【作者】 郑蔚；

【导师】 戴光明；

【作者基本信息】 中国地质大学 ， 计算机应用技术， 2007， 硕士

【摘要】 近十几年来，演化算法已逐步发展成为解决多目标优化问题的理想方法，特别为求解大规模复杂的多目标优化问题提供了有效的研究方法，因而多目标优化问题已成为演化算法领域的研究热点。随着研究和应用的不断深入，实际求解问题的复杂性对算法的各种性能技术发展提出了新的挑战。因此如何进一步提高演化算法性能，以及在多目标优化领域，如何利用被传统演化算法忽略的Pareto解集的分布规则，如何保证算法在初始化时的种群就较好地分布在可行解域里，如何将有关的局部搜索策略和演化算法的全局搜索进行有效的结合，从而最终提高算法的求解质量，是本文研究的关键问题。此外在多目标算法应用领域，多目标演化算法的触角也早已延伸到航天航空的应用研究中了。在星座设计领域中由多颗卫星组成的卫星星座可以为广大地域范围提供通信服务，是地面通信网络的有益补充，对于军事活动以及政府、各行业部门具有重要的应用价值。而针对具体应用优化设计高效、合理的卫星星座配置方案，是星座优化的一个关键问题，同时星座优化本身是一个复杂的高维、动态、多目标问题，鉴于卫星星座覆盖性能和卫星各轨道要素间存在的复杂关系，传统优化设计方法无法兼顾各种在一定范围内相互矛盾的性能指标，因而在过去的近10年里，演化算法被引入到星座优化设计中，特别是近年来多目标演化算法在区域性星座优化设计中取得了较好的效果。但是传统多目标演化算法普遍存在求解效率不高，算法收敛性不强并且未利用Pareto解集分布规则等问题，那么如何改进现有多目标演化算法或提出新的多目标演化算法，并将其应用于星座优化设计来提高算法在求解此类复杂问题的性能是本文又一个关键问题。所有的这些研究也将拓展多目标演化算法及其在星座优化设计领域的应用研究。本文首先简要介绍了多目标演化算法的背景知识，然后针对演化算法在解决多目标优化问题时的不足，提出了一种新的模型演化多目标算法(OMEA)，以增强算法的鲁棒性和局部搜索能力。新算法在保持传统基于模型演化算法的具有较好收敛性等特性的同时，还具有如下一些特点：1)构造正交设计产生初始种群，使得个体能更具代表性地分布在可行解区域上：2)引入了概率模型的思想，通过建立Pareto解集分布规则的模型来进行“目的性”较强的局部搜索来完善算法在探索未知区域的能力；3)以k-means聚类分析代替传统基于模型演化算法(MMEA)中的的L-PCA聚类分析算法，使其算法在效率上得到提高。为了验证改进算法的性能，本文通过一些目前主流的、具有代表性的测试函数进行了数值实验，并与其他多目标演化算法的结果相比较，其结果表明，新算法OMEA无论在解的多样性方面还是解的收敛性方面都有较大改观，在多样性及收敛性之间达到了一个较好的平衡，避免了解过早收敛到局部Pareto解集。性能明显优于传统的多目标演化算法。在验证了改进算法的性能并对卫星星座的数学和物理模型及相关航天动力学知识介绍之后，在第四章，本文给出了基于演化算法的区域星座优化设计流程及其方案，并把第二章提出的新算法OMEA应用到两个中低轨区域覆盖星座的优化设计实例中，以测试新算法解决实际星座优化问题的性能，并与NSGA-Ⅱ、SPEA2和传统数学推导优化方法进行了结果比较。实验结果表明，该新算法方法在解的精度和收敛性方面要强于前面提到的几种方法，同时OMEA算法计算得到的各目标覆盖率均在99％以上，能较好满足区域持续覆盖的要求。这也验证了新算法在区域通信星座的设计问题中可以发挥良好作用，同时算法优化获得的Pareto解包含更多的可能性，从而具有更大的灵活性，决策者可以根据目标偏好或专家经验选择合适的星座类型进行星座设计。此外，本文对本课题所开发的星座优化设计的可视化平台进行了简要的介绍，该平台能对星座的空间三维位置、星下点轨迹和对地面站点的覆盖特性提供较为准确的评估，它对实际星座的优化设计工作具有一定的指导意义。本文的主要创新如下：1)提出了一种新的模型多目标演化算法；2)构造了基于演化算法的区域星座优化设计流程，并将新算法应用于星座优化设计领域；3)开发了一套星座优化设计可视化仿真平台，能对优化数据进行可视化仿真，并能对星座方案进行实时性能评价。本文的主要章节安排如下：第一章主要介绍了本文的研究背景、目的和意义，简单概括了求解多目标优化问题的传统方法和其优缺点，并简单综述了多目标演化算法和星座优化设计问题的发展历程。第二章首先介绍了多目标优化问题的基本概念、相关定义，然后介绍了当前主要的多目标演化算法和有待解决的问题，并针对演化算法在解决多目标优化问题时的未利用Pareto解集分布规则等问题，在引入概率模型思想和构造正交试验种群初始化、K-means，主成份分析法(PCA)的基础上，提出了一种新的模型多目标演化算法(OMEA)。同时利用当前主流的评价多目标算法性能的量化标准对模型多目标演化算法的性能进行了Benchmark问题的测试，并与其它经典多目标演化算法进行了性能对比。第三章重点对星座模型、航天动力学的基本理论和中低轨轨道摄动分析进行阐述，文末并对卫星覆盖性能的数值仿真评估方法进行了介绍。第四章先简要介绍了演化算法进行星座优化设计的流程，接着结合实例对两个中低轨区域星座优化设计问题进行了优化设计，并给出了性能评估。文末对本课题开发的到星座仿真软件进行了简要介绍。第五章对全文进行了归纳，概括了全文的主要工作和创新，提出了下一步研究工作和研究方向。更多还原

