【正文】 ring near the global optimum, and speeds up algorithm, it should be pointed out that chromosome length changing keeps individual fitness unchanged, hence it does not affect select ion(with roulette wheel selection). Description of the algorithmOwing to basic genetic algorithm not converging on the global optimum, while the genetic algorithm which reserves the best individual at current generation can, our approach adopts this evolutionary process, we track cumulative average of individual average fitness up to current is written as 1X(t)= GG229。favgStep 3 Iffavg0≥k and Flag equals 1, increase chromosome length to m times of itself, and reduce probability of crossover and mutation, and set Flag equal to 0。otherwise go to Step Test and analysisWe adopt the following two critical functions to test our approach, and pare it with the genetic algorithm which only reserves the best individual: f1(x,y)=+[1++y(222)]x,y∈ [5,5][1,1] f2(x,y)=4(x2+(3πx)(4πy))x,y∈ Analysis of convergence During function testing, we carry out the following policies: roulette wheel select ion, one point crossover, bit mutation, and the size of population is 60, l is chromosome length, Pc and Pm are the probability of crossover and mutation we randomly select four genetic algorithms reserving best individual with various fixed chromosome length and probability of crossover and mutation to pare with our gives the average converging generation in 100 our approach, we adopt initial parameter l0= 10, Pc0= , Pm0= and k= , when changing parameter condition is satisfied, we adjust parameters to l= 30, Pc= , Pm= , we know that our approach improves convergence speed of genetic algorithm significantly and it accords with above Analysis of online and offline performanceQuantitative evaluation methods of genetic algorithm are proposed by Dejong, including online and offline former tests dynamic performance。wj=229。llEck(x)k=1lSubstituting Eq.(A1)into Eq.(A2), we obtain l1PbaPPcll0, so Ec(x)187。l1 One point crossoverTheorem 4 Mathematical expectation Em(x)of chromosome searching step with bit mutation Em(x)=(ba)PmPm2=P(2i1)=(ba)本文根據(jù)幾個基本定理，提出了一種使用變異染色體長度和交叉變異概率的改進遺傳算法，它的主要思想是：在進化的開始階段，我們使用短一些的變異染色體長度和高一些的交叉變異概率來解決，在全局最優(yōu)解附近，使用長一些的變異染色體長度和低一些的交叉變異概率。遺傳算法是一種以自然界進化中的選擇和繁殖機制為基礎的自適應的搜索技術，它是由Holland 1975年首先提出的。然而它也有一些缺點，如本地搜索不佳，過早收斂，以及收斂速度慢。本文提出了一種使用變異染色體長度和交叉變異概率的改進遺傳算法。在第一部分，提出了我們的新算法。第三部分，就是所得出的結論。1算法的描述 一些定理在提出我們的算法之前，先給出一個一般性的定理（見附件），如下：我們假設有一個變量（多變量可以拆分成多個部分，每一部分是一個變量）x ∈ [ a, b ] , x ∈ R， 染色體的最小分辨率是s =ba l21定理2 染色體的第i位的權重值是bai1(i = 1,2,…l)2l1定理3 單點交叉的染色體搜索步驟的數(shù)學期望Ec(x)是wi =Ec(x)= baPc 2l其中Pc是交叉概率定理4 位變異的染色體搜索步驟的數(shù)學期望Em(x)是Em(x)=(ba)Pm其中Pm是變異概率 算法機制在進化過程中，我們假設變量的值域是固定的，交叉的概率是一個常數(shù)，所以從定理1 和定理3我們知道，較長的染色體長度有著較少的染色體搜索步驟和較高的分辨率；反之亦然。由定理4，改變?nèi)旧w的長度不影響變異的搜索步驟，而變異概率與搜索步驟也是成正比的。而全局最優(yōu)的附近，較長染色體和較低的交叉和變異概率會減少搜索的步驟，較長的染色體也提高了變異分辨率，避免在全局最優(yōu)解附近徘徊，提高了算法收斂速度。算法描述由于基本遺傳算法沒有在全局優(yōu)化時收斂，而遺傳算法保留了當前一代的最佳個體，我們的方法采用這項策略。它被寫成：1GX(t)= favg(t)229。