Evolutionary programming made faster

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进化算法

Evolutionary Computation： An interview Back and Schwefel
• We present an overview of the most important representatives of algorithms gleaned from natural evolution, so-called evolutionary algorithms. Evolution strategies, evolutionary programming, and genetic algorithms are summarized, with special emphasis on the principle of strategy parameter self-adaptation utilized by the first two algorithms to learn their own strategy parameters such as mutation variances and covariances. Some experimental results are presented which demonstrate the working principle and robustness of the self-adaptation methods used in evolution strategies and evolutionary programming. General principles of evolutionary algorithms are discussed, and we identify certain properties of natural evolution which might help to improve the problem solving capabilities of evolutionary algorithms even further.

进化计算综述

进化计算综述1.什么是进化计算在计算机科学领域，进化计算（Evolutionary Computation）是人工智能（Artificial Intelligence），进一步说是智能计算（Computational Intelligence）中涉及到组合优化问题的一个子域。

其算法是受生物进化过程中“优胜劣汰”的自然选择机制和遗传信息的传递规律的影响，通过程序迭代模拟这一过程，把要解决的问题看作环境，在一些可能的解组成的种群中，通过自然演化寻求最优解。

2.进化计算的起源运用达尔文理论解决问题的思想起源于20世纪50年代。

20世纪60年代，这一想法在三个地方分别被发展起来。

美国的Lawrence J. Fogel提出了进化编程（Evolutionary programming），而来自美国Michigan 大学的John Henry Holland则借鉴了达尔文的生物进化论和孟德尔的遗传定律的基本思想，并将其进行提取、简化与抽象提出了遗传算法（Genetic algorithms）。

在德国，Ingo Rechenberg 和Hans-Paul Schwefel提出了进化策略（Evolution strategies）。

这些理论大约独自发展了15年。

在80年代之前，并没有引起人们太大的关注，因为它本身还不够成熟，而且受到了当时计算机容量小、运算速度慢的限制，并没有发展出实际的应用成果。

到了20世纪90年代初，遗传编程（Genetic programming）这一分支也被提出，进化计算作为一个学科开始正式出现。

四个分支交流频繁，取长补短，并融合出了新的进化算法，促进了进化计算的巨大发展。

Nils Aall Barricelli在20世纪六十年代开始进行用进化算法和人工生命模拟进化的工作。

Alex Fraser发表的一系列关于模拟人工选择的论文大大发展了这一工作。

[1]Ingo Rechenberg在上世纪60 年代和70 年代初用进化策略来解决复杂的工程问题的工作使人工进化成为广泛认可的优化方法。

进化策略

当把这种算法用于函数优化时，发现它有两个缺点：
(1) 各维取定常的标准差使得程序收敛到最优解的速度很慢； (2) 点到点搜索的脆弱本质使得程序在局部极值附近容易受停
滞的影响（虽然此算法表明可以渐近地收敛到全局最优点）。
8.2 进化策略
(μ + 1)-ES:
早期的(1十1)-ES，没有体现群体的作用，只是单个个体在进化，具有明显的局限性。随后，Rechenberg又提出(μ+1)ES，在这种进化策略中，父代有μ个个体(μ＞1)，并且引入重组(Recombination)算子，使父代个体组合出新的个体。在执行重组时，从μ个父代个体中用随机的方法任选两个个体：
8.2 进化策略
在1973年，Rechenburg把该算法的期望收敛速度定义为对最优点的平均距离与要得到此改善所需要的试验次数之比。
1981年，Schwefel在进化策略中使用多重亲本和子代，这是 Rechenburg早期工作（使用多重亲本，但是仅使用单个子代）的发展，后来考察了两种方法，分别表示为(μ+λ)-ES 相(μ，λ)-ES。在前者中，μ个亲本制造λ个子代，所有解均参加生存竞争，选出最好的μ个作为下一代的亲本。在后者中，只有λ（ λ > μ ）个子代参加生存竞争，在每代中μ个亲本被完全取代。这就是说，对于每一代，每个解张成的生命是有限的。增加种群大小，就在固定数目的世代中增加了优化速率。
进化策略的基本技术
然后将其分量进行随机交换，构成子代新个体的各个分量，从而得出如下新个体：
(2) 中值重组。这种重组方式也是先随机选择两个父代个体，然后将父代个体各分量的平均值作为子代新个体的分量，构成的新个体为：
这时，新个体的各个分量兼容两个父代个体信息，而在离散重组中则只含有某一个父代个体的因子。

软件工程英文答案

Chapter 1 An Introduction to Software Engineering1. Why software engineering is important?软件工程由应对软件危机也产生，软件工程的发展极大地完善了我们的软件。

软件工程的研究使得我们对软件开发活动有个更深入的了解，并且已经找到了进行软件描述、设计和实现的有效方法。

软件工程中新的标记发和工具大大降低了制作大型、复杂系统的工作量2. What is software? What is software engineering?软件工程是一门工程学科，包括了软件开发的各个方面，从最初的系统描述一直到使用后的系统维护，都属于其学科范畴。

3. What is the difference between software engineering and computer science?计算机科学研究的是构成计算机和软件系统基础的有关理论和方法，耳软件工程则研究软件制作中的实际问题。

计算机科学侧重理论和基础; 软件工程侧重软件开发和交付的实际活动。

4. What are the attributes of good software?软件除了提供基本的功能，对用户来说是还应该是可维护的、可依赖的和可接受的。

可维护性，软件必须能够不断变化以满足变化；可依赖性，软件必须可以被信赖；有效性，软件不能浪费系统资源；可用性，使用起来比较容易5. What is CASE?CASE 工具是一些软件系统，被设计成支持软件过程中的常规活动，如编辑设计图表、检查图表的连贯性、跟踪已经运行的程序测试等。

6. What is the difference between software engineering and system engineering?系统工程侧重于计算机系统开发的所有方面，包括硬件、软件和处理工程。

软件工程是整个系统的一部分，它关心系统中基础软件、控制软件、应用软件和数据库的开发。

23个测试函数C语言代码(23个函数来自论文：Evolutionary Programming Made Faster)

