群体智能算法研究及其应用
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摘要
群体智能优化算法是一种近年来新兴的优化方法,是受到关注最多的优化研究领域之一,其模拟社会性动物的各种群体行为,利用群体中的个体之间的信息交互和合作来实现寻优的目的。与其它类型的优化方法相比,其实现较为简单、效率较高。
粒子群优化算法(Particle Swarm Optimization,PSO算法)源于鸟群和鱼群群体运动行为的研究,是一种新的群体智能优化算法,是演化计算领域中的一个新的分支。它的主要特点是原理简单、参数少、收敛速度较快,所需领域知识少。具有量子行为的粒子群优化(Quantum-behaved Particle Swarm Optimization,QPSO)算法是在深入研究PSO算法单个粒子收敛行为的基础上,受量子物理学的启发而提出,QPSO算法具有控制参数更少,收敛速度快,全局搜索能力强等特点。
本文以PSO算法与QPSO算法的理论分析及改进方法研究为重点,系统的研究了QPSO算法及其改进算法在相关方面的应用,具体内容如下:
(1)从最优化问题概念及其求解方法入手,阐述了智能智能优化算法研究背景,详细介绍了几种常见的智能优化算法;通过阐述了没有免费午餐定理,说明了本文研究的基础;针对PSO算法的缺陷,提出了本课题的立题依据、研究目标、研究内容以及研究思路与方法。
(2)首先介绍了PSO算法的基本原理与基本流程,详细讨论了两种重要的改进算法:带权重的PSO算法和带压缩因子的PSO算法;阐述了QPSO算法的思想来源,给出了QPSO算法的设计思路。分析了随机算法收敛的两个判断准则,即全局搜索算法的收敛准则与局部搜索算法的收敛准则,利用这两个收敛准则作为依据,证明了QPSO算法是一个全局搜索的随机算法;对QPSO算法和PSO算法从算法本身的角度做了比较,说明QPSO的特点;最后尝试在QPSO算法中引入一种新的变异机制,提出了基于云模型变异的量子粒子群优化算法(QPSO-NCM),从而增加种群的多样性,提高算法跳出陷入局部寻优的能力,进一步增强全局搜索能力。变异操作能够增加群体的多样性,使得算法具有突跳的能力,进入新的搜索区域。
(3)针对QPSO算法在解决多峰优化问题中也可能出现局部收敛的现象,分析了出局部收敛的主要原因在于群体多样性较低而使得群体失去了在大范围内进行搜索的能力,通过使用物种形成策略的概念,结合QPSO算法提出了一种SQPSO(The Species-Based QPSO)算法,将粒子群系统中的粒子根据相似度进行划分,用来实现对多峰函数的优化。通过对静态多峰环境和动态多峰环境的测试仿真证明,改进后的算法全局搜索能力和局部搜索能力均得到很大提升。
(4)为了可以克服最小二乘法难于处理的时滞在线辨识,在QPSO算法中引入单神经元结构,提高算法的局部搜索能力,实现线性离散系统的在线辨识。改进QPSO算法收敛速度快,窗口长度更小,更适用于实时要求比较高的在线辨识应用。在时变时滞系统在线辨识的仿真结果也验证了改进QPSO算法具有很好的跟踪能力和稳定性,更适合实际的工程。通过引入接纳时间比控制机制,提出并设计了一种基于QPSO算法在线辨识的自适应反馈控制方法,实现了动态调整QoS的性能控制。
(5)将QPSO算法分别用于混沌系统、周期系统和稳定系统中的参数辨识研究,通过仿真实验验证了QPSO算法在系统参数辨识中比PSO算法和GA算法具有更好的性能。对于存在噪声的混沌系统,提出基于QPSO算法的在线参数辨识并证明了该方法的有效性。
(6) QPSO算法在故障诊断方面的研究。智能故障诊断技术是人工智能和故障诊断相结合的产物,通过人工的方法使用计算机模拟人类专家对复杂系统进行诊断。单一径向基(RBF)神经网络是一种性能良好的前向网络,其既有生物背景,又与函数逼近理论相配,适合于多变量函数逼近。用遗传算法优化RBF神经网络结构和权重等参数的方法具有一定的有效性,但遗传算法复杂的遗传操作(如选择、交叉、变异)使神经网络的训练时间随问题规模及复杂程度的增大而呈指数级增长。针对这些问题采用基于QPSO算法优化的RBF神经网络,进行故障进行诊断,可以有效地提高故障的正辩率。
论文最后对所做工作与主要研究成果进行了总结,并提出了进一步的研究方向。
Swarm Intelligent (SI) algorithm is an algorithmic approach, which has gradually attracted more attention. To achieve the purpose of optimizing, SI simulated social behavior of various groups of animals and the individuals in the groups exchange information and cooperate each other. Compared with other optimization algorithms SI is easier to performe and more efficient.
