基于分布估计的人机结合演化设计方法研究
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摘要
卫星舱空间布局设计对缩短卫星设计周期、节约成本、提高性能等方面有着重要作用,是卫星总体设计的关键技术之一。该问题在数学上属于混合(离散与连续)组合最优化问题和NP-难(NP-hard)或NP-完全(NP-complete)问题,在工程上属于方案设计和复杂工程系统问题,其求解面临的主要困难是既要解决数学上的组合爆炸问题,又要解决工程系统复杂性问题。
本论文以委托项目“航天器布局优化设计平台研究与开发”为应用背景,在国家自然科学基金资助下,研究该类布局空间结构本质,研究统计学习技术以及人机结合设计策略在演化计算中的应用,用于一类以改善卫星舱质量特性为目标的空间布局设计问题的求解。
本文主要工作包括以下几个方面:
1.给出一种基于主元分析(Principle Components Analysis,简称PCA)的分布估计算法(PCA-EDA)。分布估计算法(Estimation of Distribution Algorithms,简称EDAs)是一类比较新的演化算法,用以解决遗传算法求解变量耦合问题时算法运行效率不高的问题。PCA-EDA算法将主元分析的变量相关性分析功能与高斯分布概率模型相结合,在获得概率模型的学习精度与效率的相对平衡的同时,实现了设计变量间内在关联关系的学习及演化,可有效解决变量耦合问题:同时提出自适应控制主元变量的方差收敛的机制,解决分布估计算法的早熟问题。函数优化算例及布局仿真实验表明,PCA-EDA算法求解性能优于遗传算法及常规分布估计算法。
2.给出一种多阶段贪心聚类机制,用于PCA-EDA算法,利用贪心期望最大化算法实现解群体自适应的聚类操作,实现算法对问题解空间的空间结构分析,以有效改进PCA-EDA算法对复杂布局问题的综合求解性能。本文对装填布局问题的空间结构进行了分析,指出其具有的一些复杂特点。在此基础上,提出利用高斯混合模型(GaussianMixture Model,简称GMM),将基于聚类的空间结构分析技术引入到PCA-EDA算法中,具有三方面的作用:(1)实现解空间的分解,将高性能解聚集的区域更精确地提取出来,这对于设计者深入了解设计问题,对于提高算法求解的效率都有明显的促进作用:(2)用多个高斯分布来更精确地逼近多峰值解空间,使基于单高斯分布的线性EDA算法非线性化,更适合求解具有复杂空间结构的设计问题;(3)本质上实现了一种具有多个独立群体的演化算法,有助于保持群体多样化。
3.给出一种针对PCA-EDA算法的人机结合策略,最终形成基于分布估计的人机结合演化设计方法。本文从设计知识提取的层面,深入分析了PCA-EDA算法的内在运行机制,实现利用变量相关关系的学习将原问题分解为若干子问题,并分析了主元变量方差与载入系数矩阵在原始变量相关性分析中的应用,以及变量相关性与搜索空间的形态之间的关系。通过对布局仿真实验的求解表明,应用该策略可使设计者能以更有效的方式将设计思想传递给算法。此外,为解决人机结合过程中如何有效获取关键信息的问题,在对可视化技术以及演化算法可视化进行综述的基础上,本文从构成演化算法结构要素特征的可视化以及问题的解空间结构可视化两个方面,提出几种新的演化算法可视化交互界面,用于人机结合演化设计方法的多层面多角度可视化。
综上所述,本文分别从变量相关性分析,可视化及定性与定量分析相结合、解空间结构分析三个方面展开研究,并结合演化计算的特点,充分利用概率统计及机器学习领域中相关技术,使三方面的研究内容既能各有侧重,又能有机统一,最终实现一种基于分布估计的人机结合的演化设计方法。通过对返回式卫星舱和通讯卫星舱的布局优化设计的实例验证,验证了本文方法的可行性和有效性。本文工作期望在理论上可有助于机器学习与演化算法相结合研究,以及人机结合演化设计和航天器布局设计理论研究进展,在实践上可有助于一类航天器布局设计问题的求解,并可望推广应用于其它复杂布局设计问题。
The layout design of satellite module is one of the key issues in the global design of satellite,which has an important impact upon reducing the design period,saving the cost,improving the performance for the satellite.It is known as a hybrid combinatorial optimization and NP-hard problem in mathematics,and a scheme design and complex system problem in engineering.There exist two primary challenges in the layout problem, which are the combinatorial explosion in mathematics and the complexity in engineering system.
A project of Research and Development of a Software Platform for Layout Design of Spacecraft from a research institute of China Aerospace Science and Technology corporation (CAST) is taken as a background.The work aims to improve the global mass properties of a satellite by adjusting the locations and orientations of given components. Moreover,it is supported by the National Nature Science Foundation of China.
The main contributions of this work are as follows.
