粒子群优化算法的改进及其在图像中的应用研究
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摘要
群体智能优化算法的基本思想是模拟自然界的群体行为来构造随机优化算法。典型的群体智能优化算法有M. Dorigo提出的蚁群算法(Ant Colony Optimization, ACO)和J.Kennedy与R.Eberhart提出的粒子群算法(Particle Swarm Optimization, PSO)。近年来,群体智能优化算法在很多领域都得到了有效的研究和应用,已经成为人工智能以及经济、社会学、生物科学、计算机科学等交叉学科的研究热点。研究群体智能优化算法内在的原理,探索算法的改进措施,不仅可以改进群智能优化算法的优化性能,更为其应用于大规模的组合优化问题等提供了可能性。
本文主要研究量子行为粒子群算法(Quantum-behaved Particle Swarm Optimization, QPSO),分析研究了算法的基本原理,针对该算法执行过程中可能出现的早熟问题,提出了几种算法的改进方法;与此同时,为了进一步提高算法的速度,对该算法的并行化进行了研究,以进一步提高算法的全局性和性能,在上述研究的基础上,对它在实际优化问题中的应用进行了研究。主要研究内容包括:
(1)针对算法在解一些多峰函数或具有局部最优解的复杂优化问题时,因mbest参数而存在粒子快速收敛于局部最优解趋于同一化,导致算法在后期的收敛速度和搜索能力变差的缺点。提出了基于邻域模型的QPSO算法(Neighborhood Topology QPSO,NQPSO)。通过动态调整算法的邻域,使得算法保持多个吸引子来避免早熟,增强了个体的寻优能力。实验证明,该算法有效地提高了种群的多样性,其全局搜索能力和局部搜索能力均优于QPSO和SPSO算法,尤其体现在解决高维的优化问题。
(2)针对算法可能的早熟问题,提出了它的一种改进算法。即在算法中引入Gauss扰动,通过施加于群体的平均最好位置上的扰动,使得粒子种群保持群体的活性与多样性,从而防止算法早熟的发生。对一些标准测试函数的仿真实验表明,改进算法的性能比一般QPSO算法有所提高。
(3)提出了算法的另外两种改进,即具有多阶段的QPSO算法(A Multi-Phased QPSO,MQPSO)以及多样性维持的QPSO算法(Diversity-Maintained QPSO,DMQPSO)。前者引入了多个子群体和多个搜索阶段,使群体能保持持续的搜索能力;后者通过对群体多样性的控制,使之维持在一定的水平,同样能保持粒子群的持续运行能力。这两种方法是防止早熟收敛的有效方法并且可能在很多方面使得算法性能得到提高。
(4)研究了算法的并行化处理方法,通过研究常用和较新出现的进化算法的并行化方法,利用岛屿模型将粒子群分割成若干子群体,每个子群体分别在不同的处理机上进行搜索,定期相互交换信息,从而维持整个群体的多样性,提高算法的性能。与此同时,利用群体智能算法内在的并行性,设计和构建了基于动态邻域拓扑结构的并行计算模型,分别采用MPI、OpenMP以及MPI+OpenMP混合编程实现了基于邻域模型的并行QPSO算法。实验显示基于邻域模型的并行QPSO算法在求解非线性优化问题上表现出良好的性能。
(5)研究了算法在实际优化问题中的应用,包括图像对准、图像分割等,仿真实验显示,QPSO算法及其改进能有效的应用于图像处理等实际优化问题。
文章首先介绍课题的研究背景、研究目标,以及常用进化算法。第二章介绍PSO算法的基本原理和实现方式,然后介绍基于Delta势阱的量子行为PSO算法,即QPSO算法的基本原理。第三章针对QPSO算法存在的问题,在算法中引入了动态可变的邻域拓扑模型和算子,提出了基于邻域模型的QPSO算法。第四章针对算法在运行过程中存在的多样性缺失问题,提出利用高斯扰动来改善算法运行过程中粒子的多样性,即带有高斯扰动的QPSO算法(GQPSO)。给出了GQPSO算法的基本原理和工作流程,然后给出了三种方法加入高斯扰动,最后利用标准测试函数对三种算法的性能进行了实验测试。第五章将算法进行阶段划分,通过不同阶段的参数设置,改善算法的性能,提出了多阶段QPSO算法,利用两种方法来改进QPSO算法的性能,一种是维持粒子群多样性的方法来提高QPSO算法的全局搜索能力,称之为DQPSO算法。另一种是具有多群体和多阶段的量子行为的QPSO算法(MQPSO)。第六章根据大规模复杂优化问题对算法速度和时间上的要求,研究算法的并行化方法,以提高算法的性能和速度。第七章详细描述了算法在实际优化问题中的应用,如约束函数优化、医学图像配准、图像分割等方面的具体应用。本章对QPSO算法、并行QPSO算法在图像处理领域的应用进行了初步的研究,首先分析医学图像配准问题,然后采用基于最大互信息的相似性度量和QPSO算法,对采用核磁共振成像MR图像和计算机断层扫描成像CT图像进行了图像配准实验,其次研究了QPSO算法及具有高斯扰动的QPSO算法(GQPSO)在图像聚类分割中的应用,提出了基于QPSO算法的聚类算法,并利用三种算法对9幅图像进行了聚类分割实验比较。第八章为总结和展望,总结本课题在研究改进算法中取得的成果,提出未来研究的方向。
Swarm intelligence algorithm is a kind of stochastic algorithm based on the behavior simulation of biology swarm, such as ants and birds. The ant colony optimization algorithm, ACO and particle swarm optimization algorithm, PSO provided by M. Dorigo and J. Kennedy respectively are the two examples of swarm intelligence algorithm. Recently, swarm intelligence algorithm research on various engineer optimization problem has got more and more good results. The swarm intelligence optimization algorithm has become a hotspot in artificial intelligence, economic, sociology, biological sciences, computer science research area, etc. The study on algorithm principle and algorithm improvement can improve not only the optimization performance but also the possibility of swarm intelligence algorithm when it is used in the large scale combinatorial optimization problems.
This paper focuses on the quantum-behaved particle swarm optimization algorithm(QPSO). By analyzing the principle of the algorithm, it gives out some improved versions to avoid the premature convergence problem. Meanwhile, in order to speed up the algorithm running process, some parallel QPSO algorithms are studied in detail. Experiments on benchmark functions and image process problems show that the parallel algorithm shows better performance in many optimization problems. In this paper, the improvement and parallelization research of the algorithm includes:
