面向动态环境的粒子群算法研究
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摘要
粒子群算法(Particle Swarm Optimization, PSO)是一种基于群体智能的优化方法,由Kennedy和Eberhart于1995年提出。由于其具有快速收敛和易于实现等特点,因此粒子群算法在智能计算、任务调度、交通优化、电信路由、电路设计等多个领域得以广泛应用,成为计算智能领域研究的新热点。
虽然粒子群算法及其众多的改进算法已经被成功地运用到一些静态问题的优化上,但是,很多现实问题往往是随时间变化而变化的,这些动态变化的问题要求算法能够对环境的变化快速反应,对变化的最优解快速跟踪。这给粒子群算法以及整个演化计算方法带来了新的挑战。
本文从理论、方法和应用三个方面对动态环境下粒子群算法进行研究。论文内容主要包括以下三个部分：
第一部分旨在对粒子的运动行为和粒子群算法的收敛性进行分析。首先构造李雅普诺夫函数,对单个粒子的运动行为进行了分析,给出了粒子运动稳定的条件。然后利用随机过程理论,证明了粒子位置序列均方稳定。在对单个粒子运动行为分析的基础上,分析了粒子群体运动行为,证明了群体运动的稳定性。最后从随机优化算法收敛性判定标准入手,分析了粒子群算法的收敛性,提出了一种保证全局收敛的改进粒子群算法,通过对基准测试函数仿真,验证了改进算法的有效性。
第二部分主要研究了如何利用改进粒子群算法解决动态环境下单目标、多目标和高维优化问题。
对于动态单目标优化问题的研究,本文首先对环境的变化模式进行了数学描述,分析了粒子群算法无法有效对动态问题优化的原因,然后提出了一种基于柯西变异和斥力势场的多粒子群改进算法,定量分析了柯西变异优于其它变异的原因。对动态基准测试函数的仿真表明,改进算法能够对动态环境下变化的极值点进行有效跟踪。
对于动态多目标优化问题的研究,本文首先对动态多目标优化问题的定义进行了描述,分析了算法的性能评价标准,在此基础上,提出了一种基于多种群协同优化的粒子群算法,并从理论上证明了多种群协同搜索优于单种群独自搜索。改进算法采用了竞争模式和协作模式自适应切换的方法对Pareto前端和Pareto最优解集进行跟踪。竞争模式采用了隐式空间分解,主要目的是对整个解空间进行勘探,进行粗粒度的搜索,在竞争产生非支配解集失效后,多种群进行协作搜索,协作搜索采用显式空间分解,其主要目的是对局部搜索空间开采,进行精度搜索。通过对动态多目标测试函数仿真,验证了改进算法可以对变化的Pareto前端和Pareto最优解集快速跟踪。
对于动态高维优化问题的研究,首先分析了高维优化问题难以优化的原因,并提出了一种基于局部极值点维度自适应学习的粒子群改进算法,随后通过对高维测试函数的仿真,验证了改进算法的有效性。
第三部分对垃圾焚烧系统PID控制器参数自适应整定进行了研究。垃圾焚烧系统由于系统噪声、设备折旧等因素的影响,系统参数容易发生变化,因此可以看成动态系统的PID控制器的参数要不断进行调整。本部分首先定义了一个包含系统超调量、上升时间和稳态误差指标项的适应度函数,根据控制系统的实际要求对各指标项进行适当加权,利用改进粒子群算法对PID控制器的参数进行优化。随后基于Pareto优化理论,利用改进的多目标粒子群算法,在每次环境变化时给出了完整的Pareto非劣最优解,可供决策者根据超调量和上升时间的不同满意度,选择相应的PID控制参数。
最后对全文进行总结,对本文存在的不足进行了阐述,并对粒子群算法的发展进行了展望。
Particle Swarm Optimization (PSO) is an optimization method based on swarm intelligence, by Kennedy and Eberhart in 1995. Because of its fast convergence and easy to realize, PSO is widely used in many fields such as computational intelligence, task schedule, traffic optimization, telecommunications routing, circuit design. Now it has become a hot topic in field of computational intelligence research.
Although PSO and its variants have been successfully applied to static optimization problem, in many real-world optimization problems, the objective function, the problem instance, or constraints may change over time, and thus, the optimum of that problem might change as well. This brings new challenges to PSO even to evolutionary computation as a whole.
