人工智能及其應用大作業(yè)（一） 題 目： 基本遺傳算法及其在函數(shù)優(yōu)化中的作用 學 號： 姓 名： 基本遺傳算法及其在函數(shù)優(yōu)化中的應用摘要：從遺傳算法的編碼、遺傳算子等方面剖析了遺傳算法求解無約束函數(shù)優(yōu)化問題的一般步驟,并以一個實例說明遺傳算法能有效地解決函數(shù)優(yōu)化問題。本文利用基本遺傳算法求解函數(shù)優(yōu)化問題，選用 f(x)=xsin(10x)+2.0，取值范圍在中，利用基本遺傳算法求解兩個函數(shù)的最優(yōu)值，遺傳算法每次100代，一共執(zhí)行10次，根據(jù)運算結(jié)果分析得到最優(yōu)解。關(guān)鍵字：遺傳算法 選擇 交叉 變異 函數(shù)優(yōu)化1.前言1.1基本概念 遺傳算法（Genetic Algorithm）是一類借鑒生物界的進化規(guī)律（適者生存，優(yōu)勝劣汰遺傳機制）演化而來的隨機化搜索方法。遺傳算法是一種群體型操作，該操作以群體中的所有個體為對象。選擇（Selection）、交叉（Crossover）和變異（Mutation）是遺傳算法的3個主要操作算子，它們構(gòu)成了所謂的遺傳操作（genetic operation），使遺傳算法具有了其它傳統(tǒng)方法所沒有的特性。1.2 遺傳算法的特點 其主要特點是直接對結(jié)構(gòu)對象進行操作，不存在求導和函數(shù)連續(xù)性的限定；具有內(nèi)在的隱并行性和更好的全局尋優(yōu)能力；采用概率化的尋優(yōu)方法，能自動獲取和指導優(yōu)化的搜索空間，自適應地調(diào)整搜索方向，不需要確定的規(guī)則。1.3遺傳算法的應用 函數(shù)優(yōu)化，組合優(yōu)化，機器人智能控制，及組合圖像處理和模式識別等。 2. 基本遺傳算法2.1簡單遺傳算法的求解步驟Step1：參數(shù)設置及種群初始化；Step2：適應度評價；Step3：選擇操作；Step4：交叉操作；Step5：變異操作；Step6：終止條件判斷，若未達到終止條件，則轉(zhuǎn)到Step3；Step7：輸出結(jié)果。2.2停機準則（1） 完成了預先給定的進化代數(shù)則停止；（2） 群體中的最優(yōu)個體在連續(xù)若干代沒有改進或平均適應度在連續(xù)若干代基本沒有改進時停止。2.3基本遺傳算法框圖開始Gen=0編碼隨機產(chǎn)生M個初始個體滿足終止條件?計算群體中各個體適應度從左至右依次執(zhí)行遺傳算子j = 0j = 0j = 0根據(jù)適應度選擇復制個體選擇兩個交叉?zhèn)€體選擇個體變異點執(zhí)行變異執(zhí)行交叉執(zhí)行復制將復制的個體添入新群體中將交叉后的兩個新個體添入新群體中將變異后的個體添入新群體中j = j+1j = j+2j = j+1 j = M? j = pcM? j = pmLM?Gen=Gen+1輸出結(jié)果終止YNYYYNNNpcpm3.實驗與結(jié)果 本小節(jié)采用以下函數(shù)： f(x)=xsin(10x)+2.0，x-1,23.1編碼 表現(xiàn)型：x 基因型：二進制編碼（串長取決于求解精度） 按編碼原理：假設要求求解精度到6位小數(shù)，區(qū)間長度為2-(-1)3，即需將區(qū)間分為3/0.000001=3106等份。 所以編碼的二進制串長應為22位。3.2產(chǎn)生初始種群 產(chǎn)生的方式：隨機 產(chǎn)生的結(jié)果：長度為22的二進制串 產(chǎn)生的數(shù)量：種群的大?。ㄒ?guī)模），如30，50， 1111010011100001011000 1100110011101010101110 1010100011110010000100 1011110010011100111001 0001100101001100000011 0000011010010000000000 .3.3計算適應度直接用目標函數(shù)作為適應度函數(shù) 解碼：將個體s轉(zhuǎn)化為-1,2區(qū)間的實數(shù)： s=<1000101110110101000111> x=0.637197 計算x的函數(shù)值（適應度）： f(x)=xsin(10x)+2.0=2.5863453.4遺傳操作 選擇：比例選擇法； 交叉：單點交叉； 變異：小概率變異3.5模擬結(jié)果 設置的參數(shù)： 種群大小80；交叉概率0.75；變異概率0.05；最大代數(shù)100。 運行結(jié)果如下表： 12345678910best_fit16.850316.850316.845416.850316.846116.849116.795216.850016.8120 16.8500best_f3.85033.85033.84543.85033.84613.84913.79523.85003.81203.8501best_x1.80061.80091.80381.80121.79791.79921.79031.80151.80001.810由上表可以分析得出的最優(yōu)解為x=1.8，最大值為3.85。4.結(jié)論 遺傳算法在適應度函數(shù)選擇不當?shù)那闆r下有可能收斂于局部最優(yōu)，而不能達到全局最優(yōu)。 選擇的過程很重要，決定著最終結(jié)果和收斂速度等。對于任何一個具體的優(yōu)化問題，調(diào)節(jié)遺傳算法的參數(shù)可能會有利于更好的更快的收斂，這些參數(shù)包括個體數(shù)目、交叉律和變異律。 遺傳算法并不一定總是最好的優(yōu)化策略，優(yōu)化問題要具體情況具體分析。參考文獻：（1）蔡自興，徐光祐人工智能及其應用（2）馬永，賈俊芳.遺傳算法研究綜述.第23卷.第三期.2007年12月；附錄：1.