一种新的基于蚂蚁混沌行为的群智能优化算法及其应用研究

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1、附件6论文中英文摘要作者姓名：李丽香 论文题目：一种新的基于蚂蚁混沌行为的群智能优化算法及其应用研究作者简介：李丽香，女， 1978年6月出生，2003年9月师从于北京邮电大学杨义先教授，于2006年7月获博士学位。中 文 摘 要混沌是存在于非线性系统中的一种较为普遍的非线性现象，混沌并不是一片“混乱”，而是有着精致的内在结构的一类非线性现象。混沌的特性主要有伪随机性、遍历性和对初始条件的敏感性。由于遍历性可作为避免搜索过程陷入局部极小的有效机制，因此混沌理论已成为一种新颖且有潜力的优化工具。从20世纪90年代初开始，混沌优化的研究引起了人们极大的兴趣，并成为当前混沌理论研究的一个热点。90年

2、代初，受蚁群可在巢和食物源间建立最短路径的著名试验的启发，学者Marco Dorigo首先开创性地提出了著名的蚁群最优化算法，此后群智能理论研究迅速展开。由于群智能理论在生产计划与调度、商业运作、金融管理、电子技术、通讯、自动控制、光学、生物学等许多领域中具有巨大的应用潜力及发展前景，已经引起国内外学者的广泛关注，从而成为近期计算机、运筹学和智能控制等领域研究中的热点及前沿。现有的受蚂蚁种群行为启发而产生的优化算法，大多都是基于随机搜索机制的非确定性的概率理论发展而来的。但是近年来生物学家Cole发现整个蚁群行为是一种周期行为，然而单个蚂蚁的行为却是混沌行为。蚁群显然是具有智能的团队，这个团队

3、在不断地协作完成一个又一个任务，我们认为种群周期行为的产生正是蚂蚁由独自作业到自组织起来协作完成一个又一个任务的过程。从动力学的角度来说，显然单个蚂蚁的混沌行为和种群强大的自组织能力之间必然存在着某种内在的关系。这种关系是蚁群对周围生存环境适应性的一种自然选择，这些行为有利于蚂蚁的生存。然而混沌现象用Marco Dorigo依据概率理论建立的蚁群优化模型是无法解释的。单个蚂蚁的混沌行为与群体的自组织和蚁群捕食以及最短路径的建立之间是一种什么关系，这一点目前并没有引起国际群智能理论研究者广泛的关注。本文从全新的角度分析了蚂蚁外出捕食、在巢和食物源之间建立最短路径的过程。我们通过构造一个“巢食物源

4、巢”之间的映射关系，将蚂蚁的外出捕食过程和建立最短食物路径过程统一起来进行考虑。我们认为蚂蚁的外出捕食过程是一个混沌搜索的过程，最短食物路径的建立过程则是由混沌搜索逐渐过渡到暂态混沌直到收敛到最短食物路径的过程。也就是说，蚂蚁处于一个在信息素和混沌共同作用下的自组织过程，一个类似于混沌退火的过程。在整个过程中蚂蚁通过不断的分泌信息素来传递最好路径信息，并通过信息素形成自组织。本文的这个思想完全不同于Marco Dorigo的关于蚁群通过概率选择来建立最短路径的思想。受蚂蚁外出捕食和建立巢和食物源之间建立最短路径行为的启发，基于混沌搜索机理、自组织理论和群理论，我们创造性地构建了一个新的解决最优

5、化问题的数学模型。这个模型不但可以解释蚂蚁的混沌搜索行为（此时蚂蚁并没有被组织起来），而且可以解释群体建立最佳食物路径的过程。它是一个完全不同于Marco Dorigo的蚁群最优化算法的全新的群智能优化模型。这种模型可以用来表示一种新的在搜索空间中求解非线性函数的全局最优解或者次优解的启发式搜索算法，一个新的基于混沌、自组织和群体协作的群智能优化算法。本文主要创造性地构建了一个用来解决优化问题的新型群智能优化算法模型，即混沌蚁群优化模型，详细分析了这个模型的动力学行为，并对它进行了算法性能测试研究。为了进一步测试算法的有效性、可行性以及算法应用领域范围，本文还开展了混沌蚁群优化算法在参数辨识、

6、模糊系统设计、神经网络训练和PID控制器参数整定等方面的应用研究，并且取得了很好的效果，形成了一个新的关于群智能优化的理论方案。论文的主要研究内容如下：（1）经过对混沌理论和群智能理论的深入探讨，综合了混沌优化和群智能优化的优点，创造性地提出了一个新的现代启发式智能优化算法模型，即混沌蚁群优化算法模型。系统地分析了混沌蚁群优化算法模型的非线性动力学行为，讨论了蚂蚁邻居间的信息交换方式。为了检验所给出新算法的性能，进行了大量的测试工作。首先用多模态函数进行算法性能测试，并和免疫系统优化算法进行了比较；然后，采用标准的高维测试函数进行了测试研究，并且在相同条件下与粒子群和凯尔曼群的算法性能测试的结

