本文選題：約束優(yōu)化問題 + 初始內(nèi)點(diǎn)�。� 參考：《東北農(nóng)業(yè)大學(xué)》2017年碩士論文

【摘要】：約束優(yōu)化問題所涉及的領(lǐng)域非常廣泛,為系統(tǒng)的優(yōu)化和管理提供了有力的支持。約束極值問題的理論和方法來源于最優(yōu)化理論和優(yōu)化設(shè)計(jì),主要研究內(nèi)容是在眾多的方案中如何找到那個(gè)最優(yōu)的方案。內(nèi)點(diǎn)法和復(fù)合形法等優(yōu)化算法是求解這一類問題較為常用的方法。但在應(yīng)用內(nèi)點(diǎn)法和復(fù)合形法等優(yōu)化算法時(shí),首先要找到一個(gè)初始內(nèi)點(diǎn)。對(duì)于有些問題,由于缺少先驗(yàn)知識(shí),很難人為給出一個(gè)可行的初始內(nèi)點(diǎn),所以,對(duì)有約束優(yōu)化問題初始內(nèi)點(diǎn)的研究就有了重大的理論意義和應(yīng)用價(jià)值。為此,本文在這一方面進(jìn)行了深入的分析與研究,給出了基于實(shí)數(shù)遺傳算法來求解約束優(yōu)化問題初始內(nèi)點(diǎn)的一種新方法。本文通過對(duì)國內(nèi)外有關(guān)文獻(xiàn)的深入研究,采用數(shù)學(xué)、計(jì)算機(jī)科學(xué)等多學(xué)科的綜合分析法,以制約函數(shù)法的相關(guān)理論為基礎(chǔ),提出了基于改進(jìn)實(shí)數(shù)遺傳算法求解有約束優(yōu)化問題初始內(nèi)點(diǎn)的模型,并進(jìn)行了示例計(jì)算。取得的主要研究成果如下:(1)本文經(jīng)研究分析給出了求解約束優(yōu)化問題初始內(nèi)點(diǎn)的一種方法——實(shí)數(shù)遺傳算法。相對(duì)傳統(tǒng)方法需要約束條件是可導(dǎo)的,本文提出的新方法則沒有這些要求,因此更具有普適性。(2)提出了基于改進(jìn)實(shí)數(shù)遺傳算法求解有約束優(yōu)化問題初始內(nèi)點(diǎn)的數(shù)學(xué)模型。(3)給出了用實(shí)數(shù)遺傳算法求解約束優(yōu)化問題初始內(nèi)點(diǎn)時(shí)適應(yīng)度函數(shù)的構(gòu)造方法與模型。(4)本文給出的進(jìn)化策略具有如下特點(diǎn):1)在交叉操作時(shí)將交叉概率取1,以保證所有的父代配對(duì)個(gè)體都需要進(jìn)行交叉,即:選擇這樣的交叉概率能夠增加產(chǎn)生子代個(gè)體的數(shù)量,能夠增大產(chǎn)生更加優(yōu)秀個(gè)體的可能性,使算法的運(yùn)算速度能夠得到提高。2)將交叉產(chǎn)生的個(gè)體與父代中精英保留的m個(gè)個(gè)體放在一起排序,重新選出精英保留的m個(gè)個(gè)體。這樣可以避免交叉操作產(chǎn)生的優(yōu)秀個(gè)體在變異操作過程中遭到破壞的不足,使得交叉操作產(chǎn)生的優(yōu)秀個(gè)體能夠得到生存。3)對(duì)變異操作后的個(gè)體排序,然后用精英保留的m個(gè)優(yōu)秀個(gè)體對(duì)變異操作后最差的m個(gè)個(gè)體進(jìn)行替換,形成新的種群。這樣既有效的保證了種群的多樣性,同時(shí)又使得求得的最優(yōu)結(jié)果不會(huì)比前一次求得的結(jié)果差。(5)進(jìn)行了實(shí)例計(jì)算,結(jié)果表明該方法是一種行之有效的方法。由于該方法不用對(duì)約束條件進(jìn)行求導(dǎo),所以較傳統(tǒng)方法具有更廣泛的實(shí)用性。
[Abstract]:Constrained optimization problems involve a wide range of fields and provide strong support for system optimization and management. The theory and method of constrained extremum problem come from optimization theory and optimization design. The main research content is how to find the optimal scheme in many schemes. Optimization algorithms such as interior point method and complex method are commonly used to solve this kind of problems. But when we apply the interior point method and the complex method, we must find an initial interior point. For some problems, due to the lack of prior knowledge, it is difficult to artificially give a feasible initial interior point. Therefore, the study of initial interior point of constrained optimization problems has great theoretical significance and application value. In this paper, a new method of solving the initial interior point of constrained optimization problem based on real genetic algorithm is presented. In this paper, through the in-depth study of relevant literature at home and abroad, the comprehensive analysis method of mathematics, computer science, and so on, is adopted, which is based on the relevant theories of the restriction function method. A model for solving initial interior points of constrained optimization problems based on improved real genetic algorithm is proposed and an example is given. The main research results are as follows: (1) in this paper, a real genetic algorithm is presented to solve the initial interior point of constrained optimization problem. Compared with the traditional method, the constraint condition is derivable, but the new method presented in this paper does not have these requirements. Therefore, a mathematical model based on improved real genetic algorithm for solving initial interior point of constrained optimization problem is proposed. The fitness function of real genetic algorithm for solving initial interior point of constrained optimization problem is given. The evolutionary strategy given in this paper has the following characteristics: 1: 1) in order to ensure that all parent pairs need to cross each other, the crossover probability is taken as 1 in the crossover operation. That is, choosing such a crossover probability can increase the number of individuals who produce offspring, increase the likelihood of producing better individuals, The computation speed of the algorithm can be improved. 2) the cross generated individuals are sorted together with the m individuals retained by the elite in the parent generation, and the m individuals retained by the elite generation are re-selected. In this way, we can avoid the deficiency that the excellent individual generated by the crossover operation will be destroyed in the mutation operation, so that the excellent individual generated by the crossover operation can get survival. 3) the individual after the mutation operation can be sorted. A new population was formed by replacing the worst m individuals with the best ones retained by the elite. This not only effectively guarantees the diversity of the population, but also makes the optimal result not worse than the previous one. The result shows that this method is an effective method. The method is more practical than the traditional method because it does not have to derive the constraint conditions.
【學(xué)位授予單位】：東北農(nóng)業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP18

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