【正文】 、 遺傳編程 、 機(jī)器學(xué)習(xí)等。 遺傳算法是一種特別有效的算法，它能在搜索過程中自動(dòng)獲取和積累有關(guān)搜索空間的知識(shí)，并自適應(yīng)地控制搜索過程，從而得到最優(yōu)解或準(zhǔn)最優(yōu)解。傳統(tǒng)的解決非線性規(guī)劃問題的方法有多種，如 搜索法、梯度法、變尺度法、罰函數(shù)法、拉格朗日乘子法 、 可行方向法等， 雖然解法很多 ， 非線性規(guī)劃目前還沒有能適用于各種問題的算法 ， 各個(gè)方法都有自己特定的適用范圍。 隨著計(jì)算機(jī)的產(chǎn)生與發(fā)展，非線性規(guī)劃作為一門獨(dú)立的學(xué)科越來越受到人們的重視。 50 年代末到 60 年代末出現(xiàn)了許多解非線性規(guī)劃問題的有效的算法 ， 70 年代又得到進(jìn)一步的發(fā)展。 1951 年 于最優(yōu)性條件 (后來稱為庫(kù)恩－塔克條件 )的論文是非線性規(guī)劃正式誕生的一個(gè)重要標(biāo)志。 SUMT Algorithm I 目 錄 1 概論 .................................................................................................................................. 1 背景介紹 ............................................................................................................... 1 非線性規(guī)劃簡(jiǎn)介 ........................................................................................ 1 遺傳算法簡(jiǎn)介 ............................................................................................ 1 研究?jī)?nèi)容 ............................................................................................................... 2 2 非線 性規(guī)劃 ...................................................................................................................... 3 非線性規(guī)劃的概念 ............................................................................................... 3 非線性規(guī)劃的數(shù)學(xué)模型 ....................................................................................... 3 非線性規(guī)劃的求解方法 ....................................................................................... 4 一維最優(yōu)化方法 ........................................................................................ 4 無約束最優(yōu)化方法 .................................................................................... 4 約束最優(yōu)化方法 ........................................................................................ 5 非線性規(guī)劃的應(yīng)用 ............................................................................................... 5 3 傳統(tǒng)非線性規(guī)劃算法 —— 外點(diǎn)罰函數(shù)法 ...................................................................... 6 算法概述 ............................................................................................................... 6 算法描述 ............................................................................................................... 6 算法性能分析 ....................................................................................................... 7 外點(diǎn) 罰函數(shù) 法的程序設(shè)計(jì) ................................................................................... 8 程序步驟 ..................................................................................................... 8 程序流程圖 ................................................................................................. 8 4 遺傳算法 ........................................................................................................................ 10 遺傳算法概述 ..................................................................................................... 10 遺傳算法的生物學(xué)基礎(chǔ) .......................................................................... 10 遺傳算法的一般結(jié)構(gòu) .............................................................................. 10 遺傳算法的特點(diǎn) ...................................................................................... 12 II 遺傳算法的應(yīng)用 ...................................................................................... 12 遺傳算法實(shí)現(xiàn)的關(guān)鍵技術(shù) ................................................................................. 13 5 求解非線性規(guī)劃問題的遺傳算法設(shè)計(jì) ........................................................................ 16 實(shí)用遺傳算法設(shè)計(jì) ............................................................................................. 16 求解非線性規(guī)劃問題的遺傳算法程序設(shè)計(jì) ..................................................... 21 算法過程描述 .......................................................................................... 21 遺傳算法程序流程圖 .............................................................................. 22 遺傳算法中所設(shè)計(jì)的輔助算法的設(shè)計(jì) .................................................. 23 6 算法的結(jié)果分析 ............................................................................................................ 24 概述 ..................................................................................................................... 24 結(jié)果比較 ............................................................................................................. 24 7 總結(jié) ................................................................................................................................ 28 致謝 .................................................................................................................................... 29 參考文獻(xiàn) ............................................................................................................................ 30 1 1 概 論 背景介紹 非線性規(guī)劃簡(jiǎn)介 具有非線性約束條件或目標(biāo)函數(shù)的 數(shù)學(xué)規(guī)劃 ，稱為非線性規(guī)劃。s geic selection and biological evolution of natural selection. Geic algorithm is a global search algorithm. It has simple, universal, robust features, and does not request the objective function to be continuous and differential, and is suitable in parallel distribution processing. Geic algorithm is widely applied in many areas. Based on the analysis of the disadvantage of traditional nonlinear programming algorithm and the advantage of geic algorithm, geic algorithm is applied to nonlinear programming in this paper. The introduction of the concept of penalty function is used to construct the fitness function with punishment. By using realcoded, Roulette Wheel selection method, twopoint crossover, uniform mutation, we formed a geic algorithm to solve the nonlinear programming problem. Compared with the most classical and widely used traditional nonlinear programming problem algorithm –SUMT algorithm, the results show that the new algorithm could effectively overe the defect of the traditional algorithm in a certain extent. The new algorithm is more stable, less sensitive to the function initial value and co