In this paper, theory, method and application of PSO are studied. Paper mainly includes the following three parts:
The first part is mainly on the theory of PSO. First, by the Lyapunov time-varying model, the movement of single particle is analyzed, and stability condition is given, and then using stochastic processes theory to prove that the particle's position sequences converge in mean square. Furthermore, the movement of the whole swarm is analyzed. Finally according to the convergence criterion of stochastic optimization algorithm, a guaranteed global convergence PSO is proposed, which is tested on a few benchmark functions, the simulation shows the effectiveness of the improved algorithm.
The second part is on the improved PSO in dynamic environments, mainly including dynamic single-objective PSO, dynamic multi-objective PSO, and dynamic high-dimensional PSO.
This paper first represents the model of dynamic environment, makes an analysis of the difficulty to solve the dynamic optimization problems by PSO, and then propose a improved multi-swarm PSO based on Cauchy mutation and the repulsion potential field, the new algorithm is tested on CEC09 benchmark functions and the DF1, the simulation shows that the improved algorithm can track the changing extreme points effectively.
For the dynamic multi-objective problem, the definition is given and performance evaluation criteria is analyzed in detail, then a collaborative multi-swarm PSO is proposed, which adaptively switching from competitive model to cooperative model to track for the Pareto front and Pareto solution set. The purpose of competition is to explore in the search space, on the contrary, the purpose of cooperation is to exploit in the search space. The improved algorithm is compared with the other two algorithms and performs well in tracking performance by tested on moving peaks benchmark and dynamic functions.
As the dimension of the search space rise, almost all the evolutionary computation suffers "the curse of dimensionality". This paper first makes an analysis of reasons and put forward a dimensional adaptive learning PSO for the local extreme points. The simulation verifies the excellent tracking performance of the improved algorithm.
The third part is the application of PSO in dynamic environment. This paper proposes an improved PSO to optimize the parameters of PID controller for the dynamic system. First the fitness function is defined by the rising time, overshoot and steady state error with appropriate weighting according to actual control system. Improved PSO is proposed to optimize the parametres of PID controller. Then based on Pareto optimization theory, the improved multi-objective PSO is proposed to provided a complete Pareto nondominated solutions, which could satisfy decision-makers to choose corresponding the parameters of PID controller according to their preference to the overshoot and rise time.
Finally, the full text of this article is summarized, the deficiencies are explained and the future of PSO is prospected.
虽然粒子群算法及其众多的改进算法已经被成功地运用到一些静态问题的优化上,但是,很多现实问题往往是随时间变化而变化的,这些动态变化的问题要求算法能够对环境的变化快速反应,对变化的最优解快速跟踪。这给粒子群算法以及整个演化计算方法带来了新的挑战。
本文从理论、方法和应用三个方面对动态环境下粒子群算法进行研究。论文内容主要包括以下三个部分：
第一部分旨在对粒子的运动行为和粒子群算法的收敛性进行分析。首先构造李雅普诺夫函数,对单个粒子的运动行为进行了分析,给出了粒子运动稳定的条件。然后利用随机过程理论,证明了粒子位置序列均方稳定。在对单个粒子运动行为分析的基础上,分析了粒子群体运动行为,证明了群体运动的稳定性。最后从随机优化算法收敛性判定标准入手,分析了粒子群算法的收敛性,提出了一种保证全局收敛的改进粒子群算法,通过对基准测试函数仿真,验证了改进算法的有效性。
第二部分主要研究了如何利用改进粒子群算法解决动态环境下单目标、多目标和高维优化问题。
对于动态单目标优化问题的研究,本文首先对环境的变化模式进行了数学描述,分析了粒子群算法无法有效对动态问题优化的原因,然后提出了一种基于柯西变异和斥力势场的多粒子群改进算法,定量分析了柯西变异优于其它变异的原因。对动态基准测试函数的仿真表明,改进算法能够对动态环境下变化的极值点进行有效跟踪。
对于动态多目标优化问题的研究,本文首先对动态多目标优化问题的定义进行了描述,分析了算法的性能评价标准,在此基础上,提出了一种基于多种群协同优化的粒子群算法,并从理论上证明了多种群协同搜索优于单种群独自搜索。改进算法采用了竞争模式和协作模式自适应切换的方法对Pareto前端和Pareto最优解集进行跟踪。竞争模式采用了隐式空间分解,主要目的是对整个解空间进行勘探,进行粗粒度的搜索,在竞争产生非支配解集失效后,多种群进行协作搜索,协作搜索采用显式空间分解,其主要目的是对局部搜索空间开采,进行精度搜索。通过对动态多目标测试函数仿真,验证了改进算法可以对变化的Pareto前端和Pareto最优解集快速跟踪。
对于动态高维优化问题的研究,首先分析了高维优化问题难以优化的原因,并提出了一种基于局部极值点维度自适应学习的粒子群改进算法,随后通过对高维测试函数的仿真,验证了改进算法的有效性。
