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直接优化方法在核电厂堆芯换料中的可行性研究报告DOC

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换料方案的选择直接关系到核电厂运行的安全性和经济性,它是 一个非常复杂的优化问题,至今仍未得到解决。本文将采用直接优化 方法来解决核电厂换料优化问题。和其他优化方法不同,直接优化方 法直接利用描述中子物理行为的数学方程来建立优化模型,模型求解 过程中换料方案的搜索和评价同时进行。 本文以一维平板燃料排列问题和三批料二维堆芯换料问题为对 象,对直接优化方法在核电厂换料优化中的可行性进行了研究。 首先,分别利用 1D 1G 中子扩散方程和 HHLP 方法,建立了一 维平板燃料排列问题和批料二回路堆芯换料问题的混合整数非线性 规划模型;通过利用优化软件 LINGO 对该非线性模型进行求解,发 现非线性模型只能获得局部最优解,不能搜索到全局解; 然后,本文在一维问题的非线性模型基础上,尝试了三种混合整 数线性化模型:基于 eff K 二进制离散的精确线性化模型、基于基础方 案的近似线性化模型及基于分步搜索的线性化模型。通过优化软件 LINGO 和 ILOG CPLEX 的求解,发现基于分步搜索的线性化模型具 有快速、精确搜索最优解的能力; 接着,基于一维问题上建立的分步搜索线性化模型的思想及 HHLP 方法的特点,建立了二维问题的线性化模型。利用 ILOGII CPLEX 求解器对该模型进行了求解。结果表明,在给定的 Keff 搜索 范围内,该模型同样能精确搜索到最优解,但计算非常耗时。 最后,为解决速度问题,本文进行了多种尝试,但到目前为止仍 然没有得到解决。 通过本文的研究表明,在目前,拟通过直接优化方法搜索出核电 厂最优换料方案的想法尚不可行。 关键词:换料方案搜索,直接优化方法,CPLEX,LINGO,混合整 数非线性规划,混合整数线性规划,全局最优解III FEASIBILITY STUDY OF LOADING PATTERN SEARCH VIA DIRECT OPTIMIZATION ABSTRACT Fuel shuffling optimization is very important for economical and safe operation of a nuclear reactor. It is a very complicated and unsolved optimal problem. In this paper, the direct optimization method is proposed to solve the loading pattern search problem. Contrary to most current methods,the direct optimization method uses algebraic equations describing the physical core behavior to build the optimization model. Through solving the model, the pattern search and the pattern evaluation can be completed synchronously. In this paper, based on 1D problem and 3-batch 2D problem, the feasibility of loading pattern search via direct optimization is investigated. Firstly, two mixed-integer nonlinear programming models(MINLP) are developed based on fine mesh finite difference method and hybrid harmonics and linearized perturbation(HHLP) method for 1D and 2D problem respectively. Programming solver LINGO is used to solve the problems. Numerical results indicate that using MINLP model can only find the local optimum, not find the global optimum.IV Secondly, based on the MINLP model of 1D problem, three mixed-integer linear programming models (MILP) are built: exact MILP model based on binary expression for Keff, approximate MILP model based on base LP and approximate MILP model based on mult-bands search for Keff. Both ILOG CPLEX and LINGO solvers are used to solve the three models, and numerical results indicate that the third model can perform the direct LP search and can fast and accurately find the global optimum. Thirdly, base on the idea of mult-bands search and the characteristic of HHLP method, MILP model of 2D problem is built. CPLEX solver is used to solve the model. The numerical results show that the global optimal LP can be accurately found in the given bound of Keff, but it is very time-consuming. Finally, some methods are tried to speed up the model, but the results are negative. Through this paper, we have a preliminary conclusion that the idea of solving a real reactor core loading pattern search problem via direct optimization is not feasible yet. Key words: Loading patter search , Direct optimization method , MINLP,MILP,CPLEX,LINGO, Global optimalV 目 录 第一章 绪论 ....................................................................................................................................1 1.1 选题背景............................................................................................................................1 1.2 研究现状及意义................................................................................................................2 1.3 主要研究工作....................................................................................................................3 第二章 直接优化方法及优化软件简介.........................................................................................4 2.1 直接优化的基本思想.........................................................................................................4 2.2 商用优化软件简介............................................................................................................5 2.2.1 LINGO 软件简介 ....................................................................................................5 2.2.2 CPLEX 软件简介 ....................................................................................................6 第三章 非线性的直接优化方法.....................................................................................................8 3.1 1D 1G 平板燃料排列优化问题 .........................................................................................8 3.1.1 问题描述.................................................................................................................8 3.1.2 固定方案下的模型验证.......................................................................................10 3.1.3 最优方案搜索.......................................................................................................11 3.2 二维堆芯换料优化问题..................................................................................................11 3.2.1 问题描述...............................................................................................................11 3.2.2 基于 HHLP 方法的非线性模型 ...........................................................................12 3.2.3 非线性模型的验证...............................................................................................13 3.2.4 最优方案搜索.......................................................................................................15 3.3 本章小结..........................................................................................................................15 第四章 线性化的直接优化方法...................................................................................................17 4.1 1D 1G 问题的线性化模型 ...............................................................................................17 4.1.1 精确的线性化模型...............................................................................................17 4.1.2 基于基础方案近似的线性化模型.......................................................................20 4.1.3 分步搜索的近似线性化模型...............................................................................25 4.2 二维堆芯换料优化问题的线性化模型...........................................................................29 4.2.1 分步搜索线性化模型 I ........................................................................................29 4.2.2 分步搜索线性化模型 II .......................................................................................37 4.2.3 关于计算速度的探讨...........................................................................................49 4.3 本章小结..........................................................................................................................52 第五章 总结和建议 ......................................................................................................................53 5.1 总结..................................................................................................................................53 5.2 后续工作建议..................................................................................................................53