當累計平均適用性增加到最初個體平均適應度的k(k 1, k ∈ R)倍，我們將染色體長度變?yōu)槠渥陨淼膍(m 是一個正整數(shù))倍，然后減小交叉和變異的概率，可以提高個體分辨率、減少搜索步驟以及提高算法收斂速度。：在所保留的當代的最佳個體，進行選擇、再生、交叉和變異，并計算當代個體的累積平均適應度favgfavg0第三步：如果favg179。否則繼續(xù)進化。測試和分析我們采用以下兩種方法來測試我們的方法，和只保留最佳個體的遺傳算法進行比較：f1(x,y)=+[1++y(222)] [5,5]x,y∈ [1,1] f2(x,y)=4(x2+(3πx)(4πy))x,y∈收斂的分析在功能測試中，我們進行了以下政策：輪盤賭選擇，單點交叉，位變異。L是染色體長度，Pc和Pm分別是交叉概率和變異概率。表1給出了在100次測試的平均收斂代。 在線和離線性能的分析Dejong提出了遺傳算法的定量評價方法，包括在線和離線性能評價。為了更好地分析測試功能的在線和離線性能，我們把個體的適應性乘以10，并f1和f2分別給出了4 000和1 000代的曲線：(a)在線(b)離線圖1 f1的在線與離線性能(a)在線(b)離線從圖1和圖2可以看出，我們方法的在線性能只比第四種情況差一點點，但比第二種、第三種、第五種好很多，這幾種情況下的在線性能幾乎完全相同。一些關鍵功能的測試表明，我們的解決方案可以顯著提高遺傳算法的收斂速度，其綜合性能優(yōu)于只保留最佳個體的遺傳算法。下面給出定理3和定理4的證明過程：定理3 單點交叉的染色體搜索步驟的數(shù)學期望Ec(x)是Ec(x)= 其中Pc是交叉概率baPc 2l證明：如圖A1所示，我們假設交叉發(fā)生在第k個基因位點，從k到l的父基因位點沒有變化，基因位點1到k上的基因改變了。wj=229。ll交叉后，染色k體搜索步驟的數(shù)學期望是1Ec(x)=229。Pc(ba)11ba1(2k1)=c[(2i1)l]=c(1l)l22l2l212121k=1lba187。Pc 其中l(wèi)是非常大的，l2l21Ec(x)=229。Pm其中Pm是變異概率。PmPm2=P(2i1)=(ba) cultivation is of positive robot research status abroad 1966 Japanese professor west light wall mobile robot prototype is developed for the first time, and performance success in Osaka prefecture is a kind of rely on negative pressure adsorption climbing appeared various types of climbing robot, has already begun to the late 80 s application in the 39。s miti “l(fā)imit homework robot” national research projects, supported by day CDH, developed a large pot of negative pressure adsorption surface inspection robots used in nuclear power plants, countries are also added to the climbing robot research upsurge, such as: Seattle Henry R Seemann under the funding of the Boeing pany developed a vacuum adsorption crawler “AutoCrawler” the two tracks each containing a number of small adsorption chamber, with the moving of the crawler, adsorption chamber form continuous vacuum cavity and makes the crawler walking against the CaseWestern Reserve University developed by using four climbing robot prototype “l(fā)egs”.Similar to the first two robots, the robot depends on four “l(fā)egs” on biomimetic viscous materials to adsorption, the prototype is the four legs wheel on the sole of the foot even special distribution is more advantageous to the robot stable crawling on the quality of the robot is only 87 school in the early 1990 s, British Portsmouth has developed a climbing robot multilegged walking modular design, the robot is posed of two similar modules, each module includes two mechanical legs and leg to the task need to install a different number of legs, reconfigurable legs using bionics mechanism, simulation of the large animals arm muscle function, is two type, including upper and lower two and three doubleacting cylinder, with three degrees of stability and bearing capacity is big, the robot39。negative mobile robot can do for petrochemical enterprises to the outer wall of the metal material storage tank to spray paint, sandblasting, as well as with automatic detection system to test the tank wall in 1997