【作者】 刘运源；

【导师】 梁述明；

【作者基本信息】 武汉科技大学 ， 控制理论与控制工程， 2008， 硕士

【摘要】 混沌是指在确定性系统中出现的一种貌似无规则的类似随机的现象。由于这个性质,使它可以被应用于科学的各个领域。近年来生物学家Cloe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的,显然混沌现象用Dorigo依据概率理论建立的蚁群优化模型是无法解释的。90年代初,学者Dorigo基于蚂蚁在食物源和蚁巢间可以形成一条最短路径的著名试验提出了蚁群最优化算法理论,并用它成功地解决了大量NP组合优化和路由器选择问题。混沌群体智能的这种复杂的动力学特性使它在信息处理和优化计算等方面有着广泛的应用前景。本文对混沌群体智能进行了深入的研究。首先系统的介绍了混沌动力学的基本理论,给出了混沌的概念和定性特征、Lyapunov指数、测度熵等,并列举了两种最为典型的混沌系统——Logistic映射和洛伦兹方程,进行了详细的分析。然后给出了群体智能网络模型,并利用连续型基本蚁群算法(AS)模型求解旅行商问题(TSP)。接着在此基础上给出了一种基于最大最小型的蚁群(MMAS)算法,并进行了重点研究。它将混沌机制引入网络,利用混沌的遍历性进行随机搜索,再由混沌动态退出和倒分岔出现,使MMAS逐渐趋于一般的AS。这样既避免了陷于局部极小,又加快了收敛速度,使网络能快速收敛到一个全局最优或近似最优的稳定平衡点。仿真结果表明,这是一种能有效解决局部极值问题的全局最优化算法。最后,本文又进行了仿真,结果表明,它具有更快的收敛速度。更多还原

【Abstract】 Chaotic system is a kind of determined system and at the same time it appears random phenomenon which looks like to have no rules. Because of this property, it can be used in each realm of science.Recently biologist Cloe find that the acts of a hole ants are regular, but one the act of one ant is chaotic. In the early 90s, based on the fact that ants can find a shortest way from foods to their holes, Dorigo invented ant colony algorithm, with this algorithm, he successfully solves a lot of choose completely NP problem. It comples characteristics make it possiblely for the network to be a technology with extensively application foreground for information processing and optimality calculation.A in-depth research is done to chaotic swarm intelligence in this pape. Firstly, it introduces the basic theories of the chaotic dynamics completely, gives the concept of chaos, the qualitative attribute, the Lyapunov index, the Kolmogorov entropy, and so on. And then it makes two examples, Logistic and Lorenz Equation, which are the most typical chaotic systems, and analyses them in detail.Secondly, it introduces the model of swarm intelligence, and uses the model of continuous ant colony algorithm to solve traveling salesman problem(TSP).Thirdly, it gets a kind of max-min chaotic ant colony algorithm, and Carries on the research carefully. It introduces chaos mechanism into the system, and then applies chaotic ergodicity to stochastic search and controls the chaotic dynamics by annealing strategy to perform inverse bifurcation and disappear. MMAS gradually approaches to AS and converges to a stable point which is globally optimal or near-optimal. Simulation result shows that it is a global optimization algorithm which can effectively avoid local minimal.Lastly, it simulations the system, the simulation result shows that it has more rapid convergenced speed than AS.更多还原