7、果相比较；最后，利用有约束的测试函数进行了测试。所有这些测试结果都表明混沌蚁群优化算法可以很好地进行优化搜索。同时对混沌蚁群算法、其它混沌优化算法、蚁群算法和粒子群算法进行了对比分析。（2）基于混沌蚁群算法具有的全局优化搜索能力，提出了采用混沌蚂蚁群算法对动力学系统进行参数估计，给出了利用混沌蚁群算法进行动力学系统参数辨识的具体过程。并且在迭加测量噪声的情况下，利用混沌蚁群算法辨识动力学系统的未知参数，研究了代价函数、观测序列的长度与算法的搜索性能之间的关系，为了进一步说明所给方法的有效性和可行性，对Logistic映射和Lorenz混沌系统也进行了未知参数辨识研究，并且给出了相应的参数辨识结

8、果。（3）从模糊系统的万能逼近特性出发，通过设置合适的适值，模糊系统的设计问题转化为可采用混沌蚁群算法来处理的模糊系统参数优化问题，从而我们提出了采用混沌蚁群算法设计模糊系统，给出了利用混沌蚁群算法设计模糊系统的具体步骤，并成功地应用所设计的CAS-Fuzzy系统进行了非线性系统辨识、时间序列预测和非线性自适应控制。（4）由于混沌蚂蚁群算法具有较强的全局搜索能力，同时具有较高的精度、模型简单、计算复杂度低、不易陷入局部最优解等优点，本文提出了利用混沌蚁群算法训练神经网络的新方案，并将设计好的神经网络应用于解决函数逼近问题。结果表明，混沌蚂蚁群算法设计的神经网络确实具有下述优点：不易陷入局部最优

9、、具有较强的避免在局部区域搜索过程中的收敛停滞现象的能力、训练结果精度较高、在随机扰动或测量噪声存在的情况下，仍然可以达到较好的训练效果。（5）采用混沌蚂蚁群算法对PID控制器的参数进行整定，以误差积分型性能指标为目标函数、以设计参数的取值范围及最小增益相位裕度为约束条件建立了数学模型。最后给出两个数值实例并进行了对比分析，数值仿真结果表明，我们的方法能够较好地进行控制器的参数整定。综上所述，本文提出的混沌蚂蚁群优化算法具有明晰的物理意义、模型简单、易于工程人员理解、不仅在理论上值得深入研究，而且还具有较好的工程应用价值。关键词： 混沌优化 蚁群算法 参数辨识 神经网络 模糊系统 群智能An

10、optimization method inspired by“chaotic” ant behavior and its applicationsLi LixiangABSTRACTChaos is a general nonlinear phenomenon that lies in the nonlinear system. Chaos is not a mess of “disorder”, but a class of nonlinear phenomenon that has exquisite intrinsic structure. Chaos has the followin

11、g main characteristics: quasi-randomness; ergodicity; sensitive dependence on initial conditions. Since ergodicity is an effective mechanism to avoid trapping into local minima in the searching process, chaos has been a novel and potential optimization tool. Since 1990s, the research of chaos optimi

12、zation has attracted significant interests and it has become the hotspots of recent research on chaos theory.In the early 1990s, inspired by the well-known experiment of founding the shortest route between nest and food source, famous scholar Marco Dorigo first proposed the well-known ant colony opt

13、imization algorithm. From then on, the research of swarm intelligence theory rapidly extended. The swarm intelligence theory has attracted wide attentions from international and inland scholars. It has become the hotspots and frontal problems due to its potential developments and applications in man

14、y areas of science and technology such as manufacture arrangement and scheduling, business operation, finance administration, electronics, communication, automatic control, optics, biology.Much of the existing developed ant-inspired optimization algorithms are based on the random metaheuristic of no

15、n-deterministic probability theory. However, it has been discovered by biologist Cole that an ant colony exhibits a periodic behavior, while single ants show chaotic activity patterns. The ant colony has intelligent team which continually accomplished tasks. We believe that the existence of colony p

16、eriodic behavior is the process that individual ants works and then they present the self-organization behavior and corporate to finish complex tasks. From the aspect of dynamics, it is evident that the chaotic behavior of individual ant must have inherent relations with the strong self-organization

17、 ability of ant colony. The relations are adaptations to the surrounding environment. These behaviors are very important for the ant to survive. However, the ant colony optimization model that was founded by Marco Dorigo based on probability theory could not explain the chaotic phenomenon. And the p

18、roblem of how the chaotic behavior of single ant relates to the self-organizing and foraging behaviors of ant colony has received little concerns.From a novel aspect, this thesis analyzes the process that ant go out for foraging, build the nest and found the shortest route. We construct a map relati

19、on between nest, food source and nest and consider the process of the ants foraging and the process of chaotic search as a whole. And we believe that the process of the ants foraging as that of chaotic search. The building of shortest food route is the process that chaotic search continually transfo

