外文翻译---遗传算法在非线性模型中的应用
外文翻译---一种基于树结构的快速多目标遗传算法
附录4一种基于树结构的快速多目标遗传算法介绍：一般来讲，解决多目标的科学和工程问题，是一个非常困难的任务。
在这些多目标优化问题(MOPS)中，这些目标往往在一个高维的问题空间发生冲突，而且多目标优化也需要更多的计算资源。
一些经典的优化方法表明将多目标优化转化成为单目标优化问题，其中许多运行被要求找到多个解决方案。
这使得一种算法返回一组候选解，这比只返回一个基于目标的权重解的算法更好。
由于这个原因，在过去20年中，人们越来越感兴趣把进化算法(EAs)应用到多目标优化中。
许多多目标进化算法(MOEAs)已经被提出，这些多目标进化算法使用Pareto占优的概念来引导搜索，并返回一组非支配解作为结果。
与在单目标优化中找到最优解作为最终的解不同，在多目标优化中有二个目标：（1）收敛到Pareto最优解集（2）在Pareto最优解集中保持解的多样性。
为了解决在多目标优化中这两个有时候会冲突的任务，许多策略和方法被提出。
这些方法的一个共同的问题是，它们往往是错综复杂的。
对于这两项任务，为了得到更优秀的解，一些复杂的策略通常被使用，并且许多参数需要依据经验和已经得到的问题信息进行调整。
另外，许多多目标进化算法有高达（G是代数，M是目标函数的数量，N是种群大小。
这些符号在下文也保持相同的含义）。
在这篇文章中，我们提出了一种基于树结构的快速多目标遗传算法。
(这个数据结构是一个二进制树，它保存了在多目标优化中解的三值支配关系（例如，正在支配、被支配和非支配），因此，我们命名它为支配树(DT)。
由于一些独特的性能，使支配树能够含蓄地包含种群个体的密度信息，并且很明显地减少了种群个体之间的比较。
计算复杂度实验也表明，支配树是一种处理种群有效的工具。
基于支配树的进化算法(DTEA)统一了在支配树中的收敛性和多样性策略，即多目标进化算法中的两个目标，并且由于只有几个参数，这种算法很容易操作。
另外，基于支配树的进化算法(DTEA)使用了一种特别设计的基于支配树(DT)的消除策略。
本科毕业论文外文翻译【范本模板】
本科毕业论文外文翻译外文译文题目:不确定条件下生产线平衡：鲁棒优化模型和最优解解法学院：机械自动化专业：工业工程学号: 201003166045学生姓名: 宋倩指导教师：潘莉日期: 二○一四年五月Assembly line balancing under uncertainty: Robust optimization modelsand exact solution methodÖncü Hazır , Alexandre DolguiComputers ＆Industrial Engineering，2013,65：261–267不确定条件下生产线平衡：鲁棒优化模型和最优解解法安库·汉泽，亚历山大·多桂计算机与工业工程，2013，65：261–267摘要这项研究涉及在不确定条件下的生产线平衡，并提出两个鲁棒优化模型。
假设了不确定性区间运行的时间。
该方法提出了生成线设计方法,使其免受混乱的破坏。
基于分解的算法开发出来并与增强策略结合起来解决大规模优化实例.该算法的效率已被测试,实验结果也已经发表。
本文的理论贡献在于文中提出的模型和基于分解的精确算法的开发.另外，基于我们的算法设计出的基于不确定性整合的生产线的产出率会更高，因此也更具有实际意义。
此外,这是一个在装配线平衡问题上的开创性工作,并应该作为一个决策支持系统的基础。
关键字：装配线平衡；不确定性; 鲁棒优化；组合优化；精确算法1.简介装配线就是包括一系列在车间中进行连续操作的生产系统。
零部件依次向下移动直到完工。
它们通常被使用在高效地生产大量地标准件的工业行业之中。
在这方面，建模和解决生产线平衡问题也鉴于工业对于效率的追求变得日益重要。
生产线平衡处理的是分配作业到工作站来优化一些预定义的目标函数。
那些定义操作顺序的优先关系都是要被考虑的,同时也要对能力或基于成本的目标函数进行优化。
就生产（绍尔，1999）产品型号的数量来说，装配线可分为三类：单一模型（SALBP）,混合模型(MALBP）和多模式（MMALBP）。
外文翻译PDF
其中，Lossi-j 是母线真正的线损的到母线Ĵ，xi-JGK 是每个发电机线路损耗 的部分， PDK 是负载总线 K， yjGk 是分数每台发电机加载和 Ng 是发电机在系统 中的数量。 把 GA 传输损耗和负载流量分配问题，xi-JGK 和 yjGk 可以被视为一个优化 问题。GA 会发现这些分数对每个线路和负载的优化值。由于初始群体是随机
(5) (6)
其中β也是 0 和 1 之间的最后一步是完成与染色体的其余部分交叉，如下一 个随机值：
offspring 1 Pm1 , Pm 2 , …Pnew1 , ……PdNpar offspring 2 Pd 1 , Pd 2 , …Pnew2 , ……PmNpar
(7) (8)
[6] [3] [4]
的概念是基于发电机领域,共享和链接。功率跟踪可以做之前,需要先定义这些
本文结构如下： GA 的概念一目了然地呈现在下一部分，其次是 GA 技术损耗 和负载流量分配，结果和讨论，然后最终的结论将在本来的结尾陈述。
二 遗传算法
遗传算法（GA）是施加生物学过程的模型来解决最优化问题一种随机方法。 GA 允许个人组成在规定的法律进化到国家人口最大化“适”或最小化的成本函 数。该技术最初是由[9]开发的。遗传算法可以使用二进制和连续的方法被应用。 对于本文中，连续的 GA 用于由于它的优点在于连续参数的精度表示的术语。 A·代表性 起初 GA 二进制编码的位数工作（即 0 和 1），并连接在一起为一个字符串。 然而，本文将采用连续浮点数为代表，以解决问题。如果染色体具有由 P1 给的
虽然选择和交叉施加到染色体中每一代来获得更好的解决方案，一组新的， 偶尔它们可能变得过分热心，失去了一些有用的信息。为了保护这些不可恢复 的损失或过早收敛发生突变应用。突变是随机改变的小概率突变的（0-10％） 的参数。乘以突变率的参数总数给出应该突变参数的数目。甲突变参数被替换 为一个新的随机数。
外文文献—遗传算法
附录I 英文翻译第一部分英文原文文章来源：书名：《自然赋予灵感的元启发示算法》第二、三章出版社：英国Luniver出版社出版日期：2008Chapter 2Genetic Algorithms2.1 IntroductionThe genetic algorithm (GA), developed by John Holland and his collaborators in the 1960s and 1970s, is a model or abstraction of biolo gical evolution based on Charles Darwin’s theory of natural selection. Holland was the first to use the crossover and recombination, mutation, and selection in the study of adaptive and artificial systems. These genetic operators form the essential part of the genetic algorithm as a problem-solving strategy. Since then, many variants of genetic algorithms have been developed and applied to a wide range of optimization problems, from graph colouring to pattern recognition, from discrete systems (such as the travelling salesman problem) to continuous systems (e.g., the efficient design of airfoil in aerospace engineering), and from financial market to multiobjective engineering optimization.There are many advantages of genetic algorithms over traditional optimization algorithms, and two most noticeable advantages are: the ability of dealing with complex problems and parallelism. Genetic algorithms can deal with various types of optimization whether the objective (fitness) functionis stationary or non-stationary (change with time), linear or nonlinear, continuous or discontinuous, or with random noise. As multiple offsprings in a population act like independent agents, the population (or any subgroup) can explore the search space in many directions simultaneously. This feature makes it ideal to parallelize the algorithms for implementation. Different parameters and even different groups of strings can be manipulated at the