一类控制与布局问题中的进化算法及应用

【作者】 宫召华；

【导师】 冯恩民；

【作者基本信息】 大连理工大学 ， 运筹学与控制论， 2004， 硕士

【摘要】 三维水平井井眼轨道设计和人造卫星仪器舱布局分别是非线性多阶段最优控制和带性能约束的布局优化问题。研究这两类问题的数值优化算法具有重大理论与应用价值，本文主要内容包括： 1．针对非线性多阶段最优控制(MOC)的特点提出了能够大大减小计算量的演化策略MOC(λ+μ)-ES；并对多峰的非线性多阶段最优控制，通过引进相似性定义，提出了MMOC(λ+μ)-ES。 2．对布局优化的不干涉约束，根据不干涉理论，构造了能够计算干涉量的不干涉算法；对带性能约束的布局优化问题提出改进的遗传算法(PLGA)，该算法在迭代过程中，不要求保证布局方案必定是可行的，只要对不可行的方案根据其干涉量，给一个罚值就可以了。 3．侧钻水平井控制技术和优化设计技术是水平井钻井技术的核心，将最优控制用于水平井井眼轨迹控制，并构造一种好的算法求解，会给水平井钻井技术带来重大的突破。本文对三维水平井井眼轨道设计最优控制系统讨论了系统的可控性；然后根据系统的特点，将MOC(λ+μ)-ES应用于三维水平井井眼设计，数值结果表明该系统是多峰的；然后，又将MMOC(λ+μ)-ES用于该动力系统，给出了相应的设计方案。 4．卫星舱布局问题为带性能约束的布局优化问题，是航天设计中亟待解决的问题，属拓扑优化范畴，为NP困难的。将所提出的PLGA算法应用于卫星舱布局优化，对图元分别是五个、六个的情况进行了计算，得到了较为满意的布局方案，并与已有的算法进行了比较。更多还原

【Abstract】 The 3D-trajectory of the horizontal well and the packing problem of the artificial satellite module belong to the nonlinear multistage optimal control and the layout optimization with performance constraints respectively. So it is valuable to study numerical optimization algorithms of the problems in both theory and application. The main results in the paper may be summarized as follows:1. An improved evolution strategy (MOC( - )-ES) is constructed in combination with the characteristics of the nonlinear multistage optimal control. The algorithm greatly cuts down the running time. Then the MMOC( + )-ES is constructed to solve the multimodal optimal control by the definition of the similarity.2. Based on the non-overlap theory, we provide the non-overlap algorithm to solve the non-overlap constraint, which can compute the overlap value. An improved genetic algorithm (PLGA) is constructed to solve the layout problem with performance constraints. In this algorithm, the layout projects are unnecessary to be feasible while iterating. We only need give a penalty value to the unfeasible project.3. The control technology and optimal design technology are the core of drilling the horizontal well. If we apply the optimal control into the control of the trajectory of the horizontal well and construct a satisfactory algorithm , a great breakthrough will be made in drilling the horizontal well. In this paper, we discuss the controllability of optimal control system of the 3D design of the horizontal well trajectory . Combining the characteristics of the system, we apply MOC( + )-ES to solve it. The numerical results show that the system is mutimodal. Then we apply the MMOC( + )-ES to solve the dynamic system and provide the design projects.4. The layout of the satellite module is the layout optimization with performance constraints. It is a topological optimization, and NP-hard. We apply PLGA constructed into it and compute them when the number of the rectangular elements is five, six. The satisfactory layout projects are obtained. At last we compare the results with those obtained by another existed algorithm.更多还原