【摘要】：實(shí)際生活中,常會遇到關(guān)于多個(gè)目標(biāo)同時(shí)優(yōu)化的各種問題。比如大眾消費(fèi)時(shí)都想以便宜的價(jià)格買到優(yōu)質(zhì)的商品,這個(gè)“矛盾”就是一個(gè)關(guān)于多目標(biāo)優(yōu)化的典型事例。在生活中眾多領(lǐng)域,多目標(biāo)優(yōu)化問題皆扮演著重要角色,包括制造業(yè)、運(yùn)輸業(yè)、服務(wù)業(yè)、電信業(yè)等行業(yè),多目標(biāo)優(yōu)化問題無處不在。為了解決此類多個(gè)目標(biāo)間相互“矛盾”的問題,常常需要將與這些問題相關(guān)的多個(gè)子目標(biāo)轉(zhuǎn)化為與之對應(yīng)的函數(shù)表達(dá)式,然后再對其進(jìn)行優(yōu)化求解,這就是多目標(biāo)問題的優(yōu)化。遺傳算法(GA)在多目標(biāo)優(yōu)化方法中具有獨(dú)特的優(yōu)勢,特別是近年來廣泛研究和應(yīng)用的多目標(biāo)優(yōu)化遺傳算法(MOGA)及其相關(guān)的衍生算法,以非支配排序遺傳算法-Ⅱ(NSGA-Ⅱ)為代表。然而,傳統(tǒng)的NSGA-Ⅱ受限于模擬二進(jìn)制交叉算子(SBX)和多項(xiàng)式變異算子,使非支配個(gè)體的全局搜索能力較弱,種群的多樣性較差等。針對傳統(tǒng)NSGA-Ⅱ中存在的諸多問題,本文提出了一種改進(jìn)的NSGA-Ⅱ多目標(biāo)優(yōu)化算法,經(jīng)過仿真實(shí)驗(yàn)得到滿意的Pareto最優(yōu)解集,并通過實(shí)際應(yīng)用驗(yàn)證了改進(jìn)的理論成果,解決了多目標(biāo)優(yōu)化問題。本文提出改進(jìn)的NSGA-Ⅱ多目標(biāo)優(yōu)化算法,具體研究內(nèi)容主要體現(xiàn)在以下幾個(gè)方面:(1)針對不同的多目標(biāo)優(yōu)化問題建立數(shù)學(xué)模型,并結(jié)合正交實(shí)驗(yàn)法獲取實(shí)驗(yàn)樣本,確定最佳優(yōu)化參數(shù),提升算法效率,節(jié)省運(yùn)算時(shí)間。(2)在進(jìn)化過程中引入正態(tài)分布交叉算子(NDX),有效解決了傳統(tǒng)的NSGA-Ⅱ算法中利用模擬二進(jìn)制交叉算子(SBX)引起的搜索空間狹窄、容易陷入局部最優(yōu)等問題,增強(qiáng)了算法的空間搜索能力。(3)提出改進(jìn)的自適應(yīng)調(diào)整變異方式,提高了種群取優(yōu)速度。對于復(fù)雜的非線性優(yōu)化問題,傳統(tǒng)的NSGA-Ⅱ算法采用Deb提出的多項(xiàng)式變異方式,由于這種變異算子中含有隨機(jī)參數(shù)和主觀參數(shù),使其隨機(jī)性較大,收斂速度較慢。改進(jìn)的自適應(yīng)調(diào)整變異方式能夠通過其作用機(jī)理得到更好的收斂效果,不僅加快了種群的收斂速度,還維持了種群個(gè)體的多樣性,使得Pareto邊界分布更優(yōu)。(4)通過改進(jìn)的NSGA-Ⅱ算法優(yōu)化聚硅氧烷的合成過程中反應(yīng)溫度、反應(yīng)時(shí)間、催化劑及其助劑的量,得到單分子轉(zhuǎn)化率的最大值和粘度分子量的期望值。實(shí)驗(yàn)中定義了解集覆蓋度和空間分布量來衡量Pareto解的性能,并采用正交實(shí)驗(yàn)法確定最優(yōu)進(jìn)化參數(shù)。仿真測試結(jié)果用量化標(biāo)準(zhǔn)對比證明了改進(jìn)的NSGA-Ⅱ算法取優(yōu)特性高于傳統(tǒng)的MOGA及其衍生算法,Pareto最優(yōu)前沿進(jìn)一步顯示改進(jìn)算法的解集分布更加均勻、連續(xù),驗(yàn)證了本文提出改進(jìn)的NSGA-Ⅱ多目標(biāo)優(yōu)化算法理論在聚合優(yōu)化中應(yīng)用的正確性及合理性。
[Abstract]:In real life, there are often problems with multiple goals being optimized at the same time. For example, when people consume, they want to buy quality goods at a low price. This contradiction is a typical example of multi-objective optimization. In many fields of life, multi-objective optimization problems play an important role, including manufacturing, transportation, service, telecommunications and other industries, multi-objective optimization problems everywhere. In order to solve this kind of "contradiction" between multiple objectives, it is often necessary to transform multiple sub-objectives related to these problems into corresponding functional expressions, and then optimize them. This is the optimization of multi-objective problems. Genetic algorithm (GA) has unique advantages in multi-objective optimization, especially (MOGA) and its related derivative algorithms, which have been widely studied and applied in recent years. Undominated sorting genetic algorithm-鈪，

本文編號：2402187