//F1函数 Spheredouble calculation(double *sol){int i;double result=0;fit++; //标记评估次数for (i=0; i<dim; i++){result+= sol[i]*sol[i];}return result;}//***********************************//F2函数 Schwefel's P2.22double calculation(double *sol){int i;fit++;double result=0;double tmp1=0,tmp2=1.0;for(i=0;i<dim;i++){double temp=fabs(sol[i]);tmp1+=temp;tmp2*=temp;}result=tmp1+tmp2;return result;}//***********************************//F3函ˉ数簓 Quadricdouble calculation(double *sol){int i,j;fit++;double result=0;double tmp2=0.0;for(i=0;i<dim;i++){double tmp1=0.0;for(j=0;j<i+1;j++){tmp1+=sol[j];}tmp2+=tmp1*tmp1;}result=tmp2;return result;}//***********************************//F4函ˉ数簓double calculation(double *sol){int i,j;double result=fabs(sol[0]);fit++;for(i=1;i<dim;i++){if(result<fabs(sol[i])){result=fabs(sol[i]);}}return result;}//***********************************//F5函ˉ数簓 Rosenbrockdouble calculation(double *sol){int i,j;fit++;double result=0;double tmp1=0,tmp2=0;for(i=0;i<dim-1;i++){tmp1=100*(sol[i]*sol[i]-sol[i+1])*(sol[i]*sol[i]-sol[i+1]);tmp2=(sol[i]-1)*(sol[i]-1);result+=tmp1+tmp2;}return result;}//***********************************//F6函ˉ数簓 Stepdouble calculation(double *sol){int i;fit++;double result=0;for (i=0; i<dim; i++){result+=(floor(sol[i]+0.5))*(floor(sol[i]+0.5));}return result;}//***********************************//F7函ˉ数簓 Quadric Noisedouble calculation(double *sol){int i;fit++;double result=0;for (i=0; i<dim; i++){result+=(i+1)*sol[i]*sol[i]*sol[i]*sol[i];}result=result+1.0*rand()/RAND_MAX;return result;}//***********************************//F8函ˉ数簓 Schwefeldouble calculation(double *sol){int i;fit++;double result=0;for (i=0; i<dim; i++){result+=(-1*sol[i])*sin(sqrt(fabs(sol[i])));}return result;}//***********************************//F9函ˉ数簓 Rastrigrindouble calculation(double *sol){int i;fit++;double result=0;for (i=0; i<dim; i++){result+=(sol[i]*sol[i]-10*cos(2*pi*sol[i])+10);}return result;}//***********************************//F10函ˉ数簓 Ackley函ˉ数簓double calculation(double *sol){int i;fit++;double result=0;double tmp1=0.0,tmp2=0.0;for (i=0; i<dim; i++){tmp1+=sol[i]*sol[i];tmp2+=cos(2*pi*sol[i]);}result=20+exp(1)-20*exp(-0.2*sqrt(tmp1/dim))-exp(tmp2/dim);return result;}//***********************************//F11函ˉ数簓 griewangdouble calculation(double *sol){int i;fit++;double result=0;double temp1=0.0,temp2=1.0;for (i=0; i<dim; i++){temp1+=(sol[i]*sol[i])/4000;temp2*=cos(sol[i]/sqrt(i+1));}result=temp1-temp2+1;}//***********************************//F12函ˉ数簓 Generalized Penalizeddouble calculation(double *sol){int i;fit++;double x[dim];double result=0;double temp1=0.0,temp2=0.0;for (i=0; i<dim; i++){x[i]=1+(sol[i]+1)/4;if(sol[i]>10){temp1=100*(sol[i]-10)*(sol[i]-10)*(sol[i]-10)*(sol[i]-10);}else{if(sol[i]<-10){temp1=100*(-sol[i]-10)*(-sol[i]-10)*(-sol[i]-10)*(-sol[i]-10);}elsetemp1=0;}temp2+=temp1;}for(i=0;i<dim-1;i++){result+=(x[i]-1)*(x[i]-1)*(1+10*sin(pi*x[i+1])*sin(pi*x[i+1]));}result=pi/dim*(10*sin(pi*x[0])*sin(pi*x[0])+result+(x[dim-1]-1)*(x[dim-1]-1))+temp2;return result;}//***********************************//F13函ˉ数簓double calculation(double *sol){int i;double temp1=0.0,temp2=0.0;fit++;for (i=0; i<dim; i++){if(sol[i]>5){temp1=100*(sol[i]-5)*(sol[i]-5)*(sol[i]-5)*(sol[i]-5);}else{if(sol[i]<-5){temp1=100*(-sol[i]-5)*(-sol[i]-5)*(-sol[i]-5)*(-sol[i]-5);}elsetemp1=0;}temp2+=temp1;}for(i=0;i<dim-1;i++){result+=(sol[i]-1)*(sol[i]-1)*(1+sin(3.0*pi*sol[i+1])*sin(3.0*pi*sol[i+1]));}result=0.1*(sin(3.0*pi*sol[0])*sin(3.0*pi*sol[0])+result+(sol[dim-1]-1)*(1.0+1.0*si n(2.0*pi*sol[dim-1])))+temp2;return result;}//***********************************//F14函ˉ数簓double calculation(double sol[2]){int i,j;double top=0.0,tmp1=0.0,tmp2=0.0;fit++;double a[2][25]={{-32,-16,0,16,32,-32,-16,0,16,32,-32,-16,0,16,32,-32,-16,0,16,32,-32,-16,0,16,32},{-32,-32,-32,-32,-32,-16,-16,-16,-16,-16,0,0,0,0,0,16,16,16,16,16,32,32,32,32,32}};for(j=0;j<25;j++){top=0.0;for(i=0;i<D;i++)//这a里?D=2{tmp1=sol[i]-a[i][j];tmp1=pow(tmp1,(double)6);top=top+tmp1;}top=(j+1)+top;top=1.0/top;tmp2=tmp2+top;}top=1.0/500+tmp2;top=1.0/top;return top;}//***********************************//F15函ˉ数簓double calculation(double sol[4]){int i;fit++;double top=0.0,tmp1=0.0,tmp2=0.0;doublea[11]={0.1957,0.1947,0.1735,0.1600,0.0844,0.0627,0.0456,0.0342,0.0323,0.0235,0.0246};double b[11]={4.0,2.0,1.0,0.5,0.25,1.0/6,1.0/8,1.0/10,1.0/12,1.0/14,1.0/16};for(i=0;i<11;i++){tmp1=sol[0]*(b[i]*b[i]+b[i]*sol[1]);tmp2=1.0*tmp1/(b[i]*b[i]+b[i]*sol[2]+sol[3]);top=top+(a[i]-tmp2)*(a[i]-tmp2);}return top;}//***********************************//F16函ˉ数簓double calculation(double sol[2]){double top=0;fit++;top=4*pow(sol[0],(double)2)-2.1*pow(sol[0],(double)4)+1.0*pow(sol[0],(double)6)/3+sol[0 ]*sol[1]-4*pow(sol[1],(double)2)+4*pow(sol[1],(double)4);return top;}//***********************************//F17函ˉ数簓double calculation(double sol[2]){ double top=0;fit++;top=sol[1]-(5.1/(4*pi*pi))*pow(sol[0],(double)2)+(5.0/pi)*sol[0]-6;top=pow(top,(double)2);top=top+10.0*(1.0-1.0/(8*pi))*cos(sol[0])+10.0;return top;}//***********************************//F18函ˉ数簓double calculation(double sol[2]){fit++;double top=0,tmp1=0,tmp2=0;top=19.0-14.0*sol[0]+3.0*sol[0]*sol[0]-14*sol[1]+6.0*sol[0]*sol[1]+3.0*sol[1]*sol[1]; tmp1=(sol[0]+sol[1]+1)*(sol[0]+sol[1]+1);tmp2=18.0-32.0*sol[0]+12.0*sol[0]*sol[0]+48*sol[1]-36.0*sol[0]*sol[1]+27.0*sol[1]*sol[1 ];tmp2=30.0+(2.0*sol[0]-3.0*sol[1])*(2.0*sol[0]-3.0*sol[1])*tmp2;top=(1.0+tmp1*top)*tmp2;return top;}//***********************************//该?函ˉ数簓sol[D]是?一?个?四?维?函ˉ数簓，?搜?索÷范?围§：阰[0,1],最?优?值μ是?：阰-3.86//F19函ˉ数簓double calculation(double sol[D]){ int i,j;fit++;double top=0.0,tmp1=0.0;double c[4]={1,1.2,3,3.2};//这里a[4][D]和p[4][D]数据可能有些错误，正确的应该有4*4个数据，这里只有4*3个数据，不清楚是不是最后一个默认为0，大家在应用的时候要特别注意了double a[4][D]={{3,10,30},{0.1,10,35},{3,10,30},{0.1,10,35}};double p[4][D]={{0.3689,0.1170,0.2673},{0.4699,0.4387,0.7470},{0.1091,0.8732,0.5547},{0.03815,0.5743,0.8828}};for(i=0;i<4;i++){top=0.0;for(j=0;j<D;j++){top=top+a[i][j]*(sol[j]-p[i][j])*(sol[j]-p[i][j]);}top=-1.0*top;top=exp(top);tmp1=tmp1+c[i]*top;}tem1=-1.0*tmp1;return tem1;}//***********************************//F20函ˉ数簓double calculation(double sol[D]){int i,j;fit++;double top=0.0,tmp1=0.0;double c[4]={1,1.2,3,3.2};double a[4][D]={{10,3,17,3.5,1.7,8},{0.05,10,17,0.1,8,14},{3,3.5,1.7,10,17,8},{17,8,0.05,10,0.1,14}};double p[4][D]={{0.1312,0.1696,0.5569,0.0124,0.8283,0.5886},{0.2329,0.4135,0.8307,0.3736,0.1004,0.9991},{0.2348,0.1415,0.3522,0.2883,0.3047,0.6650},{0.4047,0.8828,0.8732,0.5743,0.1091,0.0381}};for(i=0;i<4;i++){top=0.0;for(j=0;j<D;j++){top=top+a[i][j]*(sol[j]-p[i][j])*(sol[j]-p[i][j]);}top=-1.0*top;top=exp(top);tmp1=tmp1+c[i]*top;}tem1=-1.0*tmp1;return tem1;}//***********************************//F21函ˉ数簓double calculation(double sol[D]){int i;fit++;double top=0.0,tmp1=0.0;double c[5]={0.1,0.2,0.2,0.4,0.4};double a[5][4]={{4.0,4.0,4.0,4.0},{1.0,1.0,1.0,1.0},{8.0,8.0,8.0,8.0},{6.0,6.0,6.0,6.0},{3.0,7.0,3.0,7.0}};for(i=0;i<5;i++){tmp1=(sol[0]-a[i][0])*(sol[0]-a[i][0])+(sol[1]-a[i][1])*(sol[1]-a[i][1])+(sol[2]-a[i][2])*(sol[2]-a[i][2])+(sol[3]-a[i][3])*(sol[3]-a[i][3]);tmp1=tmp1+c[i];tmp1=1.0/tmp1;top=top+tmp1;}top=-1.0*top;return top;}//***********************************//F22函ˉ数簓double calculation(double sol[D]){int i;fit++;double top=0.0,tmp1=0.0;double c[7]={0.1,0.2,0.2,0.4,0.4,0.6,0.3};double a[7][4]={{4.0,4.0,4.0,4.0},{1.0,1.0,1.0,1.0},{8.0,8.0,8.0,8.0},{6.0,6.0,6.0,6.0},{3.0,7.0,3.0,7.0},{2.0,9.0,2.0,9.0},{5.0,5.0,3.0,3.0}};for(i=0;i<7;i++){tmp1=(sol[0]-a[i][0])*(sol[0]-a[i][0])+(sol[1]-a[i][1]) *(sol[1]-a[i][1])+(sol[2]-a[i][2])*(sol[2]-a[i][2])+(sol[3]-a[i][3])*(sol[3]-a[i][3]);tmp1=tmp1+c[i];tmp1=1/tmp1;top=top+tmp1;}top=0.0-top;return top;}//***********************************//F23函ˉ数簓double calculation(double sol[D]){int i;fit++;double top=0.0,tmp1=0.0;double c[10]={0.1,0.2,0.2,0.4,0.4,0.6,0.3,0.7,0.5,0.5};double a[10][4]={{4.0,4.0,4.0,4.0},{1.0,1.0,1.0,1.0},{8.0,8.0,8.0,8.0},{6.0,6.0,6.0,6.0},{3.0,7.0,3.0,7.0},{2.0,9.0,2.0,9.0},{5.0,5.0,3.0,3.0},{8.1,1.0,8.0,1.0},{6.0,2.0,6.0,2.0},{7.0,3.6,7.0,3.6}};for(i=0;i<10;i++){tmp1=(sol[0]-a[i][0])*(sol[0]-a[i][0])+(sol[1]-a[i][1])*(sol[1]-a[i][1])+(sol[2]-a[i][2 ])*(sol[2]-a[i][2])+(sol[3]-a[i][3])*(sol[3]-a[i][3]);tmp1=tmp1+c[i];tmp1=1.0/tmp1;top=top+tmp1;}top=-1.0*top;return top;}。