代碼主函數(shù):clearclcmy_scale=50; %種群規(guī)模gen_len=22; %基因長度M=100; %迭代次數(shù)pc=0.75; %交叉概率pm=0.05; %變異概率new_scale=produscale(my_scale,gen_len); %產(chǎn)生初始種群fitfit=; fittimer=; best_f1=;best_x1=; for i=1:M my_f=cal_my_f(new_scale); %計算函數(shù)值 my_fit=cal_my_fit(my_f); %計算適應度值 next_scale=my_sellect(new_scale,my_fit); %采用賭輪盤法選擇 cross_scale=my_cross(next_scale,pc); %按概率交叉 mut_scale=my_mutat(cross_scale,pm); %按概率變異 %尋找每一代中的最優(yōu)適應度值所對應的個體 best_fit=my_fit(1); sx,sy=size(new_scale); for j=2:length(my_fit) if best_fit<my_fit(j) best_fit=my_fit(j); best_f=my_f(j); best_x=my2to10(new_scale(j,:); best_x=-2+best_x.*4./(2sy-1); end end new_scale=mut_scale; fitfit=fitfit,best_fit; best_f1=best_f1,best_f; best_x1=best_x1,best_x; fittimer=fittimer,i;end best_fit,loca=max(fitfit); best_f=best_f1(loca); best_x=best_x1(loca); disp(best_fit,best_f,best_x=)disp(best_fit,best_f,best_x)subplot(2,2,1) plot(fittimer,fitfit) xlabel(迭代次數(shù)(1)-wxb); ylabel(適應度函數(shù)) grid on%子函數(shù)：產(chǎn)生初始種群function initscale=produscale(my_scale,gen_len) initscale=round(rand(my_scale,gen_len);end%子函數(shù)：計算函數(shù)值function my_f=cal_my_f(new_scale) mychange=my2to10(new_scale); sx,sy=size(new_scale); change_x=-1+mychange.*3./(2sy-1); my_f=change_x*sin(10*change_x)+2; end%子函數(shù)：計算適應度值function my_fit=cal_my_fit(my_f) f_min=5; for i=1:length(my_f) if my_f(i)+f_min<=0 my_fit(i)=0; else my_fit(i)=my_f(i)+f_min; end end my_fit=my_fit;end %子函數(shù)：采用賭輪盤法選擇function next_scale=my_sellect(new_scale,my_fit) sum_of_f=sum(my_fit); accum=my_fit/sum_of_f; accum=cumsum(accum); sx,sy=size(new_scale); j=1; while j<=sx a=rand; for i=1:sx-1 if accum(1)>=a next_scale(j,:)=new_scale(1,:); else if accum(i)<a&&accum(i+1)>=a next_scale(j,:)=new_scale(i+1,:); j=j+1; end end end endend%子函數(shù)：按概率交叉function cross_scale=my_cross(new_scale,pc) sx,sy=size(new_scale); cross_scale=new_scale; for i=1:2:sx-1 if rand<pc a=round(rand*sy); cross_scale(i,:)=new_scale(i,1:a),new_scale(i+1,a+1:end); cross_scale(i+1,:)=new_scale(i+1,1:a),new_scale(i,a+1:end); end end %子函數(shù)：按概率變異function mut_scale=my_mutat(new_scale,pm) sx,sy=size(new_scale); mut_scale=new_scale; for i=1:sx if rand<pm a=round(rand*sy); if a<=0 a=1; end if mut_scale(i,a)=0 mut_scale(i,a)=1; else mut_scale(i,a)=0; end end end%子函數(shù)：2進制轉(zhuǎn)10進制function mychange=my2to10(new_scale) sx,sy=size(new_scale); new_scale1=new_scale; for i=1:sy new_scale1(:,i)=2.(sy-i).*new_scale(:,i); end mychange=sum(new_scale1,2);end2.實驗結(jié)果截圖g an employment tribunal claimEmployment tribunals sort out disagreements between employers and employees.You may need to make a claim to an employment tribunal if: you dont agree with the disciplinary action your employer has taken against you your employer dismisses you and you think that you have been dismissed unfairly.For more information about dismissal and unfair dismissal, seeDismissal.You can make a claim to an employment tribunal, even if you haventappealedagainst the disciplinary action your employer has taken against you. However, if you win your case, the tribunal