摘要
随着现代科技的发展,现有的确定论方法在许多的研究领域遇到了无法克服的困难,传统的经典数学规划模型不能处理所有的决策问题。不确定规划是不确定环境下的优化理论与方法,为随机、模糊、粗糙以及多重不确定环境下的优化问题提供统一的理论基础。不确定规划的理论研究已成了十分热门的课题,在电子技术、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。
鉴于不确定规划模型的复杂性,为适应大规模不确定规划问题的求解需要,有必要在算法设计方面作进一步的改善或进行新的尝试,例如设计有效和强大的新型群体智能算法。群体智能算法中许多简单个体通过交互合作产生复杂的智能行为。群体智能技术具有重大意义和广阔前景,其发展和应用领域的不断扩大,为更加复杂的决策系统中的不确定规划提供了丰富的求解算法。本文完善和充实了群体智能理论及其在不确定规划中的应用研究,设计了新型群体智能算法来求解不确定规划模型,并运用于空间机器人随机故障容错规划。论文的主要研究工作和成果体现在:
(1)对群体智能算法的统一框架、收敛性、鲁棒性、生存分析等方面理论做了证明和分析。对群体智能算法统一框架的协作、自适应和竞争这三个基本环节进行数学化描述与解释;分别基于Markov链和基于图论两种方法证明群体智能算法的收敛性;分析群体智能算法的鲁棒性与灵敏度,把参数摄动作为特殊输入量以考虑参数摄动对算法性能的影响,采用统计学测度为比较不同策略提供均值和方差;首次将多元生存分析引入进化算法,为算法收敛过程建立了带伴随变量的参数生存模型,进行Kaplan-Meier生存分析计算期望生存时间和生存函数曲线,求解COX比例危险率回归模型,运用了数据统计分析软件SPSS分析了参数选择对早熟收敛的影响。
(2)设计了多种新型群体智能算法。借鉴人类社会学活动原理,提出了基于班级选举的动态递阶差分进化算法,根据班级选举这一社会行为模式,将差分进化算法分为组内选举、选举班长和小组重建三个阶段,引入多阶性和动态可变拓扑策略;根据病毒进化理论采用纵向和横向两层结构,将主群体的全局进化和病毒群体的局部进化动态结合,提出病毒感染差分进化算法;引入多元生存分析,设计了一种生存模糊自适应的蚁群算法,将生存模型、模糊控制与蚁群算法相结合,实现对种群规模的模糊自适应调控。
(3)不确定规划的假设检验群体智能计算。对于含不确定参数的不确定规划问题,在群体智能算法中引入假设检验在统计意义下进行有效的性能评估和比较,进而提高种群的整体质量并保证种群的分散性。对差分进化算法进行多级嵌套,提出基于班级选举的动态递阶差分进化算法。以不确定环境下具有多极小值的典型Benchmark函数优化问题为实例,验证了算法在不同的噪声强度因子、设计变量维度和小组规模下,都具有较好的搜索性能和鲁棒性。
(4)双重不确定规划的鲁棒群体智能计算。描述了模糊相关机会规划模型和随机模糊机会约束规划模型;设计了一种基于模糊模拟的蚁群优化算法,证明了该算法的收敛性,并估算期望收敛时间以分析该算法的收敛速度;提出了基于随机模糊模拟的病毒感染差分进化算法,分析了其收敛性;从不确定环境、参数敏感度、初值无关性、置信水平、抗噪声干扰等五个测度,分析讨论该算法处理不确定双重规划的鲁棒性。
(5)空间机器人随机故障容错轨迹规划。分析了两自由度和六自由度空间机器人的系统不确定性,基于微分变换法,分析关节参数如杆长与关节角度的误差对轨迹精度的影响;建立了6自由度空间机器人故障容错轨迹规划的随机数学模型,以加权最小驱动力矩为优化性能指标,涉及故障前后运动学与动力学约束限制;用生存自适应的蚁群算法求解故障前后的最优轨迹,保证机械臂在发生故障后能够继续完成后续的操作任务,并应用机械系统动力学分析软件和虚拟样机分析开发工具ADAMS,联合仿真验证。
综上所述,本文为不确定规划提出了群体智能计算的理论与方法,具有科学性和有效性,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。
With the development of modern technology, the existing deterministic methods have encountered troublesome difficulties in many research areas. Many important decision problems can not be solved effectively by traditional mathematical programming models. Uncertain programming, as the theory and methodology of optimization under uncertain environment, provides a unified theoretic foundation for optimization problems under all kinds of uncertainties such as random, fuzzy, rough, birandom and fuzzy random environment. Research on the theory of uncertain programming has become the hotspots and frontal problems due to its potential developments and applicabilities in many areas of science and technology, such as electronics, communication, automatic control, optics and biology.