【Abstract】 In recent ten years, Evolution Algorithm has developed into an ideal approach to solve multi-objective optimization problems, especially the large-scale, complex ones. Thus multi-objective optimization problem has become the research hot point in the field of Evolutionary Algorithm.Further more, multi-objective evolutionary algorithm has been applied to the aerospace application. The constellation composed of multi-satellites can provide communication services for broad geographical scope, which is a useful supplement to terrestrial communication network. It is of great value to the military activities, the government, and various of industry segments. It is a key issue to design efficient and feasible constellation layout for an specific application. However, constellation itself is very complex. It is a multi-dimensional, dynamic, multi-objective problem. For the coverage performance of constellation is closely related to the orbital elements, traditional optimization methods can’t cater to the competing performance index. So in the past ten years, the evolutionary algorithm has been introduced to the constellation design. In particular, the multi-objective evolutionary algorithm has achieved better result in regional constellation design in recent years. However, there are some common disadvantages of traditional multi-objective evolutionary algorithm such as low efficiency, weak convergence, and not make use of distribution rule of pareto set. How to apply the improved or new multi-objective evolutionary algorithm to constellation design to improve the performance is another key issue of the paper. All the studies will also develop multi-objective evolutionary algorithm as well as its application in constellation design.The paper first presents background of multi-objective evolutionary algorithm. Then, for the deficiency of evolutionary algorithm in solving multi-objective optimization problem, OMEA is proposed to enhance the robustness and local search capability of the algorithm. Besides good convergence, the new algorithm based on the traditional model evolutionary algorithm has some new features. 1、generate initial population with orthogonal design so that the individuals make a more representative distribution of the feasible solutions.2、introduce the idea of probabilistic model, establish model based on pareto set distribution rule to enhance local search ability and then improve search performance of the algorithm.3, replace L-PCA cluster analysis algorithm in MMEA with k-means clustering analysis algorithm to improve efficiency of the algorithm. To test the performance of the improved algorithm, the paper does numerical experiments with some of the current representative functions, and does comparison to other multi-objective evolutionary algorithms. The results show that the new algorithm OMEA achieves much better performance in both diversity and convergence of the solutions, and avoids premature convergence to a local Pareto solution set. The performance is clearly superior to the traditional multi-objective evolutionary algorithms. After validating the improved algorithm and introducing the mathematical and physical models as well as related astrodynamics knowledge, Chapter 4 presents process and scheme of the regional constellation design based on evolutionary algorithm, and applies OMEA proposed forward to two instances of LEO/MEO regional constellation coverage to test the performance of OMEA for solving constellation optimization problem, and compares the result with NSGA-Ⅱand traditional mathematical derivation. The results show that accuracy and convergence of solutions of OMEA is superior to the other two methods. Each target coverage rate obtained by OMEA is above 99% which can better meet regional continuous coverage requirements. It proves OMEA can play a good role in regional communications constellation design. Further more, the Pareto set contains more possible solutions, thus OMEA has greater flexibility. So policy maker can select suitable constellation according to preferred target or experience. In addition, the paper gives a brief introduction to the visualization platform for constellation design. The platform provides accurate assessment to three-dimensional position of the constellation, footprint and coverage characteristics of ground sites. It is of great directive meaning to the practical optimal design of constellation.The main innovation is as follows: 1)propose a new model multi-objective evolutionary algorithm. 2)construct process of regional constellation optimal design based on evolutionary algorithm, and apply the new algorithm to constellation optimal design field. 3)develop a visualization platform for constellation design, which is able to do visualization simulation according to the optimal data and do evaluation of real-time performance to constellation scheme.The main sections are as follows:The first chapter introduces the background, the purpose and significance of the research, summarizes the traditional methods solving multi-objective optimization problem and their advantages and disadvantages, and gives a simple overview of development history of multi-objective evolutionary algorithm and constellation optimal design problem.The second chapter introduces the basic concepts and related definition of the multi-objective optimization problem at first. Then, introduces the current main multi-objective algorithm and the problems to be solved, and considering the evolutionary algorithm not make use of Pareto distribution rules, proposes a new model multi-objective evolutionary algorithm by importing idea of probabilistic model, orthogonal initialization, K-means and Principal component analysis(PCA).At last, tests the performance of OMEA with current popular benchmarks for multi-objective algorithm test, and compares OMEA with other classical multi-objective algorithms.The third chapter presents the constellation model, basic theory of aerospace dynamics and the LEO/MEO perturbation analysis. Finally, it introduces numerical simulation evaluation method of satellite coverage performance.The fourth chapter briefly describes process of constellation design with evolutionary algorithm, then designs two practical LEO/MEO regional constellation design and evaluates the performance. In the end, gives a brief presentation to the constellation simulation software.The fifth chapter summarizes the main work of the paper and describes the future work.更多还原