一类计算智能方法的停滞问题研究
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摘要
近年来,复杂优化问题寻求高效的解决方法已成为优化领域的一个极具挑战性的研究课题。除了传统优化方法,计算智能方法正在得到越来越多的研究人员的关注和重视。以遗传算法,蚁群算法和粒子群算法为代表的一类计算智能方法,它们从生物进化或动物群体协作的搜索机制中得到启发,利用群体的优势,在没有集中控制并且不提供全局模型的前提下,快速有效地搜索复杂优化问题的解空间,寻求全局最优解。
停滞问题一直是计算智能方法理论和应用饱受困扰的一大难题,这不仅关系到已有计算智能方法如何设置算法的结构和参数以确保快速求解待优化问题,同时也涉及到针对复杂的实际优化难题如何构造出快速有效的新计算智能方法的问题。本文针对以遗传算法、蚁群算法和粒子群优化算法为代表的一类计算智能方法在解决复杂优化难题时出现停滞的问题进行了深入研究,主要的创新点和研究成果有：
(1)研究了集中化搜索和多样化搜索对解集更新序列出现停滞的影响。本文通过对一类计算智能算法的搜索机理进行分析,根据在搜索过程中解集内部结构变化的性质定义解集多样度,并基于此定义了两种基本的搜索策略：多样化搜索和集中化搜索。从理论上证明集中化搜索,缩小了解空间的搜索范围,是导致解集停滞收敛的主要原因。而多样化搜索能扩大解集的搜索范围,促使算法跳出局部最优。最后,通过标准遗传算法、蚁群算法和粒子群优化算法的实际算例分析,说明典型的计算智能方法其搜索策略的集中化搜索和多样化搜索性质,以及算法出现停滞收敛的表现,验证了理论分析结论的正确性。
(2)得出了基于统一模型的一类计算智能方法几乎肯定弱收敛和几乎肯定强收敛的充分条件。本文首先分析了这类计算智能方法在方法论上的共同特点,建立起统一模型,从更一般化的角度来分析此类算法出现停滞现象的原因。接着,基于此模型,分别定义了表征解集变化强弱和解集优化程度的集组元变化率和解集改善率。同时,给出了计算智能方法搜索生成的解集更新状态转移序列的各种盖然论收敛的概念并分析了他们之间的关系。然后借助于随机过程理论,证明基于统一模型的计算智能方法在一定条件下几乎肯定弱收敛。最后,在传统的Markov链分析中运用鞅理论,证明这类计算智能方法在一定条件下几乎肯定强收敛。
(3)提出了一种用于复杂问题自适应优化且能有效克服停滞的云滴算法。本文基于云模型的特征,结合计算智能方法的基本原理,提出一种用于复杂问题自适应优化的云滴算法。该算法采用多维逆向云模型建立解集的特征参数,并根据是否出现当代精英和跨代精英自适应调整参数,再通过多维正向云模型产生新一代解集。云滴算法具有表示、再现和挖掘待优化问题的不确定知识的特点,无需预先设置其搜索策略和参数,且不论解集处于何种初始状态,整个系统能自适应地进行演化。然后借助于随机过程理论,在传统的Markov链分析中运用鞅理论,证明了云滴算法在一定条件下几乎肯定强收敛。最后通过两个标准测试问题的求解试验表明,与现有的四种算法相比,该算法不但收敛速度快,而且具有更好的自适应能力,能更有效地克服停滞现象的产生。
(4)提出了一类混沌系统未知参数辨识问题的解决方法。本文通过构造一个合适的评价函数,将混沌系统的未知参数辨识问题转换为一个多维的函数优化问题,然后利用滴算法对初始解集不敏感的优点和无需预先设置搜索策略和参数的特点,充分发挥其自适应搜索能力对混沌系统的未知参数进行辨识。以典型的Lorenz混沌系统和Chen混沌系统为例进行数值模拟,仿真结果表明,云滴优化算法能够有效克服停滞,快速对不同混沌系统的多个未知参数进行有效辨识,是一种简便易行的混沌系统参数辨识方法。
How to seek solutions of complicated optimization problems is a challenging research subject in recent years. In addition to traditional optimization methods, the computational intelligence approaches have been attractive in fundamental research and real applications. A class of computational intelligence approaches which is represented by the canonical forms of generic algorithms, ant colony optimization and particle swarm optimization is derived from the emulation of natural evolution or collective behavior of animals to seek solutions of complicated optimization problems by exploring and exploiting search spaces efficiently and effectively.
Stagnation is a crucial problem which is suffered by computational intelligence approaches when dealing with complicated optimization problems in the theory and application. On the one hand, it is related to how to set the structure and parameters of the existing computational intelligence methods to efficiently produce high-quality solutions. On the other hand, it involves how to design an effective and efficient computational intelligence method for solving complicated optimization problems.
This paper makes an investigation on the stagnation of a class of computational intelligence approaches, and the main contributions given in this dissertation are as follows.