same time.However, genetic algorithms also have some disadvantages.The formulation of fitness function, the usage of population size, the choice of the important parameters such as the rate of mutation and crossover, and the selection criteria criterion of new population should be carefully carried out. Any inappropriate choice will make it difficult for the algorithm to converge, or it simply produces meaningless results.2.2 Genetic Algorithms2.2.1 Basic ProcedureThe essence of genetic algorithms involves the encoding of an optimization function as arrays of bits or character strings to represent the chromosomes, the manipulation operations of strings by genetic operators, and the selection according to their fitness in the aim to find a solution to the problem concerned. This is often done by the following procedure:1) encoding of the objectives or optimization functions; 2) defining a fitness function or selection criterion; 3) creating a population of individuals; 4) evolution cycle or iterations by evaluating the fitness of allthe individuals in the population,creating a new population by performing crossover, and mutation,fitness-proportionate reproduction etc, and replacing the old population and iterating again using the new population;5) decoding the results to obtain the solution to the problem. These steps can schematically be represented as the pseudo code of genetic algorithms shown in Fig. 2.1.One iteration of creating a new population is called a generation. The fixed-length character strings are used in most of genetic algorithms during each generation although there is substantial research on the variable-length strings and coding structures.The coding of the objective function is usually in the form of binary arrays or real-valued arrays in the adaptive genetic algorithms. For simplicity, we use binary strings for encoding and decoding. The genetic operators include crossover,mutation, and selection from the population.The crossover of two parent strings is the main operator with a higher probability and is carried out by swapping one segment of one chromosome with the corresponding segment on another chromosome at a random position (see Fig.2.2).The crossover carried out in this way is a single-point crossover. Crossover at multiple points is also used in many genetic algorithms to increase the efficiency of the algorithms.The mutation operation is achieved by flopping the randomly selected bits (see Fig. 2.3), and the mutation probability is usually small. The selection of anindividual in a population is carried out by the evaluation of its fitness, and it can remain in the new generation if a certain threshold of the fitness is reached or the reproduction of a population is fitness-proportionate. That is to say, the individuals with higher fitness are more likely to reproduce.2.2.2 Choice of ParametersAn important issue is the formulation or choice of an appropriate fitness function that determines the selection criterion in a particular problem. For the minimization of a function using genetic algorithms, one simple way of constructing a fitness function is to use the simplest form F = A−y with A being a large constant (though A = 0 will do) and y = f(x), thus the objective is to maximize the fitness function and subsequently minimize the objective function f(x). However, there are many different ways of defining a fitness function.For example, we can use the individual fitness assignment relative to the whole populationwhere is the phenotypic value of individual i, and N is the population size. The appropriateform of the fitness function will make sure that the solutions with higher fitness should be selected efficiently. Poor fitness function may result in incorrect or meaningless solutions.Another important issue is the choice of various parameters.The crossover probability is usually very high, typically in the range of 0.7~1.0. On the other hand, the mutation probability is usually small (usually 0.001 _ 0.05). If is too small, then the crossover occurs sparsely, which is not efficient for evolution. If the mutation probability is too high, the solutions could still ‘jump around’ even if the optimal solution is approaching.The selection criterion is also important. How to select the current population so that the