本文選題：填充函數(shù) + 微分動(dòng)態(tài)系統(tǒng)�。� 參考：《華東理工大學(xué)》2015年碩士論文

【摘要】：本文提出了兩個(gè)基于微分動(dòng)態(tài)系統(tǒng)的填充函數(shù)方法,用于求解多極值帶約束的全局最優(yōu)化問題。文章提出了兩個(gè)新的填充函數(shù),在適當(dāng)?shù)募僭O(shè)下證明了它的填充性質(zhì)。在Kennedy and Chua的基礎(chǔ)上分別構(gòu)造了兩個(gè)微分動(dòng)態(tài)系統(tǒng)并討論了它們的穩(wěn)定性,將微分動(dòng)態(tài)系統(tǒng)分別和目標(biāo)函數(shù)以及填充函數(shù)結(jié)合起來,用兩階段法求解全局最優(yōu)解。第一階段：用目標(biāo)函數(shù)及其約束函數(shù)建立微分動(dòng)態(tài)系統(tǒng),通過求解系統(tǒng),求得原問題的一個(gè)局部極小點(diǎn)；第二階段：在當(dāng)前局部極小點(diǎn)處構(gòu)造填充函數(shù)和關(guān)于填充函數(shù)的微分動(dòng)態(tài)系統(tǒng),在理論上證明了此階段得到的穩(wěn)定點(diǎn)一定是在低水平集上。通過兩階段不斷循環(huán)迭代最終得到原問題的全局極小點(diǎn)。 本文根據(jù)理論分析,設(shè)計(jì)相關(guān)算法,并進(jìn)行數(shù)值試驗(yàn)。數(shù)值結(jié)果說明算法是有效的。
[Abstract]:In this paper, two filling function methods based on differential dynamic systems are proposed to solve global optimization problems with multi-extremum constraints. In this paper, two new filling functions are proposed and their filling properties are proved under proper assumptions. On the basis of Kennedy and Chua, two differential dynamic systems are constructed and their stability is discussed. The differential dynamic system is combined with objective function and filling function respectively, and the global optimal solution is solved by two-stage method. In the first stage, the differential dynamic system is established by using the objective function and its constraint function, and a local minimal point of the original problem is obtained by solving the system. In the second stage, the filling function and the differential dynamic system about the filling function are constructed at the current local minima. It is proved theoretically that the stable points obtained in this stage must be on the low level set. Finally, the global minima of the original problem is obtained by two stage continuous iteration. Based on the theoretical analysis, this paper designs relevant algorithms and carries out numerical experiments. Numerical results show that the algorithm is effective.
【學(xué)位授予單位】：華東理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O175

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本文編號(hào)：2063242