Particle swarm optimization (PSO) is an evolutionary computation technique developed by Dr. Kennedy and Dr. Eberhart in1995, inspired by social behavior of bird flocking or fish schooling. PSO is simple in concept, few in parameters, and easy in implementation. It was proved to be an efficient method to solve optimization problems. Based on the deep study of PSO algorithm and inspired by quantum physics, Quantum-behaved Particle Swarm Optimization (QPSO) algorithm is proposed. QPSO algorithm has much less parameters and much stronger global search ability than the PSO algorithm.
Theoretical analyses and algorithm improving on PSO algorithm and QPSO algorithm are mainly discussed in our work and the application of QPSO algorithm are also studied in this work. The main contents of this dissertation are as follows:
1. The concept of optimization problem and its solution are introduced to explain the research background of the swarm intelligence algorithm and several common intelligent optimization algorithms are described in detail. The basis of our study is illustrated by the no free lunch theorem. Against the defects of PSO algorithm, the research objectives, research content, research ideas and methods in the work are proposed.
2. After the principle and procedure of PSO algorithm is presented, two important versions, PSO with inertia weight and PSO with contraction coefficient, are discussed. Some improved PSO methods are also mentioned for reference. The thought of QPSO algorithm is discussed. Convergence criteria of random search algorithms are introduced, including global convergence criteria and local convergence criteria. Based on these two convergence criteria, QPSO algorithm is proven to be a global search stochastic algorithm. By comparing QPSO algorithm and PSO algorithm, the characteristics of QPSO are indicated. Finally try to introduce a new mutation mechanism in the QPSO algorithm and the quantum-behaved particle swarm optimization based on cloud model mutation (QPSO-NCM) is proposed to increase the diversity of the population and improve the ability of the algorithm to fall into local optimization so as to enhance the global search capability.
3. Premature convergence is also appeared in QPSO algorithm when solving multimodal problems. The reason for premature convergence lies in the collections of swarm which makes the swarm diversity decline and the particles lose the ability of searching in a wide space. An improved Quantum-behaved Particle Swarm Optimization using the notion of species for solving multi-peaks functions optimization problems is proposed. In the proposed Species-based QPSO (SQPSO), the swarm population is divided into paralleled species subpopulations based on their similarity and each peaks are ensure to be searched equally, regardless if they are global or local optima. Our experiments for static and dynamic multi-peaks environments demonstrate that global search ability and local search capabilities of the improved algorithm have been greatly enhanced.
4. In order to overcome the difficulty that the least-squares method cannot deal with time-delay-line identification, QPSO algorithm combined with the single neuron is proposed to improve the local search capabilities and identification accuracy. Then the improved QPSO is applied to online identify parameters of a system described by differential equations. The improve QPSO algorithm has faster convergence speed and smaller length of the identification window, so it is more suitable for real-time online identification in practice. Time-delay and parameter changes for the simulation experiment illustrates the stability and tracking capability of improved QPSO algorithm are better. By introducing a session-based admission time-ratio feedback control mechanism an adaptive control of Web QoS based on system model online identification using QPSO algorithm is designed and implemented which dynamically adjust parameters of proportional-integral (PI) controller according to the changes of system model.
5. QPSO algorithm is used to identify parameters of chaotic systems, periodic systems and stability systems. The simulation results of QPSO compared with PSO and GA demonstrate that in the system parameter identification QPSO algorithm has best performance. For the existence of noise in chaotic systems, the online parameter identification based on QPSO is proposed and the effectiveness of the method is proved.
6. The study of QPSO algorithm in fault diagnosis research. Intelligent fault diagnosis technology is a combination of artificial intelligence and fault diagnosis, which use a computer to simulate human expert through artificial methods so as to diagnosis complex systems. A single radial basis function neural network (RBF NN) is a good performance feed forward network which not only has biological context, but also match with the function approximation theory and is suitable for multi-variable function approximation. It is validity to use GA to optimize the structure and weight parameters of RBF neural network. However the complexity genetic manipulation (such as selection, crossover, and mutation) of GA causes training time of the neural network increasing exponentially with the increase of the scale and complexity of the problem. To solve these problems, a RBF network algorithm based on QPSO is presented to effectively improve faults diagnosis.