best individuals with higher fitness should be preserved and passed onto the next generation. That is often carried out in association with certain elitism. The basic elitism is to select the most fit individual (in each generation) which will be carried over to the new generation without being modified by genetic operators. This ensures that the best solution is achieved more quickly.Other issues include the multiple sites for mutation and the population size. The mutation at a single site is not very efficient, mutation at multiple sites will increase the evolution efficiency. However, too many mutants will make it difficult for the system to converge or even make the system go astray to the wrong solutions. In reality, if the mutation is too high under high selection pressure, then the whole population might go extinct.In addition, the choice of the right population size is also very important. If the population size is too small, there is not enough evolution going on, and there is a risk for the whole population to go extinct. In the real world, a species with a small population, ecological theory suggests that there is a real danger of extinction for such species. Even the system carries on, there is still a danger of premature convergence. In a small population, if a significantly more fit individual appears too early, it may reproduces enough offsprings so that they overwhelm the whole (small) population. This will eventually drive the system to a local optimum (not the global optimum). On the other hand, if the population is too large, more evaluations of the objectivefunction are needed, which will require extensive computing time.Furthermore, more complex and adaptive genetic algorithms are under active research and the literature is vast about these topics.2.3 ImplementationUsing the basic procedure described in the above section, we can implement the genetic algorithms in any programming language. For simplicity of demonstrating how it works, we have implemented a function optimization using a simple GA in both Matlab and Octave.For the generalized De Jong’s test function where is a positive integer andr > 0 is the half length of the domain. This function has a minimum of at . For the values of , r = 100 and n = 5 as well as a population size of 40 16-bit strings, the variations of the objective function during a typical run are shown in Fig. 2.4. Any two runs will give slightly different results dueto the stochastic nature of genetic algorithms, but better estimates are obtained as the number of generations increases.For the well-known Easom functionit has a global maximum at (see Fig. 2.5). Now we can use the following Matlab/Octave to find its global maximum. In our implementation, we have used fixedlength 16-bit strings. The probabilities of crossover and mutation are respectivelyAs it is a maximization problem, we can use the simplest fitness function F = f(x).The outputs from a typical run are shown in Fig. 2.6 where the top figure shows the variations of the best estimates as they approach while the lower figure shows the variations of the fitness function.% Genetic Algorithm (Simple Demo) Matlab/Octave Program% Written by X S Yang (Cambridge University)% Usage: gasimple or gasimple(‘x*exp(-x)’);function [bestsol, bestfun,count]=gasimple(funstr)global solnew sol pop popnew fitness fitold f range;if nargin<1,% Easom Function with fmax=1 at x=pifunstr=‘-cos(x)*exp(-(x-3.1415926)^2)’;endrange=[-10 10]; % Range/Domain% Converting to an inline functionf=vectorize(inline(funstr));% Generating the initil populationrand(‘state’,0’); % Reset the random generatorpopsize=20; % Population sizeMaxGen=100; % Max number of generationscount=0; % counternsite=2; % number of mutation sitespc=0.95; % Crossover probabilitypm=0.05; % Mutation probabilitynsbit=16; % String length (bits)% Generating initial populationpopnew=init_gen(popsize,nsbit);fitness=zeros(1,popsize); % fitness array% Display the shape of the functionx=range(1):0.1:range(2); plot(x,f(x));% Initialize solution <- initial populationfor i=1:popsize,solnew(i)=bintodec(popnew(i,:));end% Start the evolution loopfor i=1:MaxGen,% Record as the historyfitold=fitness; pop=popnew; sol=solnew;for j=1:popsize,% Crossover pairii=floor(popsize*rand)+1; jj=floor(popsize*rand)+1;% Cross