1.A new PCA-EDA algorithm which combines Principle Component Analysis(PCA), a classical statistical technique,and Gaussian probabilistic model is given.EDAs are population-based search algorithms based on probabilistic modeling of promising solutions in combination with the simulation of the induced models to guide their searching. The probability factorization can be employed to encode the conditional(in)dependencies among different variables and overcome the linkage problem.But there are still some problems such as premature convergence and complex model learning which limit the class of problems that EDAs can solve reliably and efficiently.PCA-EDA is aimed to keep the balance of accuracy and efficiency of model learning,as well as to avoid premature convergence by easy variance control.
2.The thesis explores the landscape of packing problem and supposes that it is characterized as the complex mixture of big-valley and symmetry structure.It has been shown that for any optimization algorithm to be successful when solving a certain problem, the structure of the problem needs to match the bias of the algorithm.So it is necessary to introduce landscape analysis method based clustering into PCA-EDA.Caussian Mixture Model(GMM) is used in the work which would improve the algorithm in three ways:(1) splitting the solution space and extracting the high performance region to help user to understand the problem and make the algorithm more efficient;(2) modeling the complex landscape of packing problem more accurately than single peak probabihty distribution; (3) equivalent to a EA with multiple populations that is help to keep diversity.To make the fusion of GMM and PCA-EDA more effectively,the thesis presents a multi-stage greedy clustering strategy inspired by the similarity of working manners of EA and Greedy EM.
3.PCA-EDA's inner working way is analyzed from the point of view of design knowledge extraction.The design knowledge inducted by PCA-EDA is the variable correlation model which can be used to decompose the large-scale layout design problem into individual sub-problems in order to help designer to understand how the algorithm work.Then the relations between the variances of principle components,the correlation of original variables and the structure of landscape of the problem are studied in order to provide a more effective interaction manner from human to computer.Moreover,to help designers to capture key information during Human Computer Cooperation,four new interactive interfaces are presented after the survey of the state of software visualization for EAs. These interfaces can be used to gain insight into the state and the course of the algorithm and the landscape of the problem,which impact the performance of HCC heavily.
Summarizing,the work focuses on variable correlation,visualizing and cooperation of qualitative analysis and quantitative analysis,and landscape structure.By considering and utilizing the characteristics of the EAs and the layout problem,the three aspects of the strategy of layout problem solving are unified closely to construct a human computer cooperative evolutionary design based on statistical learning techniques,e.g.distribution estimation.From the results of numerical experiments for the satellite module it is showed that the proposed method is feasible and effective for the layout design of satellite module. This work is expected to advance the theories of HCC evolutionary design for the complex system and layout design for satellite module in theory,and is also likely to benefit the research and development of practical methods and techniques for a layout design problem of satellite module.Finally,the main contributions of this research are likely to be applied to other complex layout problems.
本论文以委托项目“航天器布局优化设计平台研究与开发”为应用背景,在国家自然科学基金资助下,研究该类布局空间结构本质,研究统计学习技术以及人机结合设计策略在演化计算中的应用,用于一类以改善卫星舱质量特性为目标的空间布局设计问题的求解。
本文主要工作包括以下几个方面:
1.给出一种基于主元分析(Principle Components Analysis,简称PCA)的分布估计算法(PCA-EDA)。分布估计算法(Estimation of Distribution Algorithms,简称EDAs)是一类比较新的演化算法,用以解决遗传算法求解变量耦合问题时算法运行效率不高的问题。PCA-EDA算法将主元分析的变量相关性分析功能与高斯分布概率模型相结合,在获得概率模型的学习精度与效率的相对平衡的同时,实现了设计变量间内在关联关系的学习及演化,可有效解决变量耦合问题:同时提出自适应控制主元变量的方差收敛的机制,解决分布估计算法的早熟问题。函数优化算例及布局仿真实验表明,PCA-EDA算法求解性能优于遗传算法及常规分布估计算法。
2.给出一种多阶段贪心聚类机制,用于PCA-EDA算法,利用贪心期望最大化算法实现解群体自适应的聚类操作,实现算法对问题解空间的空间结构分析,以有效改进PCA-EDA算法对复杂布局问题的综合求解性能。本文对装填布局问题的空间结构进行了分析,指出其具有的一些复杂特点。在此基础上,提出利用高斯混合模型(GaussianMixture Model,简称GMM),将基于聚类的空间结构分析技术引入到PCA-EDA算法中,具有三方面的作用:(1)实现解空间的分解,将高性能解聚集的区域更精确地提取出来,这对于设计者深入了解设计问题,对于提高算法求解的效率都有明显的促进作用:(2)用多个高斯分布来更精确地逼近多峰值解空间,使基于单高斯分布的线性EDA算法非线性化,更适合求解具有复杂空间结构的设计问题;(3)本质上实现了一种具有多个独立群体的演化算法,有助于保持群体多样化。
3.给出一种针对PCA-EDA算法的人机结合策略,最终形成基于分布估计的人机结合演化设计方法。本文从设计知识提取的层面,深入分析了PCA-EDA算法的内在运行机制,实现利用变量相关关系的学习将原问题分解为若干子问题,并分析了主元变量方差与载入系数矩阵在原始变量相关性分析中的应用,以及变量相关性与搜索空间的形态之间的关系。通过对布局仿真实验的求解表明,应用该策略可使设计者能以更有效的方式将设计思想传递给算法。此外,为解决人机结合过程中如何有效获取关键信息的问题,在对可视化技术以及演化算法可视化进行综述的基础上,本文从构成演化算法结构要素特征的可视化以及问题的解空间结构可视化两个方面,提出几种新的演化算法可视化交互界面,用于人机结合演化设计方法的多层面多角度可视化。