20、rms into the transient chaos until the process converges the shortest food route. That is to say, the ant is in the self-organization process under the pheromone trails and chaos. It is similar to the process of chaos annealing. In the whole process, ants transfer the best trail information through

21、emitting pheromone continually and form the self-organization through pheromone. The above idea is different from that of Marco Dorigo, that is, the ants build the shortest trail by probability.Inspired by the behaviors of ants foraging and building the shortest trail between nest and food source an

22、d based on chaos search mechanism, self-organization theory and swarm theory, we construct a new mathematical model in a creative way in order to solve the optimization problems. The model not only can explain the chaotic search behavior of ants (at this time the ant does not been organized), but al

23、so can explain the process that ant build the best food source. It is a novel swarm intelligence optimization model that is different from Marco Dorigos ant colony optimization algorithm. This model can be used to implement a metaheuristic for the search of a global optimum or near optimum of a nonl

24、inear function in a search space. It is a new swarm intelligence optimization algorithm based on chaos, self-organization and swarm cooperation.The thesis mainly constructs a new optimization model of swarm intelligence algorithm, called the chaotic ant swarm optimization model, to solve the optimiz

25、ation problems. The thesis analyzes the nonlinear dynamical behavior in detail and research on the performance testing of the proposed algorithm. In order to verify the feasibility, effectiveness and the application fields of the proposed algorithm, further, the thesis deals with the chaotic ant swa

26、rm algorithm and its application in parameter estimation, fuzzy system design, neural network training and PID controller parameter tuning and attained many good results. Thus, the new scheme of swarm intelligence optimization is formed.The main work and contributions of the present thesis are as fo

27、llows:（1）Through the deep discussion and research on the chaos theory and swarm intelligence theory, we integrate the virtues of chaos optimization and swarm intelligence optimization and proposed a new modern heuristic intelligent optimization algorithm model, called chaotic ant swarm algorithm mod

28、el in a creative way. The nonlinear dynamical behavior of the chaotic ant swarm algorithm model is systematic analyzed. The way of information between neighbors of ants is discussed. In order to verify the performance of the new algorithm, we do a lot of work for the performance testing of the propo

29、sed algorithm. Firstly, we tested the performance of the proposed algorithm using the multi-model functions and the corresponding results are compared with immune system optimization algorithm; Then, we tested the performance of the proposed algorithm using the standard high-dimensional testing func

30、tions and compared the simulation results with particle swarm and Kalman swarm under same conditions; Finally, we tested the performance of the proposed algorithm using the constrained optimization function. All of the testing results show that the chaotic ant swarm optimization model could search w

31、ell. Further, we discuss and compare the chaotic ant swarm algorithm, other chaos optimization algorithm, ant algorithm and particle swarm.（2）Based on the global optimization search ability of chaotic ant swarm, we apply the chaotic ant swarm algorithm to estimate the dynamical system. The detailed

32、process of CAS based parameter estimation is given in this thesis. Under the circumstance that the measurable noise exists, we use the chaotic ant swarm algorithm to identify the unknown parameters of dynamical systems and research on the relations between cost function, the length of measurable ser

33、ies and the performance of algorithm. Further, in order to verify the effectiveness and feasibility of the proposed method, we research on the parameter estimation for the Logistic map and Lorenz chaotic system and give the corresponding results of parameter identification.（3）Begin from the omnipote

34、nt approaching characteristic of fuzzy system and set suitable fitness function, the design problem of fuzzy system is converted to that of fuzzy system parameter optimization and could be solved by the chaotic ant swarm algorithm. Thus we propose the scheme of using chaotic ant swarm algorithm to d

35、esign the fuzzy system. The basic step of the CAS-designed fuzzy system is developed. The designed CAS-fuzzy system was successfully applied into the nonlinear system identification, the time series forecasting and the nonlinear adaptive control.（4）Since the chaotic ant swarm has the virtues of glob

36、al optimization search, higher precision, model simplicity, the low complication degree, hardness to trap into the local optimum, we proposed the new scheme of using the chaotic ant swarm algorithm to train the neural network and applied the CAS-designed neural network into the problems of function

37、approaching and sorting. The research results show that the CAS-designed neural network is hard to trap into the local optimum, has strong ability of avoiding the converging stagnation phenomenon. The precise of the trained results are high. Under the condition that measurable noise or random distur

38、bance, the CAS-designed neural network could achieve better training results.（5）The proposed chaotic ant algorithm is used for the parameters tuning of PID controller. For the constructed optimization model, the objective function is the performance index of error integrality and the constrained con

39、ditions are the range of the designing parameter, the least gain and phase margin. The two numerical results are shown and the comparison analyses are given. The numerical results show the proposed method could tune the parameter of PID controller very well.Taken as a collection, the proposed chaoti

40、c ant swarm optimization algorithm has transparent physical meanings, model simplicity, and easiness to be understood by engineering persons. Not only does it deserve deep research in theory, but also does it have better application values for engineering.Key words: Chaos optimization, ant algorithm, parameter identification, neural network, fuzzy system, swarm intelligence