overif pc>rand,[popnew(ii,:),popnew(jj,:)]=...crossover(pop(ii,:),pop(jj,:));% Evaluate the new pairscount=count+2;evolve(ii); evolve(jj);end% Mutation at n sitesif pm>rand,kk=floor(popsize*rand)+1; count=count+1;popnew(kk,:)=mutate(pop(kk,:),nsite);evolve(kk);endend % end for j% Record the current bestbestfun(i)=max(fitness);bestsol(i)=mean(sol(bestfun(i)==fitness));end% Display resultssubplot(2,1,1); plot(bestsol); title(‘Best estimates’); subplot(2,1,2); plot(bestfun); title(‘Fitness’);% ------------- All sub functions ----------% generation of initial populationfunction pop=init_gen(np,nsbit)% String length=nsbit+1 with pop(:,1) for the Signpop=rand(np,nsbit+1)>0.5;% Evolving the new generationfunction evolve(j)global solnew popnew fitness fitold pop sol f;solnew(j)=bintodec(popnew(j,:));fitness(j)=f(solnew(j));if fitness(j)>fitold(j),pop(j,:)=popnew(j,:);sol(j)=solnew(j);end% Convert a binary string into a decimal numberfunction [dec]=bintodec(bin)global range;% Length of the string without signnn=length(bin)-1;num=bin(2:end); % get the binary% Sign=+1 if bin(1)=0; Sign=-1 if bin(1)=1.Sign=1-2*bin(1);dec=0;% floating point.decimal place in the binarydp=floor(log2(max(abs(range))));for i=1:nn,dec=dec+num(i)*2^(dp-i);enddec=dec*Sign;% Crossover operatorfunction [c,d]=crossover(a,b)nn=length(a)-1;% generating random crossover pointcpoint=floor(nn*rand)+1;c=[a(1:cpoint) b(cpoint+1:end)];d=[b(1:cpoint) a(cpoint+1:end)];% Mutatation operatorfunction anew=mutate(a,nsite)nn=length(a); anew=a;for i=1:nsite,j=floor(rand*nn)+1;anew(j)=mod(a(j)+1,2);endThe above Matlab program can easily be extended to higher dimensions. In fact, there is no need to do any programming (if you prefer) because there are many software packages (either freeware or commercial) about genetic algorithms. For example, Matlab itself has an extra optimization toolbox.Biology-inspired algorithms have many advantages over traditional optimization methods such as the steepest descent and hill-climbing and calculus-based techniques due to the parallelism and the ability of locating the very good approximate solutions in extremely very large search spaces.Furthermore, more powerful new generation algorithms can be formulated by combiningexisting and new evolutionary algorithms with classical optimization methods.Chapter 3Ant AlgorithmsFrom the discussion of genetic algorithms, we know that we can improve the search efficiency by using randomness which will also increase the diversity of the solutions so as to avoid being trapped in local optima. The selection of the best individuals is also equivalent to use memory. In fact, there are other forms of selection such as using chemical messenger (pheromone) which is commonly used by ants, honey bees, and many other insects. In this chapter, we will discuss the nature-inspired ant colony optimization (ACO), which is a metaheuristic method.3.1 Behaviour of AntsAnts are social insects in habit and they live together in organized colonies whose population size can range from about 2 to 25 millions. When foraging, a swarm of ants or mobile agents interact or communicate in their local environment. Each ant can lay scent chemicals or pheromone so as to communicate with others, and each ant is also able to follow the route marked with pheromone laid by other ants. When ants find a food source, they will mark it with pheromone and also mark the trails to and from it. From the initial random foraging route, the pheromone concentration varies and the ants follow the route with higher pheromone concentration, and the pheromone is enhanced by the increasing number of ants. As more and more ants follow the same route, it becomes the favoured path. Thus, some favourite routes (often the shortest or more efficient) emerge. This is actually a positive feedback mechanism.Emerging behaviour exists in an ant colony and such emergence arises from simple interactions among individual ants. Individual ants act according to simple and local information (such as pheromone concentration) to carry out their activities. Although there is no master ant overseeing the entire colony and broadcasting instructions to the individual ants, organized behaviour still emerges automatically. Therefore, such emergent behaviour is similar to other self-organized phenomena