
[12] XIA X W, LIU J N, HU Z B. An Improved Particle Swarm Optimizer Based on Tabu Detecting and Local Learning Strategy in a Shrunk Search Space. Applied Soft Computing, 2014, 23: 76-90.
[13] CHEN W N, ZHANG J, LIN Y, et al. Particle Swarm Optimization with an Aging Leader and Challengers. IEEE Transactions on Evolutionary Computation, 2013, 17(2): 241-258.
[14] PARSOPOULOS K E. Parallel Cooperative Micro-particle Swarm Optimization: A Master-Slave Model. Applied Soft Computing, 2012, 12(11): 3552-3579.
[15] ZHAO Z H, ZHANG J, LI Y, et al. Orthogonal Learning Particle Swarm Optimization. IEEE Transactions on Evolutionary Computation, 2011, 15(6): 832-847.
[16] LI C H, YANG S X, NGUYEN T T. A Self-learning Particle Swarm Optimizer for Global Optimization Problems. IEEE Transactions on Systems, Man, and Cybernetics(Cybernetics), 2012, 42(3): 627-646.
[17] 王东风,孟丽,赵文杰.基于自适应搜索中心的骨干粒子群算法.计算机学报, 2016, 39(12): 2652-2667.(WANG D F, MENG L, ZHAO W J. Improved Bare Bones Particle Swarm Optimization with Adaptive Search Center. Chinese Journal of Computers, 2016, 39(12): 2652-2667.)
[18] 吕柏权,张静静,李占培,等.基于变换函数与填充函数的模糊粒子群优化算法.自动化学报, 2018, 44(1): 74-86. (Lü B Q, ZHANG J J, LI Z P, et al. Fuzzy Particle Swarm Optimization Based on Filled Function and Transformation Function. Acta Automatica Sinica, 2018, 44(1): 74-86.)
[19] TAN Y, XIAO Z M. Clonal Particle Swarm Optimization and Its Applications // Proc of the IEEE Congress on Evolutionary Computation. Washington, USA: IEEE, 2007: 2303-2309.
[20] SUGANTHAN P N, HANSEN N, LIANG J J, et al. Problem Definitions and Evaluation criteria for the CEC 2005 Special Session on Real-Parameter Optimization. Technical Report. Singapore, Singapore: Nanyang Technological University, 2005.
[21] MENDES R, KENNEDY J, NEVES J. The Fully Informed Particle Swarm: Simpler, Maybe Better. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 204-210.
[22] LIANG J J, QIN A K, SUGANTHAN P N, et al. Comprehensive Learning Particle Swarm Optimizer for Global Optimization of Multimodal Functions. IEEE Transactions on Evolutionary Computation, 2006, 10(3): 281-295.