粒子群优化算法及其应用研究
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摘要
科学领域、工程领域和经济领域都涉及到很多复杂的、非线性的甚至非凸形式的最优化问题。在电力系统分析和控制系统设计中同样存在大量的这类难优化问题,如无功优化、机组组合、负荷预测以及电机参数辨识等。因此高效的优化技术成为科学工作者的研究目标之一。
粒子群优化算法(Prticle Swarm Optimization,简称PSO)是一种新的群体智能优化算法。它的主要特点是原理简单、参数少、收敛速度快、所需领域知识少。该算法的出现引起了学者们极大的关注,已在函数优化、神经网络训练、组合优化等领域获得了广泛应用,并取得了较好的效果。尽管粒子群优化算法发展近十年,但无论是理论分析还是实践应用都尚未成熟,有大量的问题值得研究。
本文就如何改进标准PSO算法性能以及该算法在电力系统领域中的应用进行了深入的研究。本文的主要研究工作和创新点可归纳如下：
(1)为了克服PSO算法在高维复杂问题寻优时有相当可能陷入局部极小的现象,提出了一种自适应粒子群优化算法。在算法进化过程中引入群体适应度方差和群体位置方差,非线性的调整惯性权重,调节算法的探索和开发能力,达到跳出局部极小点,获得全局最优的目的。在进化的中后期,根据粒子的表现不同,分别对其采用不同的变异策略和惯性权重,使群体在进化过程中始终保持惯性权重的多样性,在算法的全局收敛性和收敛速度之间做了一个较好的折中。将自适应粒子群优化算法应用于电力系统无功优化问题中,算例仿真表明该方法用于解决无功优化问题是有效可行的。
(2)对基于向量评价的粒子群算法进行了扩展,提出了基于向量评价的自适应粒子群优化算法(VEAPSO)来解决多目标优化问题。利用该方法解决多目标电力系统无功优化问题,确定出问题的Pareto最优解集。为帮助决策者在优化后得到的Pareto最优解集中选取较合适的最优解,本文提出了一种基于决策者偏好及投影寻踪模型的多属性决策法,该方法兼顾决策者的偏好,同时又力争减少主观随意性,使决策结果更加真实可靠。
(3)提出了一种基于动态双种群的粒子群优化算法(DDPSO)。DDPSO算法将种群划分成两个种群规模随进化过程不断变化的子种群,两个子种群分别采用不同的学习策略进行进化,并在进化过程中相互交换信息。为了保持种群的多样性,将免疫算法的多样性保持机制引入DDPSO算法中,提高了算法的全局收敛性。将该算法应用于机组组合问题中,采用实数矩阵编码方法对发电计划进行编码,将两层优化问题转化为单层优化问题,可直接运用DDPSO算法来求解。仿真结果表明,所提出的方法用来解决机组组合问题是有效可行的,具有良好的精度和鲁棒性。
(4)提出了一种基于物种概念的动态多种群粒子群优化算法(DMPSO)来解决多模态函数优化问题。在DMPSO中引入了物种概念,在进化过程中动态确定物种,利用种群多样性信息动态调整物种半径,通过物种对解空间的不同区域进行搜索,最终确定出各极值点。将DMPSO算法和支持向量机(SVM)相结合,形成了解决电力系统短期负荷预测问题的新方法(DMPSO-SVM)。在该方法中利用DMPSO算法来优化SVM中的参数,利用快速傅立叶变换(FFT)进行频谱分析并确定SVM的输入量。电力系统短期负荷预测的实际算例表明,与传统预测方法相比,该方法具有更高的预测精度和鲁棒性。
(5)提出了一种基于天体系统模型的粒子群优化算法(CSPSO)。在CSPSO算法中,参照天文学中的天体系统模型,将种群划分为多个相对独立的天体系统,每个系统按照自己的运行规则在不同的空间中运行,在算法的后期引入混沌优化,最终确定出优化问题的全局最优解。将CSPSO算法应用于异步电机参数辨识问题中,仿真结果表明CSPSO算法比GA算法和PSO算法具有更精确的参数辨识能力。
Many scientific, engineering and economic areas involve the optimization of complex, nonlinear and possibly non-convex problems. There are many such problems in power system analysis and control system design as reactive power optimization problem, unit commitment problem, load forecasting problem and motor parameter identification. Therefore, effective optimization methods have become one of the main objectives for scientific researchers.
Particle swarm optimization (PSO) algorithm is an evolutionary computation technique developed by Dr. Eberhart and Dr. Kennedy in 1995. Recently, PSO algorithm has been gradually attracted more attention over another intelligent algorithm. PSO is simple in concept, few in parameters and easy in implementation. It is proved to be an efficient method to solve optimization problems and has successfully been applied in the area of function optimization, neural network training and fuzzy control systems, etc. However, both theory and application of PSO are still far from mature.