which occur in many processes in nature such as the pattern formation in animal skins (tiger and zebra skins).The foraging pattern of some ant species (such as the army ants) can show extraordinary regularity. Army ants search for food along some regular routes with an angle of about apart. We do not know how they manage to follow such regularity, but studies show that they could move in an area and build a bivouac and start foraging. On the first day, they forage in a random direction, say, the north and travel a few hundred meters, then branch to cover a large area. The next day, they will choose a different direction, which is about from the direction on the previous day and cover a large area. On the following day, they again choose a different direction about from the second day’s direction. In this way, they cover the whole area over about 2 weeks and they move out to a different location to build a bivouac and forage again.The interesting thing is that they do not use the angle of (this would mean that on the fourth day, they will search on the empty area already foraged on the first day). The beauty of this angle is that it leaves an angle of about from the direction on the first day. This means they cover the whole circle in 14 days without repeating (or covering a previously-foraged area). This is an amazing phenomenon.3.2 Ant Colony OptimizationBased on these characteristics of ant behaviour, scientists have developed a number ofpowerful ant colony algorithms with important progress made in recent years. Marco Dorigo pioneered the research in this area in 1992. In fact, we only use some of the nature or the behaviour of ants and add some new characteristics, we can devise a class of new algorithms.The basic steps of the ant colony optimization (ACO) can be summarized as the pseudo code shown in Fig. 3.1.Two important issues here are: the probability of choosing a route, and the evaporation rate of pheromone. There are a few ways of solving these problems although it is still an area of active research. Here we introduce the current best method. For a network routing problem, the probability of ants at a particular node to choose the route from node to node is given bywhere and are the influence parameters, and their typical values are .is the pheromone concentration on the route between and , and the desirability ofthe same route. Some knowledge about the route such as the distance is often used so that ,which implies that shorter routes will be selected due to their shorter travelling time, and thus the pheromone concentrations on these routes are higher.This probability formula reflects the fact that ants would normally follow the paths with higher pheromone concentrations. In the simpler case when , the probability of choosing a path by ants is proportional to the pheromone concentration on the path. The denominator normalizes the probability so that it is in the range between 0 and 1.The pheromone concentration can change with time due to the evaporation of pheromone. Furthermore, the advantage of pheromone evaporation is that the system could avoid being trapped in local optima. If there is no evaporation, then the path randomly chosen by the first ants will become the preferred path as the attraction of other ants by their pheromone. For a constant rate of pheromone decay or evaporation, the pheromone concentration usually varies with time exponentiallywhere is the initial concentration of pheromone and t is time. If , then we have . For the unitary time increment , the evaporation can beapproximated by . Therefore, we have the simplified pheromone update formula:where is the rate of pheromone evaporation. The increment is the amount of pheromone deposited at time t along route to when an ant travels a distance . Usually . If there are no ants on a route, then the pheromone deposit is zero.There are other variations to these basic procedures. A possible acceleration scheme is to use some bounds of the pheromone concentration and only the ants with the current global best solution(s) are allowed to deposit pheromone. In addition, certain ranking of solution fitness can also be used. These are hot topics of current research.3.3 Double Bridge ProblemA standard test problem for ant colony optimization is the simplest double bridge