(1) When the algorithm is applied to solve multimodal problems and complicated optimization problems with local optimum, the mbest in the algorithm will cause particles convergence to the local optimum. It will lower the Algorithm's performance in convergence speed and search ability. To overcome this problem, an improved algorithm named neighborhood topology QPSO(NQPSO) is proposed. By adjusting the neighborhood of particles dynamically, the improved algorithm maintains several attractors to avoid the premature convergence and enhance the particles search ability. The experiment shows that the improved algorithm has better performance than QPSO and SPSO in collective diversity and search ability, especially in solving high-dimensional optimization problems.
(2)In order to avoid the premature convergence in the algorithm, an improved version is proposed. By introducing the Gauss disturbance on the mbest in the algorithm, the collective's activity and diversity are maintained when algorithm is running. Experiments on benchmark functions show the improvement on the algorithm with Gauss disturbance.
(3) Another improved algorithms are studied. They are multi-phased QPSO, named MQPSO and diversity-maintained QPSO algorithm, named DMQPSO. In the first algorithm, the collective is divided into several sub-groups, the search procedure is divided into different phase, thus make the particles maintain the search ability when algorithm is running. The second algorithm keeps the particle’s activity by controlling the collective's diversity to some degree. These two algorithms can avoid premature convergence and improve search performance effectively.
(4) By studying the parallelization of the algorithm, a parallel algorithm with island modal is introduced in detail. In this algorithm, particle collective is divided into several sub-groups according to the computing nodes number in parallel system. Each sub-group of particles searches independently in different computing nodes. By exchanging search results between different sub-groups in period, the algorithm can keep the diversity of particle collective and improve the search performance. Meanwhile, a parallel computing modal based on dynamic neighborhood topology is proposed. A parallel version based on neighborhood modal is programmed by MPI, OpenMPI and MPI+OpenMP respectively. Experiments on benchmark functions show the good performance of this parallel algorithm.
(5) The application of the algorithm in engineer optimization problems such as image registration and image segmentation is studied. Experiments also show the good performance of the algorithm.
At the first section of this paper, we introduced the research background, research objects and some evolutionary algorithms in detail. In chapter 2, the principle of PSO and QPSO algorithm are described, and give out the realization method of these two algorithms. Chapter 3 focuses on the convergence speed and search ability. The principle of the algorithm based on neighborhood topology algorithm is studied and tested on benchmark functions. In chapter 4, the Gauss disturbance is used to improve it's diversity. In chapter 5, two improvements are applied to the algorithm, named a multi-phased QPSO and a diversity-maintained QPSO. The test results on benchmark function are given out in detail to show the performance improvement. In chapter 6, the parallelization of the algorithm is studied, including parallel computing model, parallel algorithm, etc. Chapter 7 describes the application of the algorithm and parallel version in digital image process. At the end of this paper, there are the conclusion of this paper and the future works.