To satisfy the need of solving uncertain programming model of large scale, it is necessary to make further improvement and new attempt on algorithm designing in the light of its complication, such as designing effective and powerful new swarm intelligence algorithms. In swarm intelligence complex goups and intelligent behave can emerge through interaction and cooperation among individuals.Swarm intelligence has great significance, both theoretically and practically, which provide powerful computational tools to solve diverse complex uncertain programming problems in many decision systems. This thesis devotes to the improvement and enlargement of the theory of swarm intelligence with applications to uncertain programming. Several novel swarm intelligence algorithms are designed and applied to solve uncertain programming problems, especially to random fault tolerant trajectory planning of space manipulator. The main research work and contributions of the present thesis are as follows:
(1) The theory of swarm intelligence such as unified framework, convergence, robustness and survival analysis are proved and analyzed. Three basic courses of the uniform framework of swarm intelligence algorithms, that is, cooperation, adaptation and competition, are mathematically described and explained. The convenience of swarm intelligence is proved based on Markov chain and gragh theory, respectively. The robustness and sensitivity of swarm intelligence algorithms are analyzed. The disturbance of parameters is considered as a special input to test its influence on the performance of algorithms. The statistics measurement is used to provide mean value and variance for comparing different strategies. Multivariate survival analysis is for the first time introduced into evolutionary algorithm. Parametric survival model with concomitant variables is built up for the convergence process of ant colony optimization algorithm. Kaplan-Meier survival analysis method is used to compute the estimated survival time and survival function curve. The regression model of COX proportional danger rate is solved. The data statistics and analysis softerware, SPSS is used to analyze the influence of parameter choice on premature convergence.
(2) Several novel swarm intelligence algorithms are proposed. Inspired by the principle of human social activity, dynamic multi-level differential evolution algorithm based on group election is proposed. Based on the complex social behaviour model of western political leader election, differential evolution algorithm integrating multiple level and dynamic changeable topology strategy is made up of the following three stages: election within the group, representative election and group rebuilding. Based on virus evolution theory, virus evolutionary differential evolution algorithm with transverse orientation and longitudinal orientation two layer structure is proposed through dynamically integrating global evolution of the main population and local evolution of the virus population. With multivariate survival analysis for the first time introduced into evolutionary algorithm, an ant colony optimization algorithm is proposed. Population size and the survival time of invidiuals are adjusted by a fuzzy adaptive controller through intergrating survival analysis, fuzzy control and ant colont optimization algorithm.
(3) Swarm intelligence computation based on hypothesis test for uncertain programming. For uncertain programming with non-deterministic parameters, through integrating hypothesis test into swarm intelligence, effective performance evaluation and comparison can be done from the aspect of statistics, so as to improve the whole quality of population and guaranty the dispersion of population. Dynamic multi-level differential evolution algorithm based on group election is proposed by nesting multilayer differential evolution. Typical benchmark function optimization problems with multiple minima under uncertain environment are taken as experimental examples to validate the robustness of the proposed algorithm and its good performance of searching under different noise strength factor, the dimension of independent variable and scale of the group.
(4) Robust swarm intelligence algorithm for double uncertain programming. Fuzzy dependence chance programming model and random fuzzy chance constrained programming model are built. An ant colony optimization algorithm based on fuzzy simulation is designed. A proof of its convergence is given and its convergence speed is analyzed through evaluating the expected time needed for convergence. Virus evolutionary differential evolution algorithm based on random fuzzy simulation is developed and its convergence is analyzed. The robustness of the proposed algorithm for dealing with double uncertain programming is discussed from the following five aspects: uncertain environment, parameter sensitivity, initial value independence, confidence level and noise disturbance resistance.
(5) Random fault tolerant trajectory planning of space manipulator. The uncertainty of 6 D.O.F. space robot and 2 D.O.F. space robot systems is analyzed. The influence of joint parameters on trajectory precision such as errors of link length and joint angle is discussed based on the differential transformation method. A stochastic mathematical model of fault tolerant trajectory planning of a 6 D.O.F. space manipulator with both kinematical and dynamical restrictions before and after joint failures taken into account is built with minimal weighted driven torque as the objective of performance optimization. The optimal trajectory of the manipulator all along the work time before and after its joint failure is computed by ant colony optimization with fuzzy adaptive surviva, to guarantee that the manipulator has high manipulability after joint failure to accomplish its successive operational task continually. ADAMS, that is, the mechanical system dynamics analysis software and virtual prototype analysis development tool, is used in the simulation experiments.
Taken as a collection, the proposed theoretics and method of swarm intelligence algorithm for uncertain programming has scientific significance and validity. Not only does it deserve deep research in theory, but also does it have better application values for engineering.
引文
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