Evolutionary programming made faster

Evolutionary Programming Made Faster Xin Yao,Senior Member,IEEE,Yong Liu,Student Member,IEEE,and Guangming LinAbstract—Evolutionary programming(EP)has been applied with success to many numerical and combinatorial optimization problems in recent years.EP has rather slow convergence rates, however,on some function optimization problems.In this paper, a“fast EP”(FEP)is proposed which uses a Cauchy instead of Gaussian mutation as the primary search operator.The re-lationship between FEP and classical EP(CEP)is similar to that between fast simulated annealing and the classical version. Both analytical and empirical studies have been carried out to evaluate the performance of FEP and CEP for different function optimization problems.This paper shows that FEP is very good at search in a large neighborhood while CEP is better at search in a small local neighborhood.For a suite of23benchmark problems,FEP performs much better than CEP for multimodal functions with many local minima while being comparable to CEP in performance for unimodal and multimodal functions with only a few local minima.This paper also shows the relationship between the search step size and the probability ofﬁnding a global optimum and thus explains why FEP performs better than CEP on some functions but not on others.In addition,the importance of the neighborhood size and its relationship to the probability of ﬁnding a near-optimum is investigated.Based on these analyses, an improved FEP(IFEP)is proposed and tested empirically. This technique mixes different search operators(mutations).The experimental results show that IFEP performs better than or as well as the better of FEP and CEP for most benchmark problems tested.Index Terms—Cauchy mutations,evolutionary programming, mixing operators.I.I NTRODUCTIONA LTHOUGH evolutionary programming(EP)wasﬁrstproposed as an approach to artiﬁcial intelligence[1],it has been recently applied with success to many numerical and combinatorial optimization problems[2]–[4].Optimization by EP can be summarized into two major steps:1)mutate the solutions in the current population;2)select the next generation from the mutated and thecurrent solutions.These two steps can be regarded as a population-based version of the classical generate-and-test method[5],where mutation isManuscript received October30,1996;revised February3,1998,August 14,1998,and January7,1999.This work was supported in part by the Australian Research Council through its small grant scheme and by a special research grant from the University College,UNSW,ADFA.X.Yao was with the Computational Intelligence Group,School of Computer Science,University College,The University of New South Wales,Australian Defence Force Academy,Canberra,ACT,Australia2600.He is now with the School of Computer Science,University of Birmingham,Birmingham B15 2TT U.K.(e-mail:X.Yao@).Y.Liu and G.Lin are with the Computational Intelligence Group,School of Computer Science,University College,The University of New South Wales, Australian Defence Force Academy,Canberra,ACT,Australia2600(e-mail: liuy@.au;glin@.au).Publisher Item Identiﬁer S1089-778X(99)ed to generate new solutions(offspring)and selection is used to test which of the newly generated solutions should survive to the next generation.Formulating EP as a special case of the generate-and-test method establishes a bridge between EP and other search algorithms,such as evolution strategies,genetic algorithms,simulated annealing(SA),tabu search(TS),and others,and thus facilitates cross-fertilization among different research areas.One disadvantage of EP in solving some of the multimodal optimization problems is its slow convergence to a good near-optimum(e.g.,paper and the CEP used to solve it.The CEP algorithm given follows suggestions from Fogel[3],[6]and B¨a ck and Schwefel [7].Section III describes the FEP and its implementation. Section IV gives the23functions used in our studies.Section V presents the experimental results and discussions on FEP and CEP.Section VI investigates FEP with different scale parameters for its Cauchy mutation.Section VII analyzes FEP and CEP and explains the performance difference between FEP and CEP in depth.Based on such analyses,an improved FEP(IFEP)is proposed and tested in Section VIII.Finally, Section IX concludes with some remarks and future research directions.II.F UNCTION O PTIMIZATION BYC LASSICAL E VOLUTIONARY P ROGRAMMINGA global minimization problem can be formalized as apairis a bounded setonsuchthat.More speciﬁcally,it is required toﬁndandoes not need to be continuous but it must bebounded.This paper only considers unconstrained functionoptimization.Fogel[3],[8]and B¨a ck and Schwefel[7]have indicatedthat CEP with self-adaptive mutation usually performs betterthan CEP without self-adaptive mutation for the functions theytested.Hence the CEP with self-adaptive mutation will beinvestigated in this paper.According to the description byB¨a ck and Schwefel[7],the CEP is implemented as followsin this study.11)Generate the initial populationof.Each individual is taken as a pair of real-valuedvectors,,where,of the population based on the objectivefunction,.3)Eachparent,creates a singleoffspring-thcomponent of thevectors,respectively..Thefactorsand[7],[6].1A recent study by Gehlhaar and Fogel[9]showed that swapping the orderof(1)and(2)may improve CEP’s performance.4)Calculate theﬁtness of eachoffspring.5)Conduct pairwise comparison over the union of parentsandoffspring.Foreachindividual,individuals out ofand,that have the most wins to be parentsof the next generation.7)Stop if the halting criterion is satisﬁed;otherwise,resembles that of the Gaussian densityfunction but approaches the axis so slowly that an expectationdoes not exist.As a result,the variance of the Cauchydistribution is inﬁnite.Fig.1shows the difference betweenCauchy and Gaussian functions by plotting them in the samescale.The FEP studied in this paper is exactly the same as theCEP described in Section II except for(1)which is replacedby the following[11]and is generated anew for each valueofparison between Cauchy and Gaussian density functions.IV.B ENCHMARK F UNCTIONSTwenty-three benchmark functions [2],[7],[12],[13]were used in our experimental studies.This number is larger than that offered in many other empirical study papers.This is necessary,however,since the aim here is not to show FEP is better or worse than CEP,but to ﬁnd out when FEP is better (or worse)than CEP and why.Wolpert and Macready [14],[15]have shown that under certain assumptions no single search algorithm is best on average for all problems.If the number of test problems is small,it would be very difﬁcult to make a generalized ing too small a test set also has the potential risk that the algorithm is biased (optimized)toward the chosen problems,while such bias might not be useful for other problems of interest.The 23benchmark functions are given in Table I.A more detailed description of each function is given in the Appendix.Functionsare high-dimensional problems.Functions aremultimodal functions where the number of local minima increases exponentially with the problem dimension [12],[13].They appear to be the most difﬁcult class of problems for manyoptimization algorithms (including EP).Functions–are low-dimensional functions which have only a few local minima [12].For unimodal functions,the convergence rates of FEP and CEP are more interesting than the ﬁnal results of optimization as there are other methods which are speciﬁcally designed to optimize unimodal functions.For multimodal functions,the ﬁnal results are much more important since they reﬂect an algorithm’s ability of escaping from poor local optima and locating a good near-global optimum.V.E XPERIMENTAL S TUDIESA.Experimental SetupIn all experiments,the same self-adaptive method [i.e.,(2)],the same populationsize,and the sameinitial population were used for both CEP and FEP.These parameters follow the suggestions from B¨a ck and Schwefel [7]and Fogel [2].The initial population was generated uniformly at random in the range as speciﬁed in Table I.B.Unimodal FunctionsThe ﬁrst set of experiments was aimed to compare the convergence rate of CEP and FEP forfunctionsTABLE IT HE23B ENCHMARK F UNCTIONS U SED IN O UR E XPERIMENTAL S TUDY,W HERE n I S THE D IMENSION OF THE F UNCTION,f minI S THE M INIMUM V ALUE OF THE F UNCTION,AND S R n.A D ETAILED D ESCRIPTION OF A LL F UNCTIONS I S G IVEN IN THE A PPENDIXTABLE IIC OMPARISON B ETWEEN CEP AND FEP ON f1–f7.A LL R ESULTS H A VE B EEN A VERAGED OVER50R UNS,W HERE“M EAN B EST”I NDICATES THEM EAN B EST F UNCTION V ALUES F OUND IN THE L AST G ENERATION,AND“S TD D EV”S TANDS FOR THE S TANDARD D EVIATIONof the global optimum.CEP is capable of maintaining itsnearly constant convergence rate because its search is muchmore localized than FEP.The different behavior of CEP andFEP on(a)(b)parison between CEP and FEP on f1–f4.The vertical axis is the function value,and the horizontal axis is the number of generations. The solid lines indicate the results of FEP.The dotted lines indicate the results of CEP.(a)shows the best results,and(b)shows the average results.Both were averaged over50runs.(a)(b)parison between CEP and FEP on f 5–f 7.The vertical axis is the function value,and the horizontal axis is the number of generations.The solid lines indicate the results of FEP.The dotted lines indicate the results of CEP.(a)shows the best results,and (b)shows average results.Both were averaged over 50runs.generating long jumps than CEP.Such long jumps enable FEP to move from one plateau to a lower one with relative ease.The rapid convergence of FEP shown in Fig.3supports our explanations.C.Multimodal Functions1)Multimodal Functions with Many Local Min-ima:Multimodal functions having many local minimaare often regarded as being difﬁcult tooptimize.are such functions where the number of local minima increases exponentially as the dimension of the function increases.Fig.4shows the two-dimensional versionofwere all set to 30in our ex-periments.Table III summarizes the ﬁnal results of CEP and FEP.It is obvious that FEP performs signiﬁcantly better than CEP consistently for these functions.CEP appeared to become trapped in a poor local optimum and unable to escape from it due to its smaller probability of making long jumps.According to the ﬁgures we plotted to observe the evolutionary process,CEP fell into a poor local optimum quite early in a run whileFig.4.The two-dimensional version of f 8.TABLE IIIC OMPARISON B ETWEEN CEP AND FEP ON f 8–f 13.T HE R ESULTS A RE A VERAGED OVER 50R UNS ,W HERE “M EAN B EST ”I NDICATESTHEM EAN B EST F UNCTION V ALUES F OUND IN THE L AST G ENERATION AND “S TD D EV ”S TANDS FOR THE S TANDARD DEVIATIONTABLE IVC OMPARISON B ETWEEN CEP AND FEP ON f 14–f 23.T HE R ESULTS A RE A VERAGED OVER 50R UNS ,W HERE “M EAN B EST ”I NDICATESTHEM EAN B EST F UNCTION V ALUES F OUND IN THE L AST G ENERATION AND “S TD D EV ”S TANDS FOR THE S TANDARD DEVIATIONFEP was able to improve its solution steadily for a long time.FEP appeared to converge at least at a linear rate with respect to the number of generations.An exponential convergence rate was observed for some problems.2)Multimodal Functions with Only a Few Local Minima:To evaluate FEP more fully,additional multimodal benchmarkfunctions were also included in our experiments,i.e.,–,where the number of local minima for each function and thedimension of the function are small.Table IV summarizes the results averaged over 50runs.Interestingly,quite different results have been observed forfunctions–.For six(i.e.,–)out of ten functions,no statistically signiﬁcant difference was found between FEP and CEP.In fact,FEP performed exactly the same as CEP forTABLE VC OMPARISON B ETWEEN CEP AND FEP ON f 8TO f 13WITH n =5.T HE R ESULTS A RE A VERAGED OVER 50R UNS ,W HERE “M EAN B EST ”I NDICATES THE M EAN B ESTF UNCTION V ALUES F OUND IN THE L ASTG ENERATION AND “S TD D EV ”S TANDS FOR THE S TANDARD DEVIATIONand .For the four functions where there was statistically signiﬁcant difference between FEP and CEP,FEP performedbetterfor,but was outperformed by CEPfor–.The consistent superiority of FEP over CEP forfunctions was not observed here.The major difference betweenfunctionsand–is thatfunctions–appear to be simplerthandue to their low dimensionalities and a smaller number of local minima.To ﬁnd out whether or not the dimensionality of functions plays a signiﬁcant role in deciding FEP’s and CEP’s behavior,another set of experiments on thelow-dimensionalwas carried out.The resultsaveraged over 50runs are given in Table V.Very similar results to the previous ones onfunctionswere obtained despite the large difference in the dimensionality of functions.FEP still outperforms CEP signiﬁcantly evenwhen the dimensionality offunctionsislow inits Cauchy mutation.This value was used for its simplicity.To examine the impact of differentvalues for the Cauchy mutation.Seven benchmark functions from the three different groups in Table I were used in these experiments.The setup of these experiments is exactly the same as before.Table VI shows the average results over 50independent runs of FEP for different parameters.These results showthatis problemdependent.As analyzed later in Section VII-A,the optimalfor a given problem.A