(1) The influences of the diversification and the intensification of search strategies on the stagnation of solution set evolution are investigated. Through the analysis on the search characteristics of a class of computational intelligence approaches represented by the canonical forms of generic algorithms, ant colony optimization and particle swarm optimization, the concept of solution set diversity is introduced in this paper. And then two categories of fundamental search strategies, i.e. the diversification search and the intensification search, are defined in this paper on the basis of solution set diversity. Based on which the influences of the diversification and the intensification of search strategies on the stagnation of solution set evolution are investigated. Three popular swarm intelligent algorithms, i.e. the Canonical Generic Algorithm, the Ant Colony System and the Discrete Particle Swarm Optimization, are tested with a benchmark problem, and the results support the theoretical conclusions.
(2) The sufficient conditions are derived for the almost sure convergence of a universal model for a class of computational intelligence approaches. A universal model is built up in this paper for a class of computational intelligence approaches represented by the canonical forms of generic algorithms, ant colony optimization and particle swarm optimization in order to describe the common features of these algorithms. Two quantification indices, i.e., the variation rate and the progress rate, are defined respectively to estimate the variety and the optimality of the solution sets generated in the search process of the model. Four types of probabilistic convergence are given for the solution set updating sequences, and their relations are discussed. By introducing a martingale approach into the Markov chain analysis, the sufficient conditions are derived for the almost sure weak convergence and the almost sure strong convergence of the model.
(3) An adaptive cloud drops optimization algorithm is proposed for stagnation elimination. The feature parameters of solution sets are created by a multidimensional backward cloud model, and then adaptively adjusted based on the change of the elite solution candidates. The result is then used by a forward cloud model to produce the solution set of next generation. No any search parameters are predefined in the proposed algorithm, and, no matter what the initial solution set is, the whole system can adaptively approach to the global optimal solution. Based on the theory of stochastic processes, the almost sure convergence of the proposed algorithm is proved under certain conditions by introducing a martingale approach into traditional Markov Chain analysis. Two benchmark problems are tested with the proposed algorithm and the other four existing algorithms as a comparison. The results show that the proposed algorithm has faster convergence speed, better self-adaptability, and stronger ability to deal with stagnation phenomena effectively.
(4) The problem of unknown parameters identification for chaotic systems is addressed by the cloud drops optimization in this paper. Through establishing an appropriate evaluation function, the problem of unknown parameters identification in chaotic systems is formulated as a multi-dimensional optimization problem. And then, the cloud drops optimization algorithm, which is not sensitive to initial solution set and parameters less, is applied to obtain the original parameters of various chaotic systems. Numerical simulations on the typical Lorenz chaotic system and Chen chaotic system are conducted. Numerical simulation and comparisons with the other two existing algorithms demonstrate the effectiveness and feasibility of the proposed algorithm.
停滞问题一直是计算智能方法理论和应用饱受困扰的一大难题,这不仅关系到已有计算智能方法如何设置算法的结构和参数以确保快速求解待优化问题,同时也涉及到针对复杂的实际优化难题如何构造出快速有效的新计算智能方法的问题。本文针对以遗传算法、蚁群算法和粒子群优化算法为代表的一类计算智能方法在解决复杂优化难题时出现停滞的问题进行了深入研究,主要的创新点和研究成果有：
(1)研究了集中化搜索和多样化搜索对解集更新序列出现停滞的影响。本文通过对一类计算智能算法的搜索机理进行分析,根据在搜索过程中解集内部结构变化的性质定义解集多样度,并基于此定义了两种基本的搜索策略：多样化搜索和集中化搜索。从理论上证明集中化搜索,缩小了解空间的搜索范围,是导致解集停滞收敛的主要原因。而多样化搜索能扩大解集的搜索范围,促使算法跳出局部最优。最后,通过标准遗传算法、蚁群算法和粒子群优化算法的实际算例分析,说明典型的计算智能方法其搜索策略的集中化搜索和多样化搜索性质,以及算法出现停滞收敛的表现,验证了理论分析结论的正确性。
(2)得出了基于统一模型的一类计算智能方法几乎肯定弱收敛和几乎肯定强收敛的充分条件。本文首先分析了这类计算智能方法在方法论上的共同特点,建立起统一模型,从更一般化的角度来分析此类算法出现停滞现象的原因。接着,基于此模型,分别定义了表征解集变化强弱和解集优化程度的集组元变化率和解集改善率。同时,给出了计算智能方法搜索生成的解集更新状态转移序列的各种盖然论收敛的概念并分析了他们之间的关系。然后借助于随机过程理论,证明基于统一模型的计算智能方法在一定条件下几乎肯定弱收敛。最后,在传统的Markov链分析中运用鞅理论,证明这类计算智能方法在一定条件下几乎肯定强收敛。
(3)提出了一种用于复杂问题自适应优化且能有效克服停滞的云滴算法。本文基于云模型的特征,结合计算智能方法的基本原理,提出一种用于复杂问题自适应优化的云滴算法。该算法采用多维逆向云模型建立解集的特征参数,并根据是否出现当代精英和跨代精英自适应调整参数,再通过多维正向云模型产生新一代解集。云滴算法具有表示、再现和挖掘待优化问题的不确定知识的特点,无需预先设置其搜索策略和参数,且不论解集处于何种初始状态,整个系统能自适应地进行演化。然后借助于随机过程理论,在传统的Markov链分析中运用鞅理论,证明了云滴算法在一定条件下几乎肯定强收敛。最后通过两个标准测试问题的求解试验表明,与现有的四种算法相比,该算法不但收敛速度快,而且具有更好的自适应能力,能更有效地克服停滞现象的产生。
(4)提出了一类混沌系统未知参数辨识问题的解决方法。本文通过构造一个合适的评价函数,将混沌系统的未知参数辨识问题转换为一个多维的函数优化问题,然后利用滴算法对初始解集不敏感的优点和无需预先设置搜索策略和参数的特点,充分发挥其自适应搜索能力对混沌系统的未知参数进行辨识。以典型的Lorenz混沌系统和Chen混沌系统为例进行数值模拟,仿真结果表明,云滴优化算法能够有效克服停滞,快速对不同混沌系统的多个未知参数进行有效辨识,是一种简便易行的混沌系统参数辨识方法。