problem with two branches (see Fig. 3.2) where route (2) is shorter than route (1). The angles of these two routes are equal at both point A and pointB so that the ants have equal chance (or 50-50 probability) of choosing each route randomly at the initial stage at point A.Initially, fifty percent of the ants would go along the longer route (1) and the pheromone evaporates at a constant rate, but the pheromone concentration will become smaller as route (1) is longer and thus takes more time to travel through. Conversely, the pheromone concentration on the shorter route will increase steadily. After some iterations, almost all the ants will move along the shorter route. Figure 3.3 shows the initial snapshot of 10 ants (5 on each route initially) and the snapshot after 5 iterations (or equivalent to 50 ants have moved along this section). Well, there are 11 ants, and one has not decided which route to follow as it just comes near to the entrance.Almost all the ants (well, about 90% in this case) move along the shorter route.Here we only use two routes at the node, it is straightforward to extend it to the multiple routes at a node. It is expected that only the shortest route will be chosen ultimately. As any complex network system is always made of individual nodes, this algorithms can be extended to solve complex routing problems reasonably efficiently. In fact, the ant colony algorithms have been successfully applied to the Internet routing problem, the travelling salesman problem, combinatorial optimization problems, and other NP-hard problems.3.4 Virtual Ant AlgorithmAs we know that ant colony optimization has successfully solved NP-hard problems such asthe travelling salesman problem, it can also be extended to solve the standard optimization problems of multimodal functions. The only problem now is to figure out how the ants will move on an n-dimensional hyper-surface. For simplicity, we will discuss the 2-D case which can easily be extended to higher dimensions. On a 2D landscape, ants can move in any direction or , but this will cause some problems. How to update the pheromone at a particular point as there are infinite number of points. One solution is to track the history of each ant moves and record the locations consecutively, and the other approach is to use a moving neighbourhood or window. The ants ‘smell’ the pheromone concentration of their neighbourhood at any particular location.In addition, we can limit the number of directions the ants can move by quantizing the directions. For example, ants are only allowed to move left and right, and up and down (only 4 directions). We will use this quantized approach here, which will make the implementation much simpler. Furthermore, the objective function or landscape can be encoded into virtual food so that ants will move to the best locations where the best food sources are. This will make the search process even more simpler. This simplified algorithm is called Virtual Ant Algorithm (VAA) developed by Xin-She Yang and his colleagues in 2006, which has been successfully applied to topological optimization problems in engineering.The following Keane function with multiple peaks is a standard test functionThis function without any constraint is symmetric and has two highest peaks at (0, 1.39325) and (1.39325, 0). To make the problem harder, it is usually optimized under two constraints:This makes the optimization difficult because it is now nearly symmetric about x = y and the peaks occur in pairs where one is higher than the other. In addition, the true maximum is, which is defined by a constraint boundary.Figure 3.4 shows the surface variations of the multi-peaked function. If we use 50 roaming ants and let them move around for 25 iterations, then the pheromone concentrations (also equivalent to the paths of ants) are displayed in Fig. 3.4. We can see that the highest pheromoneconcentration within the constraint boundary corresponds to the optimal solution.It is worth pointing out that ant colony algorithms are the right tool for combinatorial and discrete optimization. They have the advantages over other stochastic algorithms such as genetic algorithms and simulated annealing in dealing with dynamical network routing problems.For continuous decision variables, its performance is still under active research. For the present example, it took about 1500 evaluations of the objective function so as to find the global optima. This is not as efficient as other metaheuristic methods, especially comparing with particle swarm optimization. This is partly because the handling of the pheromone takes time. Is it possible to eliminate the pheromone and just use the roaming ants? The answer is yes. Particle swarm optimization is just the right kind of algorithm for such further modifications which will be discussed later in detail.第二部分中文翻译第二章遗传算法2.1 引言遗传算法是由John Holland和他的同事于二十世纪六七十年代提出的基于查尔斯·达尔文的自然选择学说而发展的一种生物进化的抽象模型。