good approach toTABLE VIT HE M EAN B EST S OLUTIONS F OUND BY FEP U SING D IFFERENT S CALE P ARAMETER t IN THE C AUCHY M UTATION FOR F UNCTIONS f 1(1500);f 2(2000);f 10(1500);f 11(2000);f 21(100);f 22(100);AND f 23(100).THE V ALUES IN “()”I NDICATE THE N UMBER OF G ENERATIONS U SED INFEP.A LL R ESULTS H A VE B EEN A VERAGED OVER 50RUNSdeal with this issue is to use self-adaptation so thatvalues in a population so that the whole popu-lation can search both globally and locally.The percentage of each type of Cauchy mutation will be self-adaptive,rather than ﬁxed.Hence the population may emphasize either global or local search depending on different stages in the evolutionary process.VII.A NALYSIS OF F AST AND C LASSICALE VOLUTIONARY P ROGRAMMINGIt has been pointed out in Section III that Cauchy mutation has a higher probability of making long jumps than Gaussian mutation due to its long ﬂat tails shown in Fig.1.In fact,the likelihood of a Cauchy mutation generating a larger jump than a Gaussian mutation can be estimated by a simple heuristic argument.Fig.5.Evolutionary search as neighborhood search,where x3is the global optimum and >0is the neighborhood size. is a small positive number(0< <2 ).It is well known thatifthen(i.e.,It is obvious that Gaussian mutation is much more localizedthan Cauchy mutation.Similar results can be obtained for Gaussian distributionwithexpectationandvarianceis often regardedas the step size of the Gaussian mutation.Fig.5illustrates thesituation.Thederivative can be used toevaluate the impactof.Accordingto the mean value theorem for deﬁnite integrals[17,p.322],there exists anumber suchthat(7)That is,thelarger willbe,ifis,thesmaller will be.Similar analysis can be carried out for Cauchy mutationin FEP.Denote the Cauchy distribution deﬁned by(3)as.Then wehavemay not be the same as that in(6)and(7).It is obviousthat(9)That is,thelarger will be,ifis,thesmaller will be.Since could be regarded as search step sizes forGaussian and Cauchy mutations,the above analyses show thata large step size is beneﬁcial(i.e.,increases the probabilityofﬁnding a near-optimal solution)only when the distancebetween the neighborhoodofand.The analytical results explain why FEP achieved betterresults than CEP for most of the benchmark problems wetested,because the initial population was generated uniformlyat random in a relatively large space and was far away from theglobal optimum on average.Cauchy mutation is more likely togenerate larger jumps than Gaussian mutation and thus betterin such cases.FEP would be less effective than CEP,however,near the small neighborhood of the global optimum becauseGaussian mutation’s step size is smaller(smaller is better inthis case).The experimental results onfunctionsvalue for its Cauchy mutation would perform better wheneverCEP outperforms FEPwithfor a problem,it implies that this FEP’s search stepsize may be too large.In this case,using a Cauchy mutationwith a smaller(i.e.,Shekel-5)wasused here since it appears to pose some difﬁculties to FEP.First we made the search points closer to the global optimumby generating the initial population uniformly at random inthe rangeof ratherthan andrepeated our previous experiments.(The global optimumofisat.)Such minor variation to the experiment isexpected to improve the performance of both CEP and FEPsince the initial search points are closer to the global optimum.Note that both Gaussian and Cauchy distributions have higherprobabilities in generating points around zero than those ingenerating points far away from zero.Theﬁnal experimental results averaged over50runs aregiven in Table VII.Fig.6shows the results of CEP and FEP.It is quite clear that the performance of CEP improved muchmore than that of FEP since the smaller average distancebetween search points and the global optimum favors a smallstep size.The mean best of CEP improved signiﬁcantly from7.90,while that of FEP improved only from5.62.Then three more sets of experiments were conducted wherethe search space was expanded ten times,100times,and1000times,i.e.,the initial population was generated uniformly atrandom in the rangeofC OMPARISON OF CEP’S AND FEP’S F INAL R ESULTS ON f21W HEN THE I NITIAL P OPULATION I S G ENERATED U NIFORMLY AT R ANDOM IN THE R ANGE OF0 x i 10AND2:5 x i 5:5.T HE R ESULTS W ERE A VERAGED OVER50R UNS,W HERE“M EAN B EST”I NDICATES THE M EAN B EST F UNCTION V ALUESF OUND IN THE L ASTG ENERATION,AND“S TD D EV”S TANDS FOR THE S TANDARD D EVIATION.T HE N UMBER OF G ENERATIONS FOR E ACH R UN W AS100(a)(b)parison between CEP and FEP on f21when the initial population is generated uniformly at random in the range of2:5 x i 5:5.The solid lines indicate the results of FEP.The dotted lines indicate the results of CEP.(a)shows the best result,and(b)shows the average result.Both were averaged over50runs.The horizontal axis indicates the number of generations.The vertical axis indicates the function value.space is expected to make the problem more difﬁcult and thusmake CEP and FEP less efﬁcient.The results of the sameexperiment averaged over50runs are shown in Table VIIIand Figs.7–9.It is interesting to note that the performance ofFEP was less affected by the larger search space than CEP.When the search space was increased todisappeared.There was no statistically signiﬁcant differencebetween CEP and FEP.When the search space was increasedfurther to,FEP even outperformed CEPsigniﬁcantly.It is worth pointing out that a population size of100and the maximum number of generations of100are verysmall numbers for such a huge search space.The populationmight not have converged by the end of generation100.This,however,does not affect our conclusion.The experimentsstill show that Cauchy mutation performs much better thanGaussian mutation when the current search points are far awayfrom the global optimum.Even if’s were not multiplied by10,100,and1000,similar results can still be obtained as long as the initialpopulation was generated uniformly at random in the rangeofC OMPARISON OF CEP’S AND FEP’S F INAL R ESULTS ON f21W HEN THE I NITIAL P OPULATION I S G ENERATED U NIFORMLY AT R ANDOM IN THER ANGE OF0 x i 10;0 x i 100;0 x i 1000;AND0 x i 10000,AND a i’S W ERE M ULTIPLIED BY10,100,AND1000.T HE R ESULTS W ERE A VERAGED OVER50R UNS,W HERE“M EAN B EST”I NDICATES THE M EAN B EST F UNCTION V ALUES F OUND IN THEL AST G ENERATION,AND“S TD D EV”S TANDS FOR THE S TANDARD D EVIATION.T HE N UMBER OF G ENERATIONS FOR E ACH R UN W AS100.(a)(b)parison between CEP and FEP on f21when the initial population is generated uniformly at random in the range of0 x i 100and a i’s were multiplied by ten.The solid lines indicate the results of FEP.The dotted lines indicate the results of CEP.(a)shows the best result,and(b)shows the average result.Both were averaged over50runs.The horizontal axis indicates the number of generations.The vertical axis indicates the function value.(a)(b)parison between CEP and FEP on f21when the initial population is generated uniformly at random in the range of0 x i 1000and a i’s were multiplied by100.The solid lines indicate the results of FEP.The dotted lines indicate the results of CEP.(a)shows the best result,and(b)shows the average result.Both were averaged over50runs.The horizontal axis indicates the number of generations.The vertical axis indicates the function value.parison between CEP and FEP on f21when the initial population is generated uniformly at random in the range of0 x i 10000and a i’s were multiplied by1000.The solid lines indicate the results of FEP.The dotted lines indicate the results of CEP.(a)shows the best result,and(b)shows the average result.Both were averaged over50runs.The horizontal axis indicates the number of generations.The vertical axis indicates the function value.TABLE IXC OMPARISON OF CEP’S AND FEP’S F INAL R ESULTS ON f21W HEN THE I NITIAL P OPULATION I S G ENERATED U NIFORMLY AT R ANDOM INTHE R ANGE OF0 x i 10;0 x i 100;0 x i 1000;and0 x i 10000.a i’S W ERE U NCHANGED.T HE R ESULTS W ERE A VERAGED OVER50R UNS,W HERE“M EAN B EST”I NDICATES THE M EAN B EST F UNCTION V ALUES F OUND IN THE L ASTG ENERATION,AND“S TD D EV”S TANDS FOR THE S TANDARD D EVIATION.T HE N UMBER OF G ENERATIONS FOR E ACH R UN W AS100and the time used toﬁnd the solution?This issue can be approached from the point of view of neighborhood size,i.e.,on the probability of generating a near-optimum in that neighborhood can be worked out.(The probability ofﬁnding a near-optimum would be the same as that of generating it when the elitism is used.)Although not an exact answer to the issue,the following analysis does provide some insights into such impact.Similar to the analysis in Section VII-A7,the following is true according to the mean value theorem for deﬁnite integrals[17,p.322]:forThat is,for)is governed by thetermThatis,grows exponentially fasteras increases.TABLE XC OMPARISON A MONG IFEP,FEP,AND CEP ON F UNCTIONS f1;f2;f10;f11;f21;f22;AND f23.A LL R ESULTS H A VE B EENA VERAGED OVER50R UNS,W HERE“M EANB EST”I NDICATES THE M EAN B EST F UNCTION V ALUES F OUND IN THE L AST GENERATIONA similar analysis can be carried out for Cauchy mutationusing its density function,i.e.,(3).Let the density functionbe.ForHence the probability of generating a near-optimum in theneighborhood always increases as the neighborhood size in-creases.While this conclusion is quite straightforward,it isinteresting to note that the rate of increase in the probabilitydiffers signiﬁcantly between Gaussian and Cauchy mutationsince.VIII.A N I MPROVED F AST E VOLUTIONARY P ROGRAMMINGThe previous analyses show the beneﬁts of FEP and CEPin different situations.Generally,Cauchy mutation performsbetter when the current search point is far away from theglobal minimum,while Gaussian mutation is better atﬁndinga local optimum in a good region.It would be ideal ifCauchy mutation is used when search points are far away fromthe global optimum and Gaussian mutation is adopted whensearch points are in the neighborhood of the global optimum.Unfortunately,the global optimum is usually unknown inpractice,making the ideal switch from Cauchy to Gaussianmutation very difﬁcult.Self-adaptive Gaussian mutation[7],[2],[8]is an excellent technique to partially address theproblem.That is,the evolutionary algorithm itself will learnwhen to“switch”from one step size to another.There is roomfor further improvement,however,to self-adaptive algorithmslike CEP or even FEP.This paper proposes an improved FEP(IFEP)based onmixing(rather than switching)different mutation operators.The idea is to mix different search biases of Cauchy andGaussian mutations.The importance of search biases has beenpointed out by some earlier studies[18,pp.375–376].Theimplementation of IFEP is very simple.It differs from FEPand CEP only in Step3of the algorithm described in SectionII.Instead of using(1)(for CEP)or(4)(for FEP)alone,IFEPgenerates two offspring from each parent,one by Cauchy mu-tation and the other by Gaussian.The better one is then chosenas the offspring.The rest of the algorithm is exactly the sameas FEP and CEP.Chellapilla[19]has recently presented somemore results on comparing different mutation operators in EP.A.Experimental StudiesTo carry out a fair comparison among IFEP,FEP,andCEP,the population size of IFEP was reduced to half ofthat of FEP or CEP in all the following experiments,sinceeach individual in IFEP generates two offspring.ReducingIFEP’s population size by half,however,actually puts IFEPat a slight disadvantage because it does not double the timefor any operators(such as selection)other than mutations.Nevertheless,such comparison offers a good and simplecompromise.IFEP was tested in the same experimental setup as before.For the sake of clarity and brevity,only some representativefunctions(out of23)from each group were tested.Functionsand are multimodal functions with many local minima.Functions–are multimodal functions with only a fewlocal minima and are particularly challenging to FEP.Table Xsummarizes theﬁnal results of IFEP in comparison with FEPand CEP.Figs.10and11show the results of IFEP,FEP,andCEP.B.DiscussionsIt is very clear from Table X that IFEP has improved FEP’sperformance signiﬁcantly for all test functions exceptfor.Even in the caseof,IFEP is better than FEP for25out of50runs.In other words,IFEP’s performance is still rather closeto FEP’s and certainly better than CEP’s(35out of50runs)on.These results show that IFEP continues to perform(a)(b)parison among IFEP,FEP,and CEP on functions f 1;f 2;f 10;and f 11.The vertical axis is the function value,and the horizontal axis is the number of generations.The solid lines indicate the results of IFEP.The dashed lines indicate the results of FEP.The dotted lines indicate the results of CEP.(a)shows the best results,and (b)shows the average results.All were averaged over 50runs.at least as well as FEP on multimodal functions with many minima and also performs very well on unimodal functions and multimodal functions with only a few local minima with which FEP has difﬁculty handling.IFEP achieved performance similar to CEP’s on these functions.For the two unimodal functions where FEP is outperformed by CEP signiﬁcantly,IFEP performs better than CEPon–,the difference be-tween IFEP and CEP is much smaller than that between FEP and CEP.IFEP has improved FEP’s performance signiﬁcantly。