How to seek solutions of complicated optimization problems is a challenging research subject in recent years. In addition to traditional optimization methods, the computational intelligence approaches have been attractive in fundamental research and real applications. A class of computational intelligence approaches which is represented by the canonical forms of generic algorithms, ant colony optimization and particle swarm optimization is derived from the emulation of natural evolution or collective behavior of animals to seek solutions of complicated optimization problems by exploring and exploiting search spaces efficiently and effectively.
Stagnation is a crucial problem which is suffered by computational intelligence approaches when dealing with complicated optimization problems in the theory and application. On the one hand, it is related to how to set the structure and parameters of the existing computational intelligence methods to efficiently produce high-quality solutions. On the other hand, it involves how to design an effective and efficient computational intelligence method for solving complicated optimization problems.
This paper makes an investigation on the stagnation of a class of computational intelligence approaches, and the main contributions given in this dissertation are as follows.
(1) The influences of the diversification and the intensification of search strategies on the stagnation of solution set evolution are investigated. Through the analysis on the search characteristics of a class of computational intelligence approaches represented by the canonical forms of generic algorithms, ant colony optimization and particle swarm optimization, the concept of solution set diversity is introduced in this paper. And then two categories of fundamental search strategies, i.e. the diversification search and the intensification search, are defined in this paper on the basis of solution set diversity. Based on which the influences of the diversification and the intensification of search strategies on the stagnation of solution set evolution are investigated. Three popular swarm intelligent algorithms, i.e. the Canonical Generic Algorithm, the Ant Colony System and the Discrete Particle Swarm Optimization, are tested with a benchmark problem, and the results support the theoretical conclusions.
(2) The sufficient conditions are derived for the almost sure convergence of a universal model for a class of computational intelligence approaches. A universal model is built up in this paper for a class of computational intelligence approaches represented by the canonical forms of generic algorithms, ant colony optimization and particle swarm optimization in order to describe the common features of these algorithms. Two quantification indices, i.e., the variation rate and the progress rate, are defined respectively to estimate the variety and the optimality of the solution sets generated in the search process of the model. Four types of probabilistic convergence are given for the solution set updating sequences, and their relations are discussed. By introducing a martingale approach into the Markov chain analysis, the sufficient conditions are derived for the almost sure weak convergence and the almost sure strong convergence of the model.
(3) An adaptive cloud drops optimization algorithm is proposed for stagnation elimination. The feature parameters of solution sets are created by a multidimensional backward cloud model, and then adaptively adjusted based on the change of the elite solution candidates. The result is then used by a forward cloud model to produce the solution set of next generation. No any search parameters are predefined in the proposed algorithm, and, no matter what the initial solution set is, the whole system can adaptively approach to the global optimal solution. Based on the theory of stochastic processes, the almost sure convergence of the proposed algorithm is proved under certain conditions by introducing a martingale approach into traditional Markov Chain analysis. Two benchmark problems are tested with the proposed algorithm and the other four existing algorithms as a comparison. The results show that the proposed algorithm has faster convergence speed, better self-adaptability, and stronger ability to deal with stagnation phenomena effectively.
(4) The problem of unknown parameters identification for chaotic systems is addressed by the cloud drops optimization in this paper. Through establishing an appropriate evaluation function, the problem of unknown parameters identification in chaotic systems is formulated as a multi-dimensional optimization problem. And then, the cloud drops optimization algorithm, which is not sensitive to initial solution set and parameters less, is applied to obtain the original parameters of various chaotic systems. Numerical simulations on the typical Lorenz chaotic system and Chen chaotic system are conducted. Numerical simulation and comparisons with the other two existing algorithms demonstrate the effectiveness and feasibility of the proposed algorithm.
引文
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