The main contributions in this work are summarized at last and further research considerations are put forward.
粒子群优化算法(Particle Swarm Optimization,PSO算法)源于鸟群和鱼群群体运动行为的研究,是一种新的群体智能优化算法,是演化计算领域中的一个新的分支。它的主要特点是原理简单、参数少、收敛速度较快,所需领域知识少。具有量子行为的粒子群优化(Quantum-behaved Particle Swarm Optimization,QPSO)算法是在深入研究PSO算法单个粒子收敛行为的基础上,受量子物理学的启发而提出,QPSO算法具有控制参数更少,收敛速度快,全局搜索能力强等特点。
本文以PSO算法与QPSO算法的理论分析及改进方法研究为重点,系统的研究了QPSO算法及其改进算法在相关方面的应用,具体内容如下:
(1)从最优化问题概念及其求解方法入手,阐述了智能智能优化算法研究背景,详细介绍了几种常见的智能优化算法;通过阐述了没有免费午餐定理,说明了本文研究的基础;针对PSO算法的缺陷,提出了本课题的立题依据、研究目标、研究内容以及研究思路与方法。
(2)首先介绍了PSO算法的基本原理与基本流程,详细讨论了两种重要的改进算法:带权重的PSO算法和带压缩因子的PSO算法;阐述了QPSO算法的思想来源,给出了QPSO算法的设计思路。分析了随机算法收敛的两个判断准则,即全局搜索算法的收敛准则与局部搜索算法的收敛准则,利用这两个收敛准则作为依据,证明了QPSO算法是一个全局搜索的随机算法;对QPSO算法和PSO算法从算法本身的角度做了比较,说明QPSO的特点;最后尝试在QPSO算法中引入一种新的变异机制,提出了基于云模型变异的量子粒子群优化算法(QPSO-NCM),从而增加种群的多样性,提高算法跳出陷入局部寻优的能力,进一步增强全局搜索能力。变异操作能够增加群体的多样性,使得算法具有突跳的能力,进入新的搜索区域。
(3)针对QPSO算法在解决多峰优化问题中也可能出现局部收敛的现象,分析了出局部收敛的主要原因在于群体多样性较低而使得群体失去了在大范围内进行搜索的能力,通过使用物种形成策略的概念,结合QPSO算法提出了一种SQPSO(The Species-Based QPSO)算法,将粒子群系统中的粒子根据相似度进行划分,用来实现对多峰函数的优化。通过对静态多峰环境和动态多峰环境的测试仿真证明,改进后的算法全局搜索能力和局部搜索能力均得到很大提升。
(4)为了可以克服最小二乘法难于处理的时滞在线辨识,在QPSO算法中引入单神经元结构,提高算法的局部搜索能力,实现线性离散系统的在线辨识。改进QPSO算法收敛速度快,窗口长度更小,更适用于实时要求比较高的在线辨识应用。在时变时滞系统在线辨识的仿真结果也验证了改进QPSO算法具有很好的跟踪能力和稳定性,更适合实际的工程。通过引入接纳时间比控制机制,提出并设计了一种基于QPSO算法在线辨识的自适应反馈控制方法,实现了动态调整QoS的性能控制。
(5)将QPSO算法分别用于混沌系统、周期系统和稳定系统中的参数辨识研究,通过仿真实验验证了QPSO算法在系统参数辨识中比PSO算法和GA算法具有更好的性能。对于存在噪声的混沌系统,提出基于QPSO算法的在线参数辨识并证明了该方法的有效性。
(6) QPSO算法在故障诊断方面的研究。智能故障诊断技术是人工智能和故障诊断相结合的产物,通过人工的方法使用计算机模拟人类专家对复杂系统进行诊断。单一径向基(RBF)神经网络是一种性能良好的前向网络,其既有生物背景,又与函数逼近理论相配,适合于多变量函数逼近。用遗传算法优化RBF神经网络结构和权重等参数的方法具有一定的有效性,但遗传算法复杂的遗传操作(如选择、交叉、变异)使神经网络的训练时间随问题规模及复杂程度的增大而呈指数级增长。针对这些问题采用基于QPSO算法优化的RBF神经网络,进行故障进行诊断,可以有效地提高故障的正辩率。
论文最后对所做工作与主要研究成果进行了总结,并提出了进一步的研究方向。
Swarm Intelligent (SI) algorithm is an algorithmic approach, which has gradually attracted more attention. To achieve the purpose of optimizing, SI simulated social behavior of various groups of animals and the individuals in the groups exchange information and cooperate each other. Compared with other optimization algorithms SI is easier to performe and more efficient.