进化计算综述

2.进化计算的起源运用达尔文理论解决问题的思想起源于20世纪50年代。

20世纪60年代，这一想法在三个地方分别被发展起来。

在德国，Ingo Rechenberg 和Hans-Paul Schwefel提出了进化策略（Evolution strategies）。

这些理论大约独自发展了15年。

到了20世纪90年代初，遗传编程（Genetic programming）这一分支也被提出，进化计算作为一个学科开始正式出现。

四个分支交流频繁，取长补短，并融合出了新的进化算法，促进了进化计算的巨大发展。

Nils Aall Barricelli在20世纪六十年代开始进行用进化算法和人工生命模拟进化的工作。

Alex Fraser发表的一系列关于模拟人工选择的论文大大发展了这一工作。

[1]Ingo Rechenberg在上世纪60 年代和70 年代初用进化策略来解决复杂的工程问题的工作使人工进化成为广泛认可的优化方法。

进化算法及其在数值计算中的应用

进化算法及其在数值计算中的应用
s 假设群体中的粒子数为，群体中所有的粒子所飞过的最好
位置为 Pg (t) ，称为全局最好位置，则：
Pg (t)
P0 (t), P1(t),, Ps (t) f (Pg (t)) min f (P0(t)), f (P1(t)),, f (Ps (t))
有了上面的定义，基本粒子群算法的进化方程可描述为：
进化算法及其在数值计算中的应用
遗传算法是一种宏观意义下的仿生算法，它模仿的机制是一切生命与智能的产生与进化过程。遗传算法通过模拟达尔文 “优胜劣汰、适者生存”的原理，激励好的结构；通过模拟
孟德尔遗传变异理论，在迭代过程中保持已有的结构，同时寻找更好的结构。适应度：遗传算法中使用适应度这个概念来度量群体中的每个个体在优化计算中可能达到或接近最优解的程度。适应度较高的个体遗传到下一代的概率较大，而适应度较低的个体遗传到下一代的概率相对较小。度量个体适应度的函数称为适应度函数（Fitness Function）。
单点交叉：
A:1 0 1 1 0 1 1 0 0 0 单点交叉 A : 1 0 1 1 0 1 1 0
B:0 1 1 0 1 0 0 1 1 1
B : 0 1 1 0 1 0 0 1
11 00
交叉点
算术交叉：
X X
t 1 A
t 1 B
X X
t B
t A
(1 )X (1 )X
t A
t B
进化算法及其在数值计算中的应用
限定于一定范围内，即 vij [vmax , vmax ] 。微粒的最大速度vmax 取决于当前位置与最好位置间区域的分辨率。若 vmax 太高，则微粒可能会飞过最好解；若 vmax 太小，则又将导致微粒移动速度过慢而影响搜索效率；而且当微粒聚集到某个较好解

Geatpy进化算法遗传算法

第二次是常被称为“重插入”或“环境选择”的选择，它是指在个体经过交叉、变异等进化操作所形成的子代（或称“育种个体”）后用某种方法来保留到下一代从而形成新一代种群的过程。这个选择过程对应的是生物学中的” 自然选择”。它可以是显性地根据适应度（再次注意：适应度并不等价于目标函数值）来进行选择的，也可以是隐性地根据适应度（即不刻意去计算个体适应度）来选择。例如在多目标优化的 NSGA-II 算法 [1] 中，父代与子代合并后，处于帕累托分层中第一层级的个体以及处于临界层中的且拥挤距离最大的若干个个体被保留到下一代。这个过程就没有显性地去计算每个个体的适应度。
算如下：
i−1 F itnessi = 2 − SP + 2 (SP − 1) N ind − 1
线性排序中选择压力SP 的值必须在 [1.0,2.0] 之间。
文献 [1] 中有这种线性排序的详细分析。其选择强度、多样性损失、选择方差 (这些
概念详见下一节) 的计算如下：
选择强度：
SelInt (SP ) = SP√− 1 π
进化算法
序言进化算法 (Evolutionary Algorithm, EA) 是一类通过模拟自然界生物自然选择和自然
进化的随机搜索算法。与传统搜索算法如二分法、斐波那契法、牛顿法、抛物线法等相比，进化算法有着高鲁棒性和求解高度复杂的非线性问题 (如 NP 完全问题) 的能力。
在过去的 40 年中，进化算法得到了不同的发展，现主要有三类： 1) 主要由美国 J. H. Holland 提出的的遗传算法 (Genetic Algorithm, GA)； 2) 主要由德国 I. Rechenberg 提出的进化策略 (Evolution strategies, ES)； 3) 主要由美国的 L. J. Fogel 提出的进化规划 (Evolutionary Programming, EP)。三种进化算法都是受相同的自然进化原则的启发下创立的，文献 [1] 以及国内的诸多资料也有详细的介绍。除此之外，进化算法还有差分进化 (Differential Evolution)、基因表达式编程 (Gene Expression Programming) 等众多分支。本文档只介绍经典的遗传算法、差分进化算法和多目标进化优化算法，不对众多改进的进化算法以及其他分支作详细介绍，如有需要进行相关研究的可以参考相关的专业和权威的文献。文档第一章是有关遗传算法的概述和基本框架；第二章介绍了编码；第三章是关于适应度的计算；第四章讲述了选择算法；在第五章中，介绍了不同的重组算法；第六章解释了如何变异；第七章详细讲解了与多目标优化有关的概念。最后值得一提的是，虽然进化算法在近 20 年来已经得到了快速的发展，在当今已经比较成熟，在金融、工程、信息学、数学等领域已经有广泛的应用，但是，众多新兴的进化算法 (如差分进化算法等) 以及不断改进和完善的拥有高维、多目标问题求解能力的进化优化算法等等，正给进化算法注入源源不断的新活力。与此同时，深度神经网络的蓬勃发展让进化算法有了一个更加前沿和广阔的前景——神经进化。量子计算机的出现，也使得拥有高度并行能力的进化算法有着更大的潜能。

遗传算法综述

遗传算法综述遗传算法是计算数学中用于解决最优化的搜索算法，是进化算法的一种。

进化算法最初是借鉴了进化生物学中的一些现象而发展起来的，这些现象包括遗传、突变、自然选择以及杂交等。

在阅读了一些相关资料后，我整理出这篇综述，将通过五个部分来介绍遗传算法以及其在计算机科学领域的相关应用、一、起源和发展分支尝试性地将生物进化过程在计算机中模拟并用于优化问题求解开始于20世纪50年代末，其目的是将生物进化的思想引入许多工程问题中而成为一种优化工具，这些开拓性的研究工作形成了遗传算法的雏形。

但当时的研究进展缓慢，收效甚微。

原因是由于缺少一种通用的编码方式，人们只有通过变异才能改变基因结构，而无法使用交叉，因而增加了迭代次数。

同时算法本身需要较大的计算量，当时的计算机速度便无法满足要求，因而限制了这一仿生过程技术的迅速发展。

20世纪60年代中期，Holland在Fraser和Bremermann等人研究成果的基础上提出了位串编码技术，这种编码技术同时适用于变异操作和交叉操作。

遗传算法的真正产生源于20世纪60年代末到70年代初，美国Michigan大学的Holland教授在设计人工适应系统中开创性地使用了一种基于自然演化原理的搜索机制，并于1975年出版了著名的专著“Adaptation in Natural andArtificial Systems”，这些有关遗传算法的基础理论为遗传算法的发展和完善奠定了的基础。

同时，Holland教授的学生De Jong首次将遗传算法应用于函数优化中，设计了遗传算法执行策略和性能评价指标，他挑选的5个专门用于遗传算法数值实验的函数至今仍被频繁使用，而他提出的在线(on-line)和离线(off-line)指标则仍是目前衡量遗传算法优化性能的主要手段。

在Holland教授和他的学生与同事De Jong进行大量有关遗传算法的开创性工作的同时，德国柏林工业大学的Rechenberg和Schwefel等在进行风洞实验时，为了对描述物体形状的参数进行优化以获得更好的实验数据，将变异操作引入计算模型中，获得了意外的优良效果。