第三部分对垃圾焚烧系统PID控制器参数自适应整定进行了研究。垃圾焚烧系统由于系统噪声、设备折旧等因素的影响,系统参数容易发生变化,因此可以看成动态系统的PID控制器的参数要不断进行调整。本部分首先定义了一个包含系统超调量、上升时间和稳态误差指标项的适应度函数,根据控制系统的实际要求对各指标项进行适当加权,利用改进粒子群算法对PID控制器的参数进行优化。随后基于Pareto优化理论,利用改进的多目标粒子群算法,在每次环境变化时给出了完整的Pareto非劣最优解,可供决策者根据超调量和上升时间的不同满意度,选择相应的PID控制参数。
最后对全文进行总结,对本文存在的不足进行了阐述,并对粒子群算法的发展进行了展望。
Particle Swarm Optimization (PSO) is an optimization method based on swarm intelligence, by Kennedy and Eberhart in 1995. Because of its fast convergence and easy to realize, PSO is widely used in many fields such as computational intelligence, task schedule, traffic optimization, telecommunications routing, circuit design. Now it has become a hot topic in field of computational intelligence research.
Although PSO and its variants have been successfully applied to static optimization problem, in many real-world optimization problems, the objective function, the problem instance, or constraints may change over time, and thus, the optimum of that problem might change as well. This brings new challenges to PSO even to evolutionary computation as a whole.
In this paper, theory, method and application of PSO are studied. Paper mainly includes the following three parts:
The first part is mainly on the theory of PSO. First, by the Lyapunov time-varying model, the movement of single particle is analyzed, and stability condition is given, and then using stochastic processes theory to prove that the particle's position sequences converge in mean square. Furthermore, the movement of the whole swarm is analyzed. Finally according to the convergence criterion of stochastic optimization algorithm, a guaranteed global convergence PSO is proposed, which is tested on a few benchmark functions, the simulation shows the effectiveness of the improved algorithm.
The second part is on the improved PSO in dynamic environments, mainly including dynamic single-objective PSO, dynamic multi-objective PSO, and dynamic high-dimensional PSO.
This paper first represents the model of dynamic environment, makes an analysis of the difficulty to solve the dynamic optimization problems by PSO, and then propose a improved multi-swarm PSO based on Cauchy mutation and the repulsion potential field, the new algorithm is tested on CEC09 benchmark functions and the DF1, the simulation shows that the improved algorithm can track the changing extreme points effectively.
For the dynamic multi-objective problem, the definition is given and performance evaluation criteria is analyzed in detail, then a collaborative multi-swarm PSO is proposed, which adaptively switching from competitive model to cooperative model to track for the Pareto front and Pareto solution set. The purpose of competition is to explore in the search space, on the contrary, the purpose of cooperation is to exploit in the search space. The improved algorithm is compared with the other two algorithms and performs well in tracking performance by tested on moving peaks benchmark and dynamic functions.
As the dimension of the search space rise, almost all the evolutionary computation suffers "the curse of dimensionality". This paper first makes an analysis of reasons and put forward a dimensional adaptive learning PSO for the local extreme points. The simulation verifies the excellent tracking performance of the improved algorithm.
The third part is the application of PSO in dynamic environment. This paper proposes an improved PSO to optimize the parameters of PID controller for the dynamic system. First the fitness function is defined by the rising time, overshoot and steady state error with appropriate weighting according to actual control system. Improved PSO is proposed to optimize the parametres of PID controller. Then based on Pareto optimization theory, the improved multi-objective PSO is proposed to provided a complete Pareto nondominated solutions, which could satisfy decision-makers to choose corresponding the parameters of PID controller according to their preference to the overshoot and rise time.
Finally, the full text of this article is summarized, the deficiencies are explained and the future of PSO is prospected.
引文
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