The dissertation focuses on the theory and application of PSO, especially, an indeep and systemic study on how to improve the conventional PSO algorithm, solving the problems such as problems of electrical system. The main achievements of this dissertation include:
(1) A new adaptive particle swarm optimization (APSO) algorithm was proposed. The exploration and exploitation ability of the algorithm were regulated through introducing two criteria in the evolutionary process, i.e. the population-fitness-variance and the population-position-variance, to preserve population diversity. The dynamic inertia weight varied with population diversity was employed to improve the convergence speed. In intermediate stage and anaphase of iterative, the inertia weight of the particle was adjusted adaptively based on the premature convergence degree of the swarm and the fitness of the particle to preserve the diversity of inertia weight. The algorithm had been applied to reactive power optimization. The simulation results of the standard IEEE-30-bus power system had indicated that it was validity, fast convergence and computation efficiency during the reactive power optimization.
(2) The VEAPSO algorithm was proposed to solve the multi-objective optimization problems. The algorithm had been applied to multi-objective reactive power optimization and can obtain the Pareto optimal solutions. Aimming at defect in the traditional evaluation of multi-objective solutions, a multiple attribute decision-making method based on preference information and projecting pursuit classification model was presented. This method made decision-making result more actual.
(3) Dynamic double-population particle swarm optimization (DDPSO) algorithm was presented, where population was divided into two sub-populations varying with their own evolutionary learning strategies and exchanged between them. The reproduction strategy based on density of immune algorithm was introducd into PSO algorithm to maintain the multiplicity of particle. The algorithm has been applied to power system unit commitment (UC). The particle consists of a two-dimensional real number matrix representing generation schedule. The DDPSO algorithm can directly solve UC. Simulation results showed the proposed method performs better in term of solution's precision and convergence property.
(4) A dynamic multi-population particle swarm optimization (DMPSO) algorithm was presented. In algorithm, the notion of species was introduced and population was divided into species according to their similarity. Species seeds were identified from the entire population and a strategy for adaptively changing the species radius based on population diversity information was proposed. Species were able to simultaneously optimize toward potentially regions containing multiple optima. A new short-term load forecasting model based on SVM with DMPSO algorithm (DMPSO-SVM) was proposed. The example of California power market revealed that the DMPSO-SVM approach outperforms the other traditional model.
(5) A new method of celestial system particle swarm optimization (CSPSO) was presented. In CSPSO algorithm, based on the celestial system model of astronomy, the population was divided into multiple independent celestial systems varying with their own movement laws in respective space. In late iteration, chaotic optimization method was introduced and the globe optimum was decided. CSPSO algorithm was applied to induction motor parameter identification. The simulation results show CSPSO method possessed stronger capability of parameter identification than GA and PSO method.
粒子群优化算法(Prticle Swarm Optimization,简称PSO)是一种新的群体智能优化算法。它的主要特点是原理简单、参数少、收敛速度快、所需领域知识少。该算法的出现引起了学者们极大的关注,已在函数优化、神经网络训练、组合优化等领域获得了广泛应用,并取得了较好的效果。尽管粒子群优化算法发展近十年,但无论是理论分析还是实践应用都尚未成熟,有大量的问题值得研究。
本文就如何改进标准PSO算法性能以及该算法在电力系统领域中的应用进行了深入的研究。本文的主要研究工作和创新点可归纳如下：
(1)为了克服PSO算法在高维复杂问题寻优时有相当可能陷入局部极小的现象,提出了一种自适应粒子群优化算法。在算法进化过程中引入群体适应度方差和群体位置方差,非线性的调整惯性权重,调节算法的探索和开发能力,达到跳出局部极小点,获得全局最优的目的。在进化的中后期,根据粒子的表现不同,分别对其采用不同的变异策略和惯性权重,使群体在进化过程中始终保持惯性权重的多样性,在算法的全局收敛性和收敛速度之间做了一个较好的折中。将自适应粒子群优化算法应用于电力系统无功优化问题中,算例仿真表明该方法用于解决无功优化问题是有效可行的。
(2)对基于向量评价的粒子群算法进行了扩展,提出了基于向量评价的自适应粒子群优化算法(VEAPSO)来解决多目标优化问题。利用该方法解决多目标电力系统无功优化问题,确定出问题的Pareto最优解集。为帮助决策者在优化后得到的Pareto最优解集中选取较合适的最优解,本文提出了一种基于决策者偏好及投影寻踪模型的多属性决策法,该方法兼顾决策者的偏好,同时又力争减少主观随意性,使决策结果更加真实可靠。
(3)提出了一种基于动态双种群的粒子群优化算法(DDPSO)。DDPSO算法将种群划分成两个种群规模随进化过程不断变化的子种群,两个子种群分别采用不同的学习策略进行进化,并在进化过程中相互交换信息。为了保持种群的多样性,将免疫算法的多样性保持机制引入DDPSO算法中,提高了算法的全局收敛性。将该算法应用于机组组合问题中,采用实数矩阵编码方法对发电计划进行编码,将两层优化问题转化为单层优化问题,可直接运用DDPSO算法来求解。仿真结果表明,所提出的方法用来解决机组组合问题是有效可行的,具有良好的精度和鲁棒性。
(4)提出了一种基于物种概念的动态多种群粒子群优化算法(DMPSO)来解决多模态函数优化问题。在DMPSO中引入了物种概念,在进化过程中动态确定物种,利用种群多样性信息动态调整物种半径,通过物种对解空间的不同区域进行搜索,最终确定出各极值点。将DMPSO算法和支持向量机(SVM)相结合,形成了解决电力系统短期负荷预测问题的新方法(DMPSO-SVM)。在该方法中利用DMPSO算法来优化SVM中的参数,利用快速傅立叶变换(FFT)进行频谱分析并确定SVM的输入量。电力系统短期负荷预测的实际算例表明,与传统预测方法相比,该方法具有更高的预测精度和鲁棒性。