非线性智能优化算法的研究与应用
非线性智能优化算法的研究与应用第一章研究背景随着信息时代的到来，人类社会已经进入了一个高速变化的时代。
在这个时代里，诸如物流、交通、金融、电力、互联网等领域的问题变得越来越复杂，传统的解决方法已经难以满足实际需求。
这时，非线性智能优化算法便应运而生，被广泛应用在各个领域，且效果显著。
第二章研究内容2.1 定义非线性智能优化算法是指以自适应性、并行性和学习能力为特征的一类计算方法。
该类算法本质上是一种搜索过程，通过迭代更新一组解决问题的可能解，直至找到最优解。
2.2 类型目前，非线性智能优化算法主要分为以下几类：（1）粒子群算法（Particle Swarm Optimization，PSO）（2）遗传算法（Genetic Algorithm，GA）（3）模拟退火算法（Simulated Annealing，SA）（4）蚁群算法（Ant Colony Optimization，ACO）（5）人工免疫系统算法（Artificial Immune System，AIS）（6）差分进化算法（Differential Evolution，DE）2.3 应用非线性智能优化算法已经广泛应用于各个领域。
其中，常用的应用包括：（1）组合优化问题，如旅行商问题、装载问题、背包问题等。
（2）连续优化问题，如函数优化、参数优化等。
（3）系统优化问题，如系统参数优化、系统控制优化等。
（4）机器学习问题，如神经网络训练、支持向量机参数调节等。
（5）图像处理问题，如图像分割、图像匹配等。
（6）信号处理问题，如数字滤波、信号降噪等。
第三章研究现状随着计算机技术的快速发展和各种学科领域知识的融合，非线性智能优化算法也得到了广泛的应用。
在各个学科领域中，都有大量优秀的学者进行相应研究，推动了非线性智能优化算法的普及和发展。
3.1 研究机构国内外许多知名高校、研究机构，如中科院计算所、清华大学计算机科学与技术系、中国科技大学计算机科学与工程系、纽约大学人工智能实验室等，都在非线性智能优化算法研究领域拥有重要的研究成果。
外文文献翻译译稿和原文
外文文献翻译译稿1卡尔曼滤波的一个典型实例是从一组有限的，包含噪声的，通过对物体位置的观察序列（可能有偏差）预测出物体的位置的坐标及速度。
在很多工程应用（如雷达、计算机视觉）中都可以找到它的身影。
同时，卡尔曼滤波也是控制理论以及控制系统工程中的一个重要课题。
例如，对于雷达来说，人们感兴趣的是其能够跟踪目标。
但目标的位置、速度、加速度的测量值往往在任何时候都有噪声。
卡尔曼滤波利用目标的动态信息，设法去掉噪声的影响，得到一个关于目标位置的好的估计。
这个估计可以是对当前目标位置的估计（滤波），也可以是对于将来位置的估计（预测），也可以是对过去位置的估计（插值或平滑）。
命名[编辑]这种滤波方法以它的发明者鲁道夫.E.卡尔曼（Rudolph E. Kalman）命名，但是根据文献可知实际上Peter Swerling在更早之前就提出了一种类似的算法。
斯坦利。
施密特（Stanley Schmidt）首次实现了卡尔曼滤波器。
卡尔曼在NASA埃姆斯研究中心访问时，发现他的方法对于解决阿波罗计划的轨道预测很有用，后来阿波罗飞船的导航电脑便使用了这种滤波器。
关于这种滤波器的论文由Swerling（1958）、Kalman (1960)与Kalman and Bucy（1961）发表。
目前，卡尔曼滤波已经有很多不同的实现。
卡尔曼最初提出的形式现在一般称为简单卡尔曼滤波器。
除此以外，还有施密特扩展滤波器、信息滤波器以及很多Bierman, Thornton开发的平方根滤波器的变种。
也许最常见的卡尔曼滤波器是锁相环，它在收音机、计算机和几乎任何视频或通讯设备中广泛存在。
以下的讨论需要线性代数以及概率论的一般知识。
卡尔曼滤波建立在线性代数和隐马尔可夫模型（hidden Markov model）上。
其基本动态系统可以用一个马尔可夫链表示，该马尔可夫链建立在一个被高斯噪声（即正态分布的噪声）干扰的线性算子上的。
系统的状态可以用一个元素为实数的向量表示。
sga-pde 遗传算法 偏微分方程
sga-pde 遗传算法偏微分方程
SGA-PDE (Steady-State Genetic Algorithm for Partial Differential Equations) 是一种应用于求解偏微分方程的遗传算法。
偏微分方程是描述自然界中许多现象的数学方程，如流体力学、热传导等。
SGA-PDE 的基本思想是将偏微分方程的求解问题转化为一个优化问题。
遗传算法则是一种模拟自然界进化过程的优化算法，通过模拟“选择、交叉、变异”等基因操作，逐步优化求解问题的解。
在 SGA-PDE 中，偏微分方程的解被编码成一个个体的基因序列。
每个个体通过解码得到对应的数值解，然后通过计算适应度函数来评估个体的适应度，即求解方程的误差。
适应度函数可以根据具体问题进行定义，常见的包括残差平方和、误差范数等。
SGA-PDE 的优化过程包括选择、交叉和变异。
选择操作根据个体的适应度选择出一部分优秀的个体作为父代，交叉操作通过交换基因序列的片段来产生新的个体，变异操作则在个体的基因序列中引入随机扰动。
通过多代的迭代，SGA-PDE 可以逐步找到适应度最高的个体，即偏微分方程的近似解。
SGA-PDE 的优点是可以求解各种类型的偏微分方程，并且不受问题维度的限制。
它在求解复杂的偏微分方程问题时具有一定的优势，但也存在着计算复杂度高、收敛性不稳定等问题。
因此，在应用
SGA-PDE 求解偏微分方程问题时，需要根据具体问题的特点进行参数选择和算法改进，以提高求解效率和精度。
遗传算法中英文对照外文翻译文献
遗传算法中英文对照外文翻译文献遗传算法中英文对照外文翻译文献（文档含英文原文和中文翻译）Improved Genetic Algorithm and Its Performance AnalysisAbstract: Although genetic algorithm has become very famous with its global searching, parallel computing, better robustness, and not needing differential information during evolution. However, it also has some demerits, such as slow convergence speed. In this paper, based on several general theorems, an improved genetic algorithm using variant chromosome length and probability of crossover and mutation is proposed, and its main idea is as follows : at the beginning of evolution, our solution with shorter length chromosome and higher probability of crossover and mutation; and at the vicinity of global optimum, with longer length chromosome and lower probability of crossover and mutation. Finally, testing with some critical functions shows that our solution can improve the convergence speed of genetic algorithm significantly , its comprehensive performance is better than that of the genetic algorithm which only reserves the best individual.Genetic algorithm is an adaptive searching technique based on a selection and reproduction mechanism found in the natural evolution process, and it was pioneered by Holland in the 1970s. It has become very