本文選題：約束優(yōu)化問題 + 差分進化��； 參考：《西安電子科技大學(xué)》2012年碩士論文

【摘要】：約束優(yōu)化問題是實際中經(jīng)常用到的一類數(shù)學(xué)規(guī)劃問題．近年來，約束優(yōu)化問題的求解已成為進化計算研究的一個重要方向．差分進化算法因其原理簡單、受控參數(shù)少、魯棒性強等特點，引起了越來越多學(xué)者的關(guān)注，但是其本質(zhì)上是一種無約束的優(yōu)化算法，在求解約束優(yōu)化問題時需要引入約束處理技術(shù)．從約束差分進化算法=約束處理技術(shù)+差分進化算法的研究框架出發(fā)，從兩方面來考慮約束優(yōu)化差分進化算法的性能具有理論意義和應(yīng)用前景． 本文首先對差分進化算法的研究背景和發(fā)展現(xiàn)狀做了簡要的描述，并就其原理、改進策略、較其他進化算法的優(yōu)點和應(yīng)用做了詳細說明；然后對基于進化算法的約束處理技術(shù)進行分類，并對每類方法的研究現(xiàn)狀做了綜述；最后將復(fù)合差分進化算法與兩種不同的約束處理技術(shù)相結(jié)合，提出了兩種改進的約束復(fù)合差分進化算法． 第一種改進算法基于懲罰函數(shù)法，利用自適應(yīng)懲罰函數(shù)的約束處理技術(shù)，引入距離作為適應(yīng)值函數(shù)，根據(jù)種群的可行率計算個體的距離，對每個個體施行兩種懲罰，分別基于目標(biāo)函數(shù)和約束違反程度；同時結(jié)合復(fù)合差分進化算法，保留后代種群中的較優(yōu)個體．這樣既保留了種群的多樣性，又使得種群可以在尋找可行解和尋找最優(yōu)解之間進行調(diào)節(jié)．?dāng)?shù)值實驗結(jié)果表明，新算法與同類算法相比，，具有較好的全局尋優(yōu)能力和自適應(yīng)性． 第二種改進算法基于多目標(biāo)法，將原問題轉(zhuǎn)化為包含原目標(biāo)函數(shù)和約束違反程度兩個目標(biāo)的多目標(biāo)優(yōu)化問題，運用多目標(biāo)優(yōu)化方法進行求解．該方法由兩部分組成：種群進化模型和不可行解替換機制．種群進化模型中復(fù)合差分進化算法作為搜索引擎進化種群，利用Pareto支配比較個體，選擇其中性能較好的個體；不可行解替換機制用于改善種群中個體的質(zhì)量和可行率，進而引導(dǎo)種群向可行域逼近．?dāng)?shù)值實驗結(jié)果表明，新算法的結(jié)果具有較高的計算精度和全局搜索能力．
[Abstract]:Constrained optimization problem is a kind of mathematical programming problem that is often used in practice. In recent years, the solution of constrained optimization problems has become an important research direction in evolutionary computing. Differential evolution algorithm has attracted more and more attention of scholars because of its simple principle, few controlled parameters and strong robustness, but it is essentially an unconstrained optimization algorithm. It is necessary to introduce constraint processing technology in solving constrained optimization problems. Based on the research framework of constrained differential evolution algorithm = constraint processing technology, the performance of constrained optimization differential evolution algorithm is considered from two aspects, which has theoretical significance and application prospect. In this paper, the research background and development status of differential evolutionary algorithm are briefly described, and its principle, improvement strategy, advantages and applications of other evolutionary algorithms are explained in detail. Then, the constraint processing technology based on evolutionary algorithm is classified, and the research status of each kind of method is summarized. Finally, the composite differential evolution algorithm is combined with two different constraint processing techniques. Two improved constrained composite differential evolution algorithms are proposed. The first improved algorithm is based on the penalty function method, using the constraint processing technique of the adaptive penalty function, introducing distance as the fitness function, calculating the individual distance according to the feasible rate of the population, and carrying out two kinds of punishment for each individual. Based on the objective function and the degree of constraint violation, combined with the composite differential evolution algorithm, the optimal individuals in the offspring population are retained. This not only preserves the diversity of the population, but also allows the population to adjust between finding the feasible solution and finding the optimal solution. The numerical results show that the new algorithm has better global optimization ability and adaptability than similar algorithms. The second improved algorithm is based on the multi-objective method. The original problem is transformed into a multi-objective optimization problem with two objectives including the original objective function and the degree of constraint violation, and the multi-objective optimization method is used to solve the problem. The method consists of two parts: population evolution model and infeasible solution replacement mechanism. In the population evolution model, composite differential evolution algorithm is used as search engine evolution population. Pareto is used to control and compare the individuals, and the better performance individuals are selected, and the infeasible solution replacement mechanism is used to improve the quality and feasibility rate of the individuals in the population. Then it leads the population to approach the feasible region. The numerical results show that the new algorithm has high computational accuracy and global search ability.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：TP18;O224

【引證文獻】

相關(guān)碩士學(xué)位論文 前1條

1 殳越;汽油調(diào)合過程建模與優(yōu)化[D];華東理工大學(xué);2013年

本文編號：1935852