基于进化计算的机器学习优化方法

基于进化计算的机器学习优化方法一、引言在当今数字化时代，人工智能越来越成为了各个领域的研究热点。

而其中，机器学习作为人工智能的核心组成部分，更是备受关注。

而在机器学习的过程中，算法优化的方法就显得尤为重要。

近年来，一种新的优化算法——基于进化计算的机器学习优化方法在学术界取得了不错的成果，成为了研究的热点。

进化算法通过将群体个体的基因进行随机交叉、变异和选择，模拟生物在自然演化中的生存竞争过程，不断寻找最优解，使得算法具有良好的全局搜索能力和适用范围。

二、基于进化计算的机器学习优化方法1. 进化计算概述进化计算，顾名思义是模拟生物进化过程，通过模仿生物间的遗传变异、适应度评价、天然选择等模式进行计算，从而不断产生新一代优质解决方案。

根据具体实现方式分为：遗传算法(Genetic Algorithm,GA)；进化策略(Evolutionary Strategies,ES)；演化规划(Evolutionary Programming,EP)；差分进化算法(Differential Evolution,DE)等多种算法可供选择。

其中个体数量和适应度评价多样化是影响算法优化效果的关键因素。

2. 基于进化计算的机器学习优化实现策略(1) 遗传算法：遗传算法可以解决高维复杂问题，易于并行化和全局优化，应用广泛。

在机器学习中，遗传算法是对已知目标函数（例如分类准确度、回归误差等）的一种优化求解方法，实现对机器学习模型的调参后期优化。

其流程主要包括如下步骤：初始化种群，交叉繁殖，个体变异，适应度评价，选择操作，并且实施精英策略。

(2) 进化策略：由于深度神经网络的特征具有高纬度的特点，所以进化策略在神经网络的特征变量优化上具有较好的表现。

一般来说，随机地生成一些样本，再进行适应度评价，对于不同的样本进行交叉、变异，最后对残存的样本进行再次适应度评价，然后把结果合并进行进一步优化。

(3) 演化规划：演化规划采用随机搜索的思想，通过不断的实验和反思、调整参与设定参数来实现最优解的寻找。

人工智能讲座心得体会

人工智能讲座心得体会人工智能讲座心得体会人工智能讲座心得体会通过这学期的学习，我对人工智能有了一定的感性认识，个人觉得人工智能是一门极富挑战性的科学，从事这项工作的人必须懂得计算机知识，心理学和哲学。

人工智能是包括十分广泛的科学，它由不同的领域组成，如机器学习，计算机视觉等等，总的说来，人工智能研究的一个主要目标是使机器能够胜任一些通常需要人类智能才能完成的复杂工作。

人工智能的定义可以分为两部分，即人工和智能。

人工比较好理解，争议性也不大。

有时我们会要考虑什么是人力所能及制造的，或者人自身的智能程度有没有高到可以创造人工智能的地步，等等。

但总的来说，人工系统就是通常意义下的人工系统。

关于什么是智能，就问题多多了。

这涉及到其它诸如意识、自我、思维等等问题。

人唯一了解的智能是人本身的智能，这是普遍认同的观点。

但是我们对我们自身智能的理解都非常有限，对构成人的智能的必要元素也了解有限，所以就很难定义什么是人工制造的智能了。

关于人工智能一个大家比较容易接受的定义是这样的：人工智能是人造的智能,是计算机科学、逻辑学、认知科学交叉形成的一门科学，简称 ai。

人工智能的发展历史大致可以分为这几个阶段：第一阶段：50 年代人工智能的兴起和冷落人工智能概念首次提出后，相继出现了一批显著的成果，如机器定理证明、跳棋程序、通用问题 s 求解程序、lisp 表处理语言等。

但由于消解法推理能力的有限，以及机器翻译等的失败，使人工智能走入了低谷。

第二阶段：60 年代末到 70 年代，专家系统出现，使人工智能研究出现新高潮。

dendral 化学质谱分析系统、mycin 疾病诊断和治疗系统、prospectior 探矿系统、hearsay-ii 语音理解系统等专家系统的研究和开发，将人工智能引向了实用化。

并且，1969 年成立了国际人工智能联合会议第三阶段：80 年代，随着第五代计算机的研制，人工智能得到了很大发展。

日本 1982 年开始了第五代计算机研制计划，即知识信息处理计算机系统 kips ，其目的是使逻辑推理达到数值运算那么快。

进化计算综述

2.进化计算的起源运用达尔文理论解决问题的思想起源于20世纪50年代。

20世纪60年代，这一想法在三个地方分别被发展起来。

在德国，Ingo Rechenberg 和Hans-Paul Schwefel提出了进化策略（Evolution strategies）。

这些理论大约独自发展了15年。

到了20世纪90年代初，遗传编程（Genetic programming）这一分支也被提出，进化计算作为一个学科开始正式出现。

四个分支交流频繁，取长补短，并融合出了新的进化算法，促进了进化计算的巨大发展。

Nils Aall Barricelli在20世纪六十年代开始进行用进化算法和人工生命模拟进化的工作。

Alex Fraser发表的一系列关于模拟人工选择的论文大大发展了这一工作。

[1] Ingo Rechenberg在上世纪60 年代和70 年代初用进化策略来解决复杂的工程问题的工作使人工进化成为广泛认可的优化方法。

朴素差分进化算法

朴素差分进化算法汪慎文;张文生;秦进;谢承旺;郭肇禄【摘要】针对变异算子学习方式的单一性,提出一种朴素变异算子,其基本思想是向优秀的个体靠近,同时远离较差个体,其实现方式是设计一种缩放因子调整策略,如果三个随机个体在某维上比较接近,则缩放因子变小,反之变大.在实验过程中通过平均适应度评价次数、成功运行次数和加速比等指标表明,基于朴素变异算子的差分进化算法能有效提高算法的收敛速度和健壮性.【期刊名称】《计算机应用》【年(卷),期】2015(035)005【总页数】3页(P1333-1335)【关键词】差分进化;朴素变异算子;缩放因子;集成进化【作者】汪慎文;张文生;秦进;谢承旺;郭肇禄【作者单位】石家庄经济学院信息工程学院,石家庄050031;中国科学院自动化研究所,北京100190;中国科学院自动化研究所,北京100190;贵州大学计算机学院,贵阳550025;华东交通大学软件学院,南昌330013;江西理工大学理学院,江西赣州341000【正文语种】中文【中图分类】TP301差分进化(Differential Evolution,DE)算法 [1],是由Storn和Price提出的一种新型进化算法,因其算法简单易执行、性能卓越等优点引起众多研究者的广泛关注。

目前研究者从三个角度对差分进化算法进行改进 [2]：1)操作算子的改进，提出一些新的参数控制方法(如：模糊适应差分进化算法(Fuzzy Adaptive DE,FADE)[3]、JADE(Adaptive DE with optional External Archive)[4]、自适应DE(Self-Adaptive DE，jDE)[5]等)和新设计的差分变异策略(如：三角变异策略[6]等)；2)基于静态知识指导的差分进化集成算法，该类算法主要是指DE与其他具有某种优良特性的策略集成，如：与分布评估算法(Estimation of Distribution Algorithm, EDA)集成的DE/EDA[7]、与反向学习策略集成的ODE(Opposition-based DE)[8]等；3)基于动态知识指导的差分进化集成算法，该类算法对进化过程中的不同变异策略产生的新解评估，其结果用于指导下一代策略选择，如：EPSDE(Ensembleof Mutation Strategies and Control Parameters with DE)[9]、SaDE(Self-adaptive DE)[10]等。