(5)提出了一种基于天体系统模型的粒子群优化算法(CSPSO)。在CSPSO算法中,参照天文学中的天体系统模型,将种群划分为多个相对独立的天体系统,每个系统按照自己的运行规则在不同的空间中运行,在算法的后期引入混沌优化,最终确定出优化问题的全局最优解。将CSPSO算法应用于异步电机参数辨识问题中,仿真结果表明CSPSO算法比GA算法和PSO算法具有更精确的参数辨识能力。
Many scientific, engineering and economic areas involve the optimization of complex, nonlinear and possibly non-convex problems. There are many such problems in power system analysis and control system design as reactive power optimization problem, unit commitment problem, load forecasting problem and motor parameter identification. Therefore, effective optimization methods have become one of the main objectives for scientific researchers.
Particle swarm optimization (PSO) algorithm is an evolutionary computation technique developed by Dr. Eberhart and Dr. Kennedy in 1995. Recently, PSO algorithm has been gradually attracted more attention over another intelligent algorithm. PSO is simple in concept, few in parameters and easy in implementation. It is proved to be an efficient method to solve optimization problems and has successfully been applied in the area of function optimization, neural network training and fuzzy control systems, etc. However, both theory and application of PSO are still far from mature.
The dissertation focuses on the theory and application of PSO, especially, an indeep and systemic study on how to improve the conventional PSO algorithm, solving the problems such as problems of electrical system. The main achievements of this dissertation include:
(1) A new adaptive particle swarm optimization (APSO) algorithm was proposed. The exploration and exploitation ability of the algorithm were regulated through introducing two criteria in the evolutionary process, i.e. the population-fitness-variance and the population-position-variance, to preserve population diversity. The dynamic inertia weight varied with population diversity was employed to improve the convergence speed. In intermediate stage and anaphase of iterative, the inertia weight of the particle was adjusted adaptively based on the premature convergence degree of the swarm and the fitness of the particle to preserve the diversity of inertia weight. The algorithm had been applied to reactive power optimization. The simulation results of the standard IEEE-30-bus power system had indicated that it was validity, fast convergence and computation efficiency during the reactive power optimization.
(2) The VEAPSO algorithm was proposed to solve the multi-objective optimization problems. The algorithm had been applied to multi-objective reactive power optimization and can obtain the Pareto optimal solutions. Aimming at defect in the traditional evaluation of multi-objective solutions, a multiple attribute decision-making method based on preference information and projecting pursuit classification model was presented. This method made decision-making result more actual.
(3) Dynamic double-population particle swarm optimization (DDPSO) algorithm was presented, where population was divided into two sub-populations varying with their own evolutionary learning strategies and exchanged between them. The reproduction strategy based on density of immune algorithm was introducd into PSO algorithm to maintain the multiplicity of particle. The algorithm has been applied to power system unit commitment (UC). The particle consists of a two-dimensional real number matrix representing generation schedule. The DDPSO algorithm can directly solve UC. Simulation results showed the proposed method performs better in term of solution's precision and convergence property.
(4) A dynamic multi-population particle swarm optimization (DMPSO) algorithm was presented. In algorithm, the notion of species was introduced and population was divided into species according to their similarity. Species seeds were identified from the entire population and a strategy for adaptively changing the species radius based on population diversity information was proposed. Species were able to simultaneously optimize toward potentially regions containing multiple optima. A new short-term load forecasting model based on SVM with DMPSO algorithm (DMPSO-SVM) was proposed. The example of California power market revealed that the DMPSO-SVM approach outperforms the other traditional model.
(5) A new method of celestial system particle swarm optimization (CSPSO) was presented. In CSPSO algorithm, based on the celestial system model of astronomy, the population was divided into multiple independent celestial systems varying with their own movement laws in respective space. In late iteration, chaotic optimization method was introduced and the globe optimum was decided. CSPSO algorithm was applied to induction motor parameter identification. The simulation results show CSPSO method possessed stronger capability of parameter identification than GA and PSO method.
引文
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