本文選題：分布魯棒優(yōu)化　切入點：概率分布集　出處：《南京航空航天大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

【摘要】：本文研究內(nèi)容為用基于新的概率分布集的分布魯棒優(yōu)化方法研究不確定情形下的Weber選址問題,并通過數(shù)值實驗表明我們的方法比常用的Min Max-Regret方法好,同時適當(dāng)增大?時所需要的樣本個數(shù)減少。論文的具體內(nèi)容如下:第一章介紹了不確定設(shè)施選址的研究背景和研究現(xiàn)狀,同時簡單介紹了本文的研究工作。第二章針對選址問題中隨機參數(shù)的協(xié)方差矩陣不一定是正定的這一事實,提出了新的概率分布集,這一改進的概率分布集及其性質(zhì)通過構(gòu)造新的虛擬隨機向量而推導(dǎo)得到。第三章首先介紹了變分不等式和隨機變分不等式的相關(guān)概念,然后構(gòu)造了Weber選址問題的殘量函數(shù)。當(dāng)權(quán)重隨機而顧客位置固定,同時目標(biāo)函數(shù)使用1-范數(shù)時,通過分割平面,在各分割后形成的每個小矩形內(nèi),我們驗證了殘量函數(shù)滿足分布魯棒優(yōu)化的假設(shè)條件,并可以將此問題通過對偶變換化為一個半定規(guī)劃問題。通過分割平面法可以使得問題的約束個數(shù)的規(guī)模由指數(shù)階降為多項式階。第四章給出了具體的算法實現(xiàn)并得出了相應(yīng)的結(jié)論。Min Max-Regret方法只考慮最壞情形下系統(tǒng)的表現(xiàn),有時最壞情形發(fā)生的概率很小,用此方法做出的決策在很多情形下可能效果較差,同時此方法沒有充分挖掘樣本的概率統(tǒng)計信息;基于新的概率分布集的分布魯棒優(yōu)化方法克服了Min Max-Regret方法的不足之處,所作出的決策在大多數(shù)情形下比常用的Min Max-Regret方法要好,同時充分利用了樣本里隱含的概率統(tǒng)計信息。通過數(shù)值實驗驗證了我們的方法在處理不確定Weber問題時比Min Max-Regret方法要好,同時表明當(dāng)???I中的?增大時,所需要的樣本個數(shù)減小,且對解的性態(tài)沒有影響。第五章總結(jié)了全文并提出了展望。
[Abstract]:In this paper, we use the new distributed robust optimization method based on the new probability distribution set to study the Weber location problem in uncertain cases. The numerical experiments show that our method is better than the usual Min Max-Regret method, and at the same time, it is increased appropriately. The main contents of this paper are as follows: chapter one introduces the research background and research status of uncertain facility location. In chapter 2, a new probability distribution set is proposed for the fact that the covariance matrix of random parameters is not necessarily positive definite. This improved probability distribution set and its properties are derived by constructing a new virtual random vector. In chapter 3, the concepts of variational inequality and random variational inequality are introduced. Then, the residual function of Weber location problem is constructed. When the weight is random and the customer position is fixed, and the objective function uses 1-norm, by dividing the plane, each small rectangle is formed after each segmentation. We verify that the residual function satisfies the assumption of distributed robust optimization. The problem can be transformed into a semi-definite programming problem by dual transformation. The size of the constraint number of the problem can be reduced from exponential order to polynomial order by partitioning plane method. Chapter 4th gives the implementation of the algorithm. It is concluded that the Min Max-Regret method only considers the performance of the system in the worst-case scenario. Sometimes the probability of the worst case is very small, the decision made by this method may be poor in many cases, at the same time, the method does not fully mine the probability and statistics information of the sample. The new distributed robust optimization method based on the new probability distribution sets overcomes the shortcomings of the Min Max-Regret method and makes better decisions than the Min Max-Regret method in most cases. At the same time, we make full use of the probability and statistics information implied in the sample. The numerical experiments show that our method is better than the Min Max-Regret method in dealing with the uncertain Weber problem. ? ? In I? When the number of samples is increased, the number of samples is reduced, and the behavior of the solution is not affected. Chapter 5th summarizes the full text and puts forward the prospect.
【學(xué)位授予單位】：南京航空航天大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O22

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相關(guān)期刊論文 前2條

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本文編號：1578446