粗糙集属性约简的方法

粗糙集属性约简的方法ComputerEngineeringandApplica~ons计算机工程与应用◎数据库,信号与信息处理@粗糙集属性约简的方法王培吉,赵玉琳27吕剑峰W ANGPeiii,ZHAOYulin,LVJianfeng1内蒙古科技大学数理与生物工程学院,内蒙古包头0140102内蒙古第一机械集团公司二分公司,内蒙古包头0140321.SchoolofMath.,Physics&BiologicalEng.,InnerMongoliaUniversityofSciencean dTechnology,Baotou,NeiMongol014010,China2.Branch2,InnerMongoliaFirstMachineryGroupCorporation,Baotou,NeiMongol01403 2,ChinaW ANGPeiji,ZHAOYulin,LVJianfeng.Newmethodofattributereductionbasedonroughse puterEngineeringandAp—plications,2012,48(2):113—115.Abstract:Objectsclassificationisstrictexcessivelyandtoosensitiveonnoise.Aimingatdeci sionsystemwithuncertainfactor.anal? gorithmofattributereductionbasedondependabilityisestablished.Theattributesinthesyste mwithuncertaininformationandnoisedataarereduced,wherebyfindingareducibleimpliedpatternofthedata,anddeletingthosere dundantrulesinthesystem.Anditcan keeptheoriginalpropertiesandfunctionsofthesystem.Theimplementationofalgorithmisd escribedbyintroducinganexample.Keywords:roughset;dependability;attributereduction;implementation摘要:传统粗糙集分类方法过于严格,对噪音过分敏感.针对带不确定因子决策系统,提出一种基于属性依赖度的约简算法,使含不确定信息及数据噪音的系统中的属性得以简化,找到一种具有广泛表达能力的数据隐含格式,删去冗余的规则,并保持系统的原有用途和性能.通过一个例子实现了该算法.关键词:粗糙集;依赖度;属性约简DOI:10.3778/j.issn.1002—8331.2012.02.032文章编号:1002.8331(2012)02.0113.03文献标识码:A中图分类号:TP311基于粗糙集理论】的知识获取的核心问题之一是属性约简,有很多学者作了这方面的工作,其中应用较多的是基于辨识矩阵以及在此基础上的一些改进算法1.一般说来,知识库中的知识(属性)并不是同等重要的,还存在冗余,这不利于做出正确而简洁的决策.属性约简要求在保持知识库的分类和决策能力不变的条件下,删除不相关或不重要的属性.一般而言,较优的属性约简有如下指标:约简后属性个数较少;约简后规则数目较少;最终范化规则数目较少等.已证明求决策表所有约简和最小约简是一个典型的NP嘲问题,不过,在实际应用中,往往只要求出某种次优的属性约简就可以了.传统粗糙集分类方法过于严格,以及数据中存在噪音,造成知识的遗漏.如:条件属性下的两个等价类.,,分别有100个元素,对决策属性等价类,,只有一个元素属于,而,只有一个元素不属于,基于传统的粗糙集模式,,,同属于的边界区,对都不能作出肯定的判断,然而A,中只有一个元素不属于,也许是由噪音导致的,说明传统粗糙集对噪音是非常敏感的,而在机器学习,专家系统等实际应用中,获得的数据含有噪音是不可避免的,因此传统粗糙集模式在一定程度上限制了它更有效的应用,本文提出的针对带不确定因子决策系统的分类方法可将原来由于噪音的影响,被划到边界的等价类划回到正区(如上面的,)或负区(如上面的),克服了粗糙集对噪音过分敏感的缺点,使在有噪音的环境下获得的知识更可靠.1带不确定因子决策系统定义1称=fU,CUD,{},,imp}为带不确定因子的决策系统,记为S,D=},d是带不确定因子(0<-I.t1)的结论属性,=1表示该元素对结论有完全肯定的判断,即该元素所在等价类属于结论属性的正区POSB(D),=0表示该元素对结论有完全否定的判断,即该元素所在等价类属于结论属性的负区NEG09);imp是中元素在中的重要度,体现元素在中的重要性./1,imp由领域知识及数据库操作得到.如表1为一带不确定因子的决策系统.表1带不确定因子的决策系统075O.67O-350750.670_35表1中U={1,2,3,4,5,6),条件属性集C={日1,口2),1={1,2),2={1,2,3),决策属性D={,={1,2,3),每一元素的重要度imp={4,3,4,4,3,4},及不确定因子={O.75,0.67,0.35,0.75,0.67,0.35}.基金项目:国家自然科学基金(No.81060238).作者简介:王培吉(1968一),男,副教授,主要研究领域为数据库,数据挖掘;赵玉琳(1968一),男,高级工程师;吕剑峰(1984_),男,助教.E-mail:*************收稿日期:2011-01.24;修回日期:2011-04.26;CNKI出版:2011-07—25;/kcms/detail/11.2127.TP.20110725.1624.020.html ComputerEngineeringandApplications计算机工程与应用2属性依赖度与属性约筒2.1属性依赖度定义2在S中,BcC,,YcU/B且处于边界,划POSB(D):rflJY;~IJ)kNEG口(D)的误差p()和,l(】,)分别定义为: ):—Z—(impi_x(1一-,ui))厶l州,,?(y):—~.,(im_Pixiai)乙Ilnl划入正区和y划入负区的误差水平分别记为,.即:p()P时,XcPOSB(D);n(】,)≤Ⅳ时,YcNEG口(D●.定义3对,在误差水平为和下,结论屙陛d对条件属性集合C依赖度Dep(C,D,,)是U/C被划入正区POSc(D)和Y划入负区NEG(D)中元素重要度的和与所有元素重要度之比.2.2属性约简定义4在中,误差水平为P和,BC,a∈B,Dep(B,D,,Ⅳ)=Dep(B-{a},D,,aN),称a为B中可省略的,否则a为当中不可省略的;当所有a∈B在中不可省略的,且Dep(B,D,,Ⅳ)=Dep(C,D,,Ⅳ),即D对B,C有相同的依赖度,则是c的一个约简u.定义5在S中U/C={,,…,},称)为的辨识矩阵,其中,"一C:a(X)~a(Xj),D()≠D()}1,其他'其中l≤f,j<t.m包含使得,具有不同结论属性值的所有属性.称/=,vm为S的分辨函数,其中V表示m中所有属性的析取运算,^表示合取运算.如果一个属性在信息系统中是可省略的,删除此属性并不影响信息系统的依赖关系,且能与c一样分辨所有元素的属性子集,但这样的约简不是唯一的,co~(c1表示C的所有约简的交集.核.表1表示的带不确定因子信息系统中P=0.3,=0.6条件属性C的等价类:={l}={2}={3}={4}={5}={6}由P()={{4×(1.0—0.75)j=0.25P()={{3x(1.0—0.67)}=0.33P()={4×(1.0～o.75)}:0.25P()={{3×(i.0一o.67)}:0.33Ⅳ()={4×0_35))=0.35Ⅳ(x6):{4×0_35)}=0.35及P=0.3,Ⅳ=0.6得P(D):{,(D):{,}BND(D)={,}DEP(C,D,P,Ⅳ)=I-(4+4+4+4)=0.73等价类,划回到正区,等价类,划回到负区;而用传统粗糙集进行分类,它们却都属于边界类,造成了知识的遗漏和偏差.3基于属性依赖度的属性约简算法步骤1根据挖掘目标,选取一屙l生为结论屙陛,其余为条件属性;对数据进行归纳,形成宜于实施挖掘的数据形式,同时,结合统计结果及领域知识为每一对象赋一重要度imp及不确定因子,形成带不确定因子的决策系统=(￡,,CUD, {},imp).步骤2由及不可分辨关系形成条件属性等价类和结论属性等价类,对处于边界的等价类,根据,imp及和划入正区和负区,由新的等价类形成可辨识矩阵.步骤3由可辨识矩阵找出该不可分辨关系的核B=COl~(C).步骤4C=C—B.步骤5对每一属性a∈C,计算Dep(BU{a},D,,,)一Dep(B,D,P,Ⅳ)并按降序排列C.步骤6DoJl[~序取a∈C,B=BU{a},C=C一{a}计算Dep(B,D,p,Ⅳ)UntilDep(B,D,P,Ⅳ)=Dep(C,D,dP,Ⅳ)步骤7For/=1to1B1Do如果a诺co~(c),则B:-{a}若Dep(B,D,,ON)~:Dep(C,D,P,Ⅳ)则B=BU{a.1.步骤8得条件属性c的约简为子集B.步骤9由约简简化带不确定因子的决策系统,形成由约简属性集为条件属性的决策系统S=,BU{d}).步骤10合并相同和相近元素(若结论相同,条件中仅有一项不同,则该项对该结论无关紧要).步骤11知识表示.4实例分析决策系统=,CU{d}),按结论属性d排序,为每一对象赋一重要度imp及不确定因子(如可将条件属性下每一等价类元素个数作为该对象的重要度imp),得到带不确定凶子的决策系统=(,CUD,{}c,,imp),见表2.由表2得条件属性C的等价类为={1),:{2}1={3},={4},={5,12},:{6j,={7,9},={8},=flo},Xl.:{1l},={13},:={14,15}.合并等价类得表3,进而得辨识矩阵(见表4).由可辨识矩阵得COl~(C)={a3}.:CORE(C)={a3),C={Ⅱ1,a2,a4,a5}.对每一属性a∈C,计算Dep(BU{aD,,).王培吉,赵玉琳,吕剑峰:粗糙集属性约简的方法2012,48(2)115 表2带不确定因子的决策系统表3=U,CUD,{)Ⅲ,,帅)表4辨识矩阵910l1a2a4a2a3a5ala2a3a5a2a4a2a3a5ala2a3a5a2a4a2a3a4a5dla2a3a4a5a2a4a2a3a4a5ala2a3a4a5ala4a5ala3a4a5a3a4a5a1a2a4ala2a3a4a5a1a2a3a4a5a2a4a5a2a3a4ala2a3a4a2a3a4a2a3a4a5ala2a3a4a5a3a4a2a3a4a3a2a3ala2a3a5ala3a3a5由条件属性co~(c)U{al}的等价类为={1,5,6,7,8,9,12,13},={2},={3),:{4,10},={14,15}及)=(1×(1—0.6)×2+2×(1—0.9)×4+1×(1—0.8)+l×(1—0.9))/12=0.158,z()=(1×0.6×2+2×0.9×4+1×0.8+1×0.9)/12=0.842 p(x2)p(X3)1×(1—0.9)/1=0.1n()n(X3)1x0.9/1=0.9P(X4)=(1×(1—0.9)+1×(1—0.8))/2=0.15H()=(1×0.9+1×0.8)/2=O.85)(2×(1—1)+2×(1—1))/4=0n(Xs)=f2×1+2x1)/4=l得正区等价类为={2)={3)x4={4,10}={14,15};边界等价类为={1,5,6,7,8,9,12,13).这样Dep(CORE(C)U1}, D,P,Ⅳ)=9/21.同理可得:Dep(CORE(C)U{a2},D,P,Ⅳ)=21/21Dep(CORE(C)[J{a4},D,,Ⅳ)=19/21Dep(CORE(COU{a5},D,P,Ⅳ):9/21按依赖度降序排列C={a2,a4,al,a5}B=cD衄(c)U{a2}:{a2,a3}Dep(B,D,P,Ⅳ)=21/21B=曰U{a4)={a2,a3,a4}可求得:Dep(B,D,,Ⅳ)=19/21a2硭CORE(C),贝0B=B-{a2)={a3,a4)又Del~B,D, P,Ⅳ)=19/21DIC,D,P,aN).这样,求得条件属性c的约简为子集B={a3,a4,.由约简B={口3,a4},表3简化为表5.=3对应的五:a3=3,a4=2及五:a3=3,a4=3中仅有口4的值不同,将对应的a4值去掉合并墨,化为表6.表5决策系统"=",BU{d})表6决策系统=,BU{d})知识表示:{(口3=3)^(a4=1)}v{(a3=2)^(a4=2)}(=2)(a3=3)=3)(a3=4)^(a4=3)=4)5结束语本文针对带不确定因子决策系统,提出了一种基于属性依赖度的属性约简算法,本算法能从属性集合中有效去除冗余属性,使属性选择的结果更合理,数据噪音的影响更小,获得的知识更可靠.在大部分情况下本算法都能快速有效地找到属性子集的最优解或令人满意的次优解.(下转129页)m56789m¨刘兴阳,毛力:基于f分布变异的自适应差分进化算法2o12,48(2)129进化代数进化代数进化代数进化代数图1sphere函数寻优曲线对比图2R0senbr0ck函数寻优曲线对比图3Griewallk函数寻优曲线对比图4Ackley函数寻优曲线对比表1三种算法寻优结果比较5结论本文提出一种基于f分布变异算子的自适应差分进化算法:其一在变异过程中使用f分布变异算子有效地将高斯变异和柯西变异进行结合;其二根据进化的不同阶段,提出新的自适应方式来调节进化策略及交叉概率.通过采用四个典型测试函数对新算法进行测试,实验结果表明本文提出的改进算法具有较好的全局探索能力和局部开发能力.参考文献:[1】StornR,PriceK.Differentialevolution-asimpleandefficient heuristicforglobaloptimizationovercontinuousspaces[J].Jour- nalofGlobalOptimization,1997,11(4):341—359.【2]ZhangM,LuoW,WangXF.Differentialevolutionwithdynamic stochasticselectionforconstrainedoptimization[J].Information 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PaaemRecognition,2009,42(9):2135-2149.【5】RahnamayanS,TizhooshHR,SalamaMMA.Opposition-based differentialevolution[J].IEEEComputationalIntelligenceSociety,2008,12(1):64—79.[6】潭跃,谭冠政,伍雪冬.基于交叉变异策略的双种群差分进化算法[J]. 计算机工程与应用,2010,46(18):9-12.[7】DasS,AbrahamA,ChakrabortyUK.Differentialevolutionusing aneighborhood—basedmutationoperator[J].IEEETransactions onEvolutionaryComputation,2009,13(3):526.553.【8】LanKuo-Tong,LanChun-Hsitmg.NotesonthedislinctionofGaussian andCauchymutations[C]//EighthInternationalConferenceonIn. telligentSystemsDesignandApplications,2008:272-277.[9】Y aoX,LiuY,LinG.Evolutinaryprogrammingmadefaster[J].IEEE TransactionsonEvolutionaryComputation,1999,3(2):82—102.【1O】周方俊,王向军,张民.基于t分布变异的进化规划【J].电子, 2008,36(4):667.671.(da接l15页)参考文献:【1】PawlakZ.Roughset[J].InterofComputerandInformationSci- ences,1982,11.【2】刘清,刘少辉,郑非.Rough逻辑及其在数据挖掘中的应用【J】.软件,2001,12(3):415—419.【3】刘银山,吴孟达,王丹.粗糙集中求取所有最小约简快速算法【J].计算机工程与科学,2007,29(I):97—100.[4】苗夺谦,胡桂荣.知识约简的一种启发式算法[J】.计算机研究与发展,1999,36(6):681.684.【51HuXiaohua,CerconeN.Learninginrelationaldatabases:a roughsetapproach[J].ComputationalIntelligence,1995,11(2):323.337.[6]胡或,李智玲,李春伟.一种基于区分矩阵的属性约简算法[J].计算机工程与应用,2007,43(9):178.181.[7】黄治国,王端.基于粗糙集的数据约简方法研究[J】.计算机工程与设计,2009,30(18).【8】WongSK,ZiarkoW.Onoptimaldecisionrulesindecisionta-bles[J].BulletinofPolishAcademyofScience,1985,33:693-696.(上接123页)【7】ZhuZhengyu,XuJingqiu,RenXiang,eta1.QueryExpansionBased onaPersonalizedWebsearchmodel[C]//ThirdInternationalCon- ferenceonSemantics,KnowledgeandGrid,2007:128—133.【8】ZhuZhengyu,ZhouZhi,YuChunlei.Aquantizedanalyzingmethod forfindingauser'sinterestedwebpagesbasedontheuser's browsingactionsandquerywords[C]//InternationalConference onWebInformationSystemsandMining,2009.【9】ZhuZhengyu,TianYunyan,YuanKunfeng,eta1.Animproved Webdocumentsclausteringmethord[J].JournalofComputational InformationSystems,2007,3(3):1087—1094.[10】蒋萍.基于用户兴趣挖掘的个性化模型研究与设计[D].苏州大学, 2005:39-40.[11】张敏,宋睿华,马少平.基于语义关系查询扩展的文档重构方法[J].计算机,2004(10).【l2】瞿瑞彩,谢伟松.数值分析【M】.天津:天津大学出版社,2001:2-3. 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A novel evolutionary algorithm for determining unified creep damage constitutive equations