Particle swarm optimization (PSO) is an evolutionary computation technique developed by Dr. Kennedy and Dr. Eberhart in1995, inspired by social behavior of bird flocking or fish schooling. PSO is simple in concept, few in parameters, and easy in implementation. It was proved to be an efficient method to solve optimization problems. Based on the deep study of PSO algorithm and inspired by quantum physics, Quantum-behaved Particle Swarm Optimization (QPSO) algorithm is proposed. QPSO algorithm has much less parameters and much stronger global search ability than the PSO algorithm.
Theoretical analyses and algorithm improving on PSO algorithm and QPSO algorithm are mainly discussed in our work and the application of QPSO algorithm are also studied in this work. The main contents of this dissertation are as follows:
1. The concept of optimization problem and its solution are introduced to explain the research background of the swarm intelligence algorithm and several common intelligent optimization algorithms are described in detail. The basis of our study is illustrated by the no free lunch theorem. Against the defects of PSO algorithm, the research objectives, research content, research ideas and methods in the work are proposed.
2. After the principle and procedure of PSO algorithm is presented, two important versions, PSO with inertia weight and PSO with contraction coefficient, are discussed. Some improved PSO methods are also mentioned for reference. The thought of QPSO algorithm is discussed. Convergence criteria of random search algorithms are introduced, including global convergence criteria and local convergence criteria. Based on these two convergence criteria, QPSO algorithm is proven to be a global search stochastic algorithm. By comparing QPSO algorithm and PSO algorithm, the characteristics of QPSO are indicated. Finally try to introduce a new mutation mechanism in the QPSO algorithm and the quantum-behaved particle swarm optimization based on cloud model mutation (QPSO-NCM) is proposed to increase the diversity of the population and improve the ability of the algorithm to fall into local optimization so as to enhance the global search capability.
3. Premature convergence is also appeared in QPSO algorithm when solving multimodal problems. The reason for premature convergence lies in the collections of swarm which makes the swarm diversity decline and the particles lose the ability of searching in a wide space. An improved Quantum-behaved Particle Swarm Optimization using the notion of species for solving multi-peaks functions optimization problems is proposed. In the proposed Species-based QPSO (SQPSO), the swarm population is divided into paralleled species subpopulations based on their similarity and each peaks are ensure to be searched equally, regardless if they are global or local optima. Our experiments for static and dynamic multi-peaks environments demonstrate that global search ability and local search capabilities of the improved algorithm have been greatly enhanced.
4. In order to overcome the difficulty that the least-squares method cannot deal with time-delay-line identification, QPSO algorithm combined with the single neuron is proposed to improve the local search capabilities and identification accuracy. Then the improved QPSO is applied to online identify parameters of a system described by differential equations. The improve QPSO algorithm has faster convergence speed and smaller length of the identification window, so it is more suitable for real-time online identification in practice. Time-delay and parameter changes for the simulation experiment illustrates the stability and tracking capability of improved QPSO algorithm are better. By introducing a session-based admission time-ratio feedback control mechanism an adaptive control of Web QoS based on system model online identification using QPSO algorithm is designed and implemented which dynamically adjust parameters of proportional-integral (PI) controller according to the changes of system model.
5. QPSO algorithm is used to identify parameters of chaotic systems, periodic systems and stability systems. The simulation results of QPSO compared with PSO and GA demonstrate that in the system parameter identification QPSO algorithm has best performance. For the existence of noise in chaotic systems, the online parameter identification based on QPSO is proposed and the effectiveness of the method is proved.
6. The study of QPSO algorithm in fault diagnosis research. Intelligent fault diagnosis technology is a combination of artificial intelligence and fault diagnosis, which use a computer to simulate human expert through artificial methods so as to diagnosis complex systems. A single radial basis function neural network (RBF NN) is a good performance feed forward network which not only has biological context, but also match with the function approximation theory and is suitable for multi-variable function approximation. It is validity to use GA to optimize the structure and weight parameters of RBF neural network. However the complexity genetic manipulation (such as selection, crossover, and mutation) of GA causes training time of the neural network increasing exponentially with the increase of the scale and complexity of the problem. To solve these problems, a RBF network algorithm based on QPSO is presented to effectively improve faults diagnosis.
The main contributions in this work are summarized at last and further research considerations are put forward.
引文
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