综上所述,本文分别从变量相关性分析,可视化及定性与定量分析相结合、解空间结构分析三个方面展开研究,并结合演化计算的特点,充分利用概率统计及机器学习领域中相关技术,使三方面的研究内容既能各有侧重,又能有机统一,最终实现一种基于分布估计的人机结合的演化设计方法。通过对返回式卫星舱和通讯卫星舱的布局优化设计的实例验证,验证了本文方法的可行性和有效性。本文工作期望在理论上可有助于机器学习与演化算法相结合研究,以及人机结合演化设计和航天器布局设计理论研究进展,在实践上可有助于一类航天器布局设计问题的求解,并可望推广应用于其它复杂布局设计问题。
The layout design of satellite module is one of the key issues in the global design of satellite,which has an important impact upon reducing the design period,saving the cost,improving the performance for the satellite.It is known as a hybrid combinatorial optimization and NP-hard problem in mathematics,and a scheme design and complex system problem in engineering.There exist two primary challenges in the layout problem, which are the combinatorial explosion in mathematics and the complexity in engineering system.
A project of Research and Development of a Software Platform for Layout Design of Spacecraft from a research institute of China Aerospace Science and Technology corporation (CAST) is taken as a background.The work aims to improve the global mass properties of a satellite by adjusting the locations and orientations of given components. Moreover,it is supported by the National Nature Science Foundation of China.
The main contributions of this work are as follows.
1.A new PCA-EDA algorithm which combines Principle Component Analysis(PCA), a classical statistical technique,and Gaussian probabilistic model is given.EDAs are population-based search algorithms based on probabilistic modeling of promising solutions in combination with the simulation of the induced models to guide their searching. The probability factorization can be employed to encode the conditional(in)dependencies among different variables and overcome the linkage problem.But there are still some problems such as premature convergence and complex model learning which limit the class of problems that EDAs can solve reliably and efficiently.PCA-EDA is aimed to keep the balance of accuracy and efficiency of model learning,as well as to avoid premature convergence by easy variance control.
2.The thesis explores the landscape of packing problem and supposes that it is characterized as the complex mixture of big-valley and symmetry structure.It has been shown that for any optimization algorithm to be successful when solving a certain problem, the structure of the problem needs to match the bias of the algorithm.So it is necessary to introduce landscape analysis method based clustering into PCA-EDA.Caussian Mixture Model(GMM) is used in the work which would improve the algorithm in three ways:(1) splitting the solution space and extracting the high performance region to help user to understand the problem and make the algorithm more efficient;(2) modeling the complex landscape of packing problem more accurately than single peak probabihty distribution; (3) equivalent to a EA with multiple populations that is help to keep diversity.To make the fusion of GMM and PCA-EDA more effectively,the thesis presents a multi-stage greedy clustering strategy inspired by the similarity of working manners of EA and Greedy EM.
3.PCA-EDA's inner working way is analyzed from the point of view of design knowledge extraction.The design knowledge inducted by PCA-EDA is the variable correlation model which can be used to decompose the large-scale layout design problem into individual sub-problems in order to help designer to understand how the algorithm work.Then the relations between the variances of principle components,the correlation of original variables and the structure of landscape of the problem are studied in order to provide a more effective interaction manner from human to computer.Moreover,to help designers to capture key information during Human Computer Cooperation,four new interactive interfaces are presented after the survey of the state of software visualization for EAs. These interfaces can be used to gain insight into the state and the course of the algorithm and the landscape of the problem,which impact the performance of HCC heavily.
Summarizing,the work focuses on variable correlation,visualizing and cooperation of qualitative analysis and quantitative analysis,and landscape structure.By considering and utilizing the characteristics of the EAs and the layout problem,the three aspects of the strategy of layout problem solving are unified closely to construct a human computer cooperative evolutionary design based on statistical learning techniques,e.g.distribution estimation.From the results of numerical experiments for the satellite module it is showed that the proposed method is feasible and effective for the layout design of satellite module. This work is expected to advance the theories of HCC evolutionary design for the complex system and layout design for satellite module in theory,and is also likely to benefit the research and development of practical methods and techniques for a layout design problem of satellite module.Finally,the main contributions of this research are likely to be applied to other complex layout problems.
引文
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