creep strain computed (theoretical) strain experimental (measured) strain stress (MPa) time (h) material constants primary state variable damage state variables computed (theoretical) time (h) experimental (measured) time (h) objective functions the shortest distance from the computed to experimental data Gaussian density function Cauchy density function
International Journal of Mechanical Sciences 44 (2002) 987 – 1002
A novel evolutionary algorithm for determining uniÿed creep damage constitutive equations
Abstract The determination of material constants within uniÿed creep damage constitutive equations from experimental data can be formulated as a problem of ÿnding the global minimum of a well deÿned objective function. However, such an objective function is usually complex, non-convex and non-di erentiable. It is di cult to be optimised by classical gradient-based methods. In this paper, the di culties in the optimisation are ÿrstly identiÿed. Two di erent objective functions are proposed, analysed and compared. Then three evolutionary programming algorithms are introduced to solve the global optimisation problem. The evolutionary algorithms are particularly good at dealing with problems which are complex, multi-modal and non-di erentiable. The results of the study shows that the evolutionary algorithms are ideally suited to the problem. Computational results of using the algorithms to determine the material constants in a set of physically based creep damage constitutive equations from experimental data for an aluminium alloy are presented in the paper to show the e ectiveness and e ciency of the three evolutionary algorithms.? 2002 Elsevier Science Ltd. All rights reserved.

人工智能心得总结2022三篇

人工智能心得总结2022三篇人，没有熊一样的力量，却能把熊关进笼子，这笼子的钥匙，叫智慧。

人类一直在思考如何让自然界的其它事物为自己所用，而不是只想着如何获取食物来填饱肚子，人类之所以会凌驾于食物链顶端，就在于对于资源的使用。

为了减轻胃的消化负担，人类开始学会使用火，让蛋白质在进入胃之前就变质而变得更好消化易于吸收。

经历了漫长的手工制造业历程，为了提高生产效率，也为了减轻工人手工劳作的负担，人们开始了工业革命，无数的机器流水线取代了效率低下的廉价劳动力，也正是从此刻起，人类使用资源的能力有了质的发展，由使用已有资源，到创造新的资源。

第一台计算机应运而生，人类开启了无限创造的时代。

时至今日，计算机技术几乎延伸到了生活的每个领域，甚至成了人们的生活必需品。

计算机能帮助人们完成人类不可能完成的计算，但一直致力于创造的人们当然不会停止对计算机的要求。

人们不光需要计算机做人类做不了的计算，还渐渐开始要求计算机做人类能做的事，这便催生了人工智能。

人类就是这样一步步用自己的智慧让自己过上傻瓜一样的生活。

人工智能目前还没有在人们生活中普及，但是已经出现萌芽。

最典型是的一些语音识别系统，如苹果公司的Siri可能是目前人们接触最多的基于人工智能和云计算技术的产品，相信这种人机交互系统的雏形经过时间的磨练会在未来形成一套完善的从界面到内核的智能体系。

在社会生活方面，与数字图像处理技术紧密结合的人工智能已经开始应用于摄像头的图像捕捉和识别，而模式识别技术的发展则使得人工智能在更广阔的领域得以实现成为了可能。

一些大公司在人工智能领域的投入和研究对于推动人工智能的发展起到了很大的作用，最值得一提的就是谷歌。

谷歌的免费搜索表面上是为了方便人们的查询，但这款搜索引擎推出的初衷，就是为了帮助人工智能的深度学习，通过上亿的用户一次又一次地查询，来锻炼人工智能的学习能力，由于我的水平还很低，对于深度学习还不敢妄自拽测。

但是，近年来谷歌公司在人工智能方面的突破一项接着一项，为人们熟知的便是智能汽车。

其他进化算法(new)(1)

分组成，每部分又可以有n个分量，即： X和σ的关系为:
τ为全局系数，常取1。
进hwefel在二元表达的基础上引入第三个因子——坐标旋转角度α。个体的描述扩展为(X, σ, α)，即：
三者的关系为：
αi——父代个体i分量与j分量间坐标的旋转角度； α’j——子代新个体i分量与j分量间坐标的旋转角度； β——系数，常取0.0873； zi——取决于σ’及α’的正态分布随机数。
5.1 进化策略
在1973年，Rechenburg把该算法的期望收敛速度定义为对最优点的平均距离与要得到此改善所需要的试验次数之比。
1981年，Schwefel在进化策略中使用多重亲本和子代，这是 Rechenburg早期工作（使用多重亲本，但是仅使用单个子代）的发展，后来考察了两种方法，分别表示为(μ+λ)-ES和 (μ，λ)-ES。在前者中，μ个亲本制造λ个子代，所有解均参加生存竞争，选出最好的μ个作为下一代的亲本。在后者中，只有λ（ λ > μ ）个子代参加生存竞争，在每代中μ个亲本被完全取代。
• 进化策略中的个体用传统的十进制实型数表示，即：
Xt——第t代个体的数值， N(0,σ)——服从正态分布的随机数，其均值为零，标准差为σ。
5.1 进化策略
• 在这个模型中，把解的分量看做个体的行为特性，而不是沿染色体排列的基因。可以和GA一样，假设这些表现型特征具有基因根源，但是它们之间的联系实质并没有被弄清楚，所以我们把着重点放在个体的行为特性上。
5.2 进化规划
标准进化规划进化规划用传统的十进制实数表达问题。在标准进化规划
（Standard EP）中，个体的表达形式为：
xi ' xi f (X ) • Ni (0,1)

人工智能心得体会

人工智能心得体会人工智能心得体会「篇一」一、人类惧怕人工智能的原因是什么？且说人类对于未知的事物总是心怀敬畏的，对于人工智能这种类人物种，可预见不仅能力于人类，占用资少工作效率极高，可以不吃不睡，还没生老病死的限制，最主要的是它不可能一直被人类所掌控。

这种威胁人类生存的担忧，是我们惧怕人工智能最根本、最深层的原因。

虽然可预见面对未来超人类人工智能人们是无法掌控的，但现阶段由于科学探索的需要，生产力升级的需要，经济发展的需要，人工智能仍然会大步向前。

即使明知道可能播下让人类灭亡的种子，但任何人或团体的都无法阻止人工智能前进的巨轮。

所以与其担忧无能为力的事情不如拥抱变化，抓住当下难得的机遇，站在风口上。

二、人工智能未来会有哪些发展和机会？1、未来2年，5G网络升级，引发手机更新换代风潮，同时也是在为人工智能应用提供技术环境和开拓道路。

2、未来5年，得益于大数据及深度学习算法，人工智能应用细分领域发展遍地开花。

如图相识别，生物分析，语音识别，智能家居，智能超市，智慧医疗，智能办公，智慧投资，智能全息技术，物联网技术应用将获得突破性发展。

3、未来10年，自动驾驶汽车及相关行业将成为最大产业，是中国在科技甚至经济上可能超越美国重大机遇。

人工智能心得体会「篇二」今天是我学习人工智能的第一堂课，也是我上大学以来第一次接触人工智能这门课，通过老师的讲解，我对人工智能有了一些简单的感性认识，我知道了人工智能从诞生，发展到今天经历一个漫长的过程，许多人为此做出了不懈的努力。

我觉得这门课真的是一门富有挑战性的科学，而从事这项工作的人不仅要懂得计算机知识，还必须懂得心理学和哲学。

人工智能在很多领域得到了发展，在我们的日常生活和学习中发挥了重要的作用。

如：机器翻译，机器翻译是利用计算机把一种自然语言转变成另一种自然语言的过程，用以完成这一过程的软件系统叫做机器翻译系统。

利用这些机器翻译系统我们可以很方便的完成一些语言翻译工作。