【摘要】：隨機(jī)規(guī)劃的研究進(jìn)入了一個嶄新的時期,己經(jīng)成為當(dāng)今運(yùn)籌學(xué)優(yōu)化領(lǐng)域內(nèi)的重要課題。其中的補(bǔ)償型隨機(jī)規(guī)劃一般假定隨機(jī)變量的概率分布具有完備信息,但實(shí)際情況往往只能獲得部分信息。針對此種情況,本文基于線性部分信息(Linear partial information,簡稱LPI)理論將補(bǔ)償型兩階段線性隨機(jī)規(guī)劃模型、二次隨機(jī)規(guī)劃模型、非線性隨機(jī)規(guī)劃模型作為研究對象,在現(xiàn)有的求解算法基礎(chǔ)上探討更有效的算法,旨在提高運(yùn)行速度并且得到更精確的解。首先針對離散概率的補(bǔ)償型隨機(jī)規(guī)劃,基于最大化最小期望補(bǔ)償準(zhǔn)則,即Max-Min(簡稱MaxEMin)評判準(zhǔn)則,建立了一類帶有LPI的補(bǔ)償型兩階段隨機(jī)線性規(guī)劃模型,并借助二次規(guī)劃和對偶分解方法得到了模型的可行性切割和最優(yōu)切割,給出了基于L-型的改進(jìn)求解算法、收斂性證明以及算例驗(yàn)證;進(jìn)一步地,針對不完備信息概率分布條件下的補(bǔ)償型兩階段二次隨機(jī)規(guī)劃問題,建立帶有LPI并在MaxEMin評判準(zhǔn)則下的一類補(bǔ)償型隨機(jī)規(guī)劃模型。對于該模型考慮將精確的割平面法改成不精確切割,這是因?yàn)橥ㄟ^給予其模糊范圍能更快的在可行域中找到最優(yōu)解,稱該算法為不精確切割算法,而后通過一個驗(yàn)證性的算例說明該算法的可行有效性;最后對于兩階段非線性隨機(jī)規(guī)劃問題,依據(jù)經(jīng)典的信賴域?yàn)V子求解算法,分別求解兩階段問題的近似二次規(guī)劃問題以獲得決策變量的最優(yōu)解,并將兩階段的函數(shù)目標(biāo)值作為一對二維數(shù)組加入濾子中。最終考慮將濾子中二維數(shù)組的和作為目標(biāo)函數(shù),其中最小的即為模型的最優(yōu)值,所對應(yīng)的決策變量即為最優(yōu)解。鑒于此得出了非線性隨機(jī)規(guī)劃的濾子算法,并予以證明。本文所研究的模型算法對于隨機(jī)規(guī)劃理論與應(yīng)用的深入討論奠定了基礎(chǔ)。
[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.
【學(xué)位授予單位】：華北電力大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O221.5

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 戴_g虹,袁亞湘;三項(xiàng)共軛梯度法收斂性分析[J];計算數(shù)學(xué);1999年03期

2 戴或虹,袁亞湘;廣義Wolfe線搜索下Fletcher-Reeves方法的收斂性[J];高等學(xué)校計算數(shù)學(xué)學(xué)報;1996年02期

，

本文編號：2123821