本文主要研究量子行为粒子群算法(Quantum-behaved Particle Swarm Optimization, QPSO),分析研究了算法的基本原理,针对该算法执行过程中可能出现的早熟问题,提出了几种算法的改进方法;与此同时,为了进一步提高算法的速度,对该算法的并行化进行了研究,以进一步提高算法的全局性和性能,在上述研究的基础上,对它在实际优化问题中的应用进行了研究。主要研究内容包括:
(1)针对算法在解一些多峰函数或具有局部最优解的复杂优化问题时,因mbest参数而存在粒子快速收敛于局部最优解趋于同一化,导致算法在后期的收敛速度和搜索能力变差的缺点。提出了基于邻域模型的QPSO算法(Neighborhood Topology QPSO,NQPSO)。通过动态调整算法的邻域,使得算法保持多个吸引子来避免早熟,增强了个体的寻优能力。实验证明,该算法有效地提高了种群的多样性,其全局搜索能力和局部搜索能力均优于QPSO和SPSO算法,尤其体现在解决高维的优化问题。
(2)针对算法可能的早熟问题,提出了它的一种改进算法。即在算法中引入Gauss扰动,通过施加于群体的平均最好位置上的扰动,使得粒子种群保持群体的活性与多样性,从而防止算法早熟的发生。对一些标准测试函数的仿真实验表明,改进算法的性能比一般QPSO算法有所提高。
(3)提出了算法的另外两种改进,即具有多阶段的QPSO算法(A Multi-Phased QPSO,MQPSO)以及多样性维持的QPSO算法(Diversity-Maintained QPSO,DMQPSO)。前者引入了多个子群体和多个搜索阶段,使群体能保持持续的搜索能力;后者通过对群体多样性的控制,使之维持在一定的水平,同样能保持粒子群的持续运行能力。这两种方法是防止早熟收敛的有效方法并且可能在很多方面使得算法性能得到提高。
(4)研究了算法的并行化处理方法,通过研究常用和较新出现的进化算法的并行化方法,利用岛屿模型将粒子群分割成若干子群体,每个子群体分别在不同的处理机上进行搜索,定期相互交换信息,从而维持整个群体的多样性,提高算法的性能。与此同时,利用群体智能算法内在的并行性,设计和构建了基于动态邻域拓扑结构的并行计算模型,分别采用MPI、OpenMP以及MPI+OpenMP混合编程实现了基于邻域模型的并行QPSO算法。实验显示基于邻域模型的并行QPSO算法在求解非线性优化问题上表现出良好的性能。
(5)研究了算法在实际优化问题中的应用,包括图像对准、图像分割等,仿真实验显示,QPSO算法及其改进能有效的应用于图像处理等实际优化问题。
文章首先介绍课题的研究背景、研究目标,以及常用进化算法。第二章介绍PSO算法的基本原理和实现方式,然后介绍基于Delta势阱的量子行为PSO算法,即QPSO算法的基本原理。第三章针对QPSO算法存在的问题,在算法中引入了动态可变的邻域拓扑模型和算子,提出了基于邻域模型的QPSO算法。第四章针对算法在运行过程中存在的多样性缺失问题,提出利用高斯扰动来改善算法运行过程中粒子的多样性,即带有高斯扰动的QPSO算法(GQPSO)。给出了GQPSO算法的基本原理和工作流程,然后给出了三种方法加入高斯扰动,最后利用标准测试函数对三种算法的性能进行了实验测试。第五章将算法进行阶段划分,通过不同阶段的参数设置,改善算法的性能,提出了多阶段QPSO算法,利用两种方法来改进QPSO算法的性能,一种是维持粒子群多样性的方法来提高QPSO算法的全局搜索能力,称之为DQPSO算法。另一种是具有多群体和多阶段的量子行为的QPSO算法(MQPSO)。第六章根据大规模复杂优化问题对算法速度和时间上的要求,研究算法的并行化方法,以提高算法的性能和速度。第七章详细描述了算法在实际优化问题中的应用,如约束函数优化、医学图像配准、图像分割等方面的具体应用。本章对QPSO算法、并行QPSO算法在图像处理领域的应用进行了初步的研究,首先分析医学图像配准问题,然后采用基于最大互信息的相似性度量和QPSO算法,对采用核磁共振成像MR图像和计算机断层扫描成像CT图像进行了图像配准实验,其次研究了QPSO算法及具有高斯扰动的QPSO算法(GQPSO)在图像聚类分割中的应用,提出了基于QPSO算法的聚类算法,并利用三种算法对9幅图像进行了聚类分割实验比较。第八章为总结和展望,总结本课题在研究改进算法中取得的成果,提出未来研究的方向。
Swarm intelligence algorithm is a kind of stochastic algorithm based on the behavior simulation of biology swarm, such as ants and birds. The ant colony optimization algorithm, ACO and particle swarm optimization algorithm, PSO provided by M. Dorigo and J. Kennedy respectively are the two examples of swarm intelligence algorithm. Recently, swarm intelligence algorithm research on various engineer optimization problem has got more and more good results. The swarm intelligence optimization algorithm has become a hotspot in artificial intelligence, economic, sociology, biological sciences, computer science research area, etc. The study on algorithm principle and algorithm improvement can improve not only the optimization performance but also the possibility of swarm intelligence algorithm when it is used in the large scale combinatorial optimization problems.