may reduce any compensation awarded to you as a result of your failure to appeal.Remember that in most cases you must make an application to an employment tribunal within three months of the date when the event you are complaining about happened. If your application is received after this time limit, the tribunal will not usually accept it.If you are worried about how the time limits apply to you, take advice from one of the organisations listed underFurther help.Employment tribunals are less formal than some other courts, but it is still a legal process and you will need to give evidence under an oath or affirmation.Most people find making a claim to an employment tribunal challenging. If you are thinking about making a claim to an employment tribunal, you should get help straight away from one of the organisations listed underFurther help.If you are being represented by a solicitor at the tribunal, they may ask you to sign an agreement where you pay their fee out of your compensation if you win the case. This is known as adamages-based agreement. In England and Wales, your solicitor cant charge you more than 35% of your compensation if you win the case.If you are thinking about signing up for a damages-based agreement, you should make sure youre clear about the terms of the agreement. It might be best to get advice from an experienced adviser, for example, at a Citizens Advice Bureau. To find your nearest CAB, including those that give advice by e-mail, click onnearest CAB.For more information about making a claim to an employment tribunal, seeEmployment tribunals.The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier League match at Chelsea on Sunday."I am going to be at the match tomorrow and I have asked to meet Yaya Toure," he told BBC Sport."For me its about how he felt and I would like to speak to him first to find out what his experience was."Uefa hasopened disciplinary proceedings against CSKAfor the "racist behaviour of their fans" duringCitys 2-1 win.Michel Platini, president of European footballs governing body, has also ordered an immediate investigation into the referees actions.CSKA said they were "surprised and disappointed" by Toures complaint. In a statement the Russian side added: "We found no racist insults from fans of CSKA."Age has reached the end of the beginning of a word. May be guilty in his seems to passing a lot of different life became the appearance of the same day; May be back in the past, to oneself the paranoid weird belief disillusionment, these days, my mind has been very messy, in my mind constantly. Always feel oneself should go to do something, or write something. Twenty years of life trajectory deeply shallow, suddenly feel something, do it.一字開頭的年齡已經(jīng)到了尾聲。或許是愧疚于自己似乎把轉(zhuǎn)瞬即逝的很多個不同的日子過成了同一天的樣子；或許是追溯過去，對自己那些近乎偏執(zhí)的怪異信念的醒悟，這些天以來，思緒一直很凌亂，在腦海中不斷糾纏。