基于L型及滤子的随机规划算法研究
发布时间：2018-07-15 10:50
【摘要】：随机规划的研究进入了一个崭新的时期,己经成为当今运筹学优化领域内的重要课题。其中的补偿型随机规划一般假定随机变量的概率分布具有完备信息,但实际情况往往只能获得部分信息。针对此种情况,本文基于线性部分信息(Linear partial information,简称LPI)理论将补偿型两阶段线性随机规划模型、二次随机规划模型、非线性随机规划模型作为研究对象,在现有的求解算法基础上探讨更有效的算法,旨在提高运行速度并且得到更精确的解。首先针对离散概率的补偿型随机规划,基于最大化最小期望补偿准则,即Max-Min(简称MaxEMin)评判准则,建立了一类带有LPI的补偿型两阶段随机线性规划模型,并借助二次规划和对偶分解方法得到了模型的可行性切割和最优切割,给出了基于L-型的改进求解算法、收敛性证明以及算例验证;进一步地,针对不完备信息概率分布条件下的补偿型两阶段二次随机规划问题,建立带有LPI并在MaxEMin评判准则下的一类补偿型随机规划模型。对于该模型考虑将精确的割平面法改成不精确切割,这是因为通过给予其模糊范围能更快的在可行域中找到最优解,称该算法为不精确切割算法,而后通过一个验证性的算例说明该算法的可行有效性;最后对于两阶段非线性随机规划问题,依据经典的信赖域滤子求解算法,分别求解两阶段问题的近似二次规划问题以获得决策变量的最优解,并将两阶段的函数目标值作为一对二维数组加入滤子中。最终考虑将滤子中二维数组的和作为目标函数,其中最小的即为模型的最优值,所对应的决策变量即为最优解。鉴于此得出了非线性随机规划的滤子算法,并予以证明。本文所研究的模型算法对于随机规划理论与应用的深入讨论奠定了基础。
[Abstract]:The study of stochastic programming has entered a new period and has become an important subject in the field of operational research optimization. The compensatory stochastic programming generally assumes that the probability distribution of random variables has complete information, but only partial information can be obtained in practice. In this paper, based on linear partial information (LPI) theory, the compensatory two-stage linear stochastic programming model, quadratic stochastic programming model and nonlinear stochastic programming model are studied. Based on the existing algorithms, a more effective algorithm is discussed, which aims to improve the running speed and obtain a more accurate solution. Based on Max-Min (MaxEMin) criterion, a class of compensated two-stage stochastic linear programming model with LPI is established for discrete probabilistic compensatory stochastic programming. With the aid of quadratic programming and duality decomposition, the feasibility and optimal cutting of the model are obtained. The improved algorithm based on L-type, the proof of convergence and the verification of numerical examples are given. A class of compensatory stochastic programming model with LPI and MaxEMin criterion is established for the compensatory two-stage quadratic stochastic programming problem under the condition of incomplete information probability distribution. For the model, the exact cutting plane method is considered to be changed to imprecise cutting because by giving it a fuzzy range, the optimal solution can be found more quickly in the feasible domain, and the algorithm is called imprecise cutting algorithm. Finally, for the two-stage nonlinear stochastic programming problem, the classical trust region filter algorithm is used to solve the problem. The approximate quadratic programming problem of the two-stage problem is solved to obtain the optimal solution of the decision variables, and the target value of the two-stage function is added to the filter as a pair of two-dimensional arrays. Finally, the sum of the two-dimensional array in the filter is considered as the objective function, where the minimum is the optimal value of the model, and the corresponding decision variable is the optimal solution. In view of this, the filter algorithm of nonlinear stochastic programming is obtained and proved. The model algorithm studied in this paper lays a foundation for further discussion of stochastic programming theory and application.
【学位授予单位】：华北电力大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O221.5
本文编号：2123821
[Abstract]:The study of stochastic programming has entered a new period and has become an important subject in the field of operational research optimization. The compensatory stochastic programming generally assumes that the probability distribution of random variables has complete information, but only partial information can be obtained in practice. In this paper, based on linear partial information (LPI) theory, the compensatory two-stage linear stochastic programming model, quadratic stochastic programming model and nonlinear stochastic programming model are studied. Based on the existing algorithms, a more effective algorithm is discussed, which aims to improve the running speed and obtain a more accurate solution. Based on Max-Min (MaxEMin) criterion, a class of compensated two-stage stochastic linear programming model with LPI is established for discrete probabilistic compensatory stochastic programming. With the aid of quadratic programming and duality decomposition, the feasibility and optimal cutting of the model are obtained. The improved algorithm based on L-type, the proof of convergence and the verification of numerical examples are given. A class of compensatory stochastic programming model with LPI and MaxEMin criterion is established for the compensatory two-stage quadratic stochastic programming problem under the condition of incomplete information probability distribution. For the model, the exact cutting plane method is considered to be changed to imprecise cutting because by giving it a fuzzy range, the optimal solution can be found more quickly in the feasible domain, and the algorithm is called imprecise cutting algorithm. Finally, for the two-stage nonlinear stochastic programming problem, the classical trust region filter algorithm is used to solve the problem. The approximate quadratic programming problem of the two-stage problem is solved to obtain the optimal solution of the decision variables, and the target value of the two-stage function is added to the filter as a pair of two-dimensional arrays. Finally, the sum of the two-dimensional array in the filter is considered as the objective function, where the minimum is the optimal value of the model, and the corresponding decision variable is the optimal solution. In view of this, the filter algorithm of nonlinear stochastic programming is obtained and proved. The model algorithm studied in this paper lays a foundation for further discussion of stochastic programming theory and application.
【学位授予单位】：华北电力大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O221.5
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