This paper focuses on the quantum-behaved particle swarm optimization algorithm(QPSO). By analyzing the principle of the algorithm, it gives out some improved versions to avoid the premature convergence problem. Meanwhile, in order to speed up the algorithm running process, some parallel QPSO algorithms are studied in detail. Experiments on benchmark functions and image process problems show that the parallel algorithm shows better performance in many optimization problems. In this paper, the improvement and parallelization research of the algorithm includes:
(1) When the algorithm is applied to solve multimodal problems and complicated optimization problems with local optimum, the mbest in the algorithm will cause particles convergence to the local optimum. It will lower the Algorithm's performance in convergence speed and search ability. To overcome this problem, an improved algorithm named neighborhood topology QPSO(NQPSO) is proposed. By adjusting the neighborhood of particles dynamically, the improved algorithm maintains several attractors to avoid the premature convergence and enhance the particles search ability. The experiment shows that the improved algorithm has better performance than QPSO and SPSO in collective diversity and search ability, especially in solving high-dimensional optimization problems.
(2)In order to avoid the premature convergence in the algorithm, an improved version is proposed. By introducing the Gauss disturbance on the mbest in the algorithm, the collective's activity and diversity are maintained when algorithm is running. Experiments on benchmark functions show the improvement on the algorithm with Gauss disturbance.
(3) Another improved algorithms are studied. They are multi-phased QPSO, named MQPSO and diversity-maintained QPSO algorithm, named DMQPSO. In the first algorithm, the collective is divided into several sub-groups, the search procedure is divided into different phase, thus make the particles maintain the search ability when algorithm is running. The second algorithm keeps the particle’s activity by controlling the collective's diversity to some degree. These two algorithms can avoid premature convergence and improve search performance effectively.
(4) By studying the parallelization of the algorithm, a parallel algorithm with island modal is introduced in detail. In this algorithm, particle collective is divided into several sub-groups according to the computing nodes number in parallel system. Each sub-group of particles searches independently in different computing nodes. By exchanging search results between different sub-groups in period, the algorithm can keep the diversity of particle collective and improve the search performance. Meanwhile, a parallel computing modal based on dynamic neighborhood topology is proposed. A parallel version based on neighborhood modal is programmed by MPI, OpenMPI and MPI+OpenMP respectively. Experiments on benchmark functions show the good performance of this parallel algorithm.
(5) The application of the algorithm in engineer optimization problems such as image registration and image segmentation is studied. Experiments also show the good performance of the algorithm.
At the first section of this paper, we introduced the research background, research objects and some evolutionary algorithms in detail. In chapter 2, the principle of PSO and QPSO algorithm are described, and give out the realization method of these two algorithms. Chapter 3 focuses on the convergence speed and search ability. The principle of the algorithm based on neighborhood topology algorithm is studied and tested on benchmark functions. In chapter 4, the Gauss disturbance is used to improve it's diversity. In chapter 5, two improvements are applied to the algorithm, named a multi-phased QPSO and a diversity-maintained QPSO. The test results on benchmark function are given out in detail to show the performance improvement. In chapter 6, the parallelization of the algorithm is studied, including parallel computing model, parallel algorithm, etc. Chapter 7 describes the application of the algorithm and parallel version in digital image process. At the end of this paper, there are the conclusion of this paper and the future works.
引文
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