總覺得自己自己似乎應該去做點什么，或者寫點什么。二十年的人生軌跡深深淺淺，突然就感覺到有些事情，非做不可了。The end of our life, and can meet many things really do?而窮盡我們的一生，又能遇到多少事情是真正地非做不可？During my childhood, think lucky money and new clothes are necessary for New Year, but as the advance of the age, will be more and more found that those things are optional; Junior high school, thought to have a crush on just means that the real growth, but over the past three years later, his writing of alumni in peace, suddenly found that isnt really grow up, it seems is not so important; Then in high school, think dont want to give vent to out your inner voice can be in the high school children of the feelings in a period, but was eventually infarction when graduation party in the throat, later again stood on the pitch he has sweat profusely, looked at his thrown a basketball hoops, suddenly found himself has already cant remember his appearance.童年時，覺得壓歲錢和新衣服是過年必備，但是隨著年齡的推進，會越來越發(fā)現(xiàn)，那些東西根本就可有可無；初中時，以為要有一場暗戀才意味著真正的成長，但三年過去后，自己心平氣和的寫同學錄的時候，突然就發(fā)現(xiàn)是不是真正的成長了，好像并沒有那么重要了；然后到了高中，覺得非要吐露出自己的心聲才能為高中生涯里的懵懂情愫劃上一個句點，但畢業(yè)晚會的時候最終還是被梗塞在了咽喉，后來再次站在他曾經(jīng)揮汗如雨的球場，看著他投過籃球的球框時，突然間發(fā)現(xiàn)自己已經(jīng)想不起他的容顏。Originally, this world, can produce a chemical reaction to an event, in addition to resolutely, have to do, and time.原來，這個世界上，對某個事件能產(chǎn)生化學反應的，除了非做不可的堅決，還有，時間。A persons time, your ideas are always special to clear. Want, want, line is clear, as if nothing could shake his. Also once seemed to be determined to do something, but more often is he backed out at last. Dislike his cowardice, finally found that there are a lot of love, there are a lot of miss, like shadow really have been doomed. Those who do, just green years oneself give oneself an arm injection, or is a self-righteous spiritual.一個人的時候，自己的想法總是特別地清晰。想要的，不想要的，界限明確，好像沒有什么可以撼動自己。也曾經(jīng)好像已經(jīng)下定了決心去做某件事，但更多的時候是最后又打起了退堂鼓。嫌惡過自己的怯懦，最終卻發(fā)現(xiàn)有很多緣分，有很多錯過，好像冥冥之中真的已經(jīng)注定。那些曾經(jīng)所謂的非做不可，只是青蔥年華里自己給自己注射的一支強心劑，或者說，是自以為是的精神寄托罷了。At the moment, the sky is dark, the air is fresh factor after just rained. Suddenly thought of blue plaid shirt; Those were broken into various shapes of stationery; From the corner at the beginning of deep friendship; Have declared the end of the encounter that havent start planning. Those years, those days of do, finally, like youth, will end in our life.此刻，天空是陰暗的，空氣里有著剛下過雨之后的清新因子。突然想到那件藍格子襯衫；那些被折成各種各樣形狀的信紙；那段從街角深巷伊始的友誼；還有那場還沒有開始就宣告了終結(jié)的邂逅計劃那些年那些天的非做不可，終于和青春一樣，都將在我們的人生中謝幕。Baumgartner the disappointing news: Mission aborted. r plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.The supersonic descent could happen as early as Sunda.The weatheThe balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end. Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).cause there