famous with its global searching,________________________________ 遗传算法中英文对照外文翻译文献 ________________________________ parallel computing, better robustness, and not needing differential information during evolution. However, it also has some demerits, such as poor local searching, premature converging, as well as slow convergence speed. In recent years, these problems have been studied.In this paper, an improved genetic algorithm with variant chromosome length andvariant probability is proposed. Testing with some critical functions shows that it can improve the convergence speed significantly, and its comprehensive performance is better than that of the genetic algorithm which only reserves the best individual.In section 1, our new approach is proposed. Through optimization examples, insection 2, the efficiency of our algorithm is compared with the genetic algorithm which only reserves the best individual. And section 3 gives out the conclusions. Finally, some proofs of relative theorems are collected and presented in appendix.1 Description of the algorithm1.1 Some theoremsBefore proposing our approach, we give out some general theorems (see appendix)as follows: Let us assume there is just one variable (multivariable can be divided into many sections, one section for one variable) x £ [ a, b ] , x £ R, and chromosome length with binary encoding is 1.Theorem 1 Minimal resolution of chromosome isb 一 a2l — 1Theorem 3 Mathematical expectation Ec(x) of chromosome searching stepwith one-point crossover iswhere Pc is the probability of crossover.Theorem 4 Mathematical expectation Em ( x ) of chromosome searching step with bit mutation isE m ( x ) = ( b- a) P m 遗传算法中英文对照外文翻译文献Theorem 2 wi = 2l -1 2 i -1 Weight value of the ith bit of chromosome is(i = 1,2,・・・l )E *)= P c1.2 Mechanism of algorithmDuring evolutionary process, we presume that value domains of variable are fixed, and the probability of crossover is a constant, so from Theorem 1 and 3, we know that the longer chromosome length is, the smaller searching step of chromosome, and the higher resolution; and vice versa. Meanwhile, crossover probability is in direct proportion to searching step. From Theorem 4, changing the length of chromosome does not affect searching step of mutation, while mutation probability is also in direct proportion to searching step.At the beginning of evolution, shorter length chromosome( can be too shorter, otherwise it is harmful to population diversity ) and higher probability of crossover and mutation increases searching step, which can carry out greater domain searching, and avoid falling into local optimum. While at the vicinity of global optimum, longer length chromosome and lower probability of crossover and mutation will decrease searching step, and longer length chromosome also improves resolution of mutation, which avoid wandering near the global optimum, and speeds up algorithm converging.Finally, it should be pointed out that chromosome length changing keeps individual fitness unchanged, hence it does not affect select ion ( with roulette wheel selection) .2.3 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 policy. During evolutionary process, we track cumulative average of individual average fitness up to current generation. It is written as1 X G x(t)= G f vg (t)t=1where G is the current evolutionary generation, 'avg is individual average fitness.When the cumulative average fitness increases to k times ( k> 1, k £ R) of initial individual average fitness, we change chromosome length to m times ( m is a positive integer ) of itself , and reduce probability of crossover and mutation, which_______________________________ 遗传算法中英文对照外文翻译文献________________________________can improve individual resolution and reduce searching step, and speed up algorithm converging. The procedure is as follows:Step 1 Initialize population, and calculate individual average fitness f avg0, and set change parameter flag. Flag equal to 1.Step 2 Based on reserving the best individual of current generation, carry out selection, regeneration, crossover and mutation, and calculate cumulative average of individual average fitness up to current generation 'avg ;f avgStep 3 If f vgg0 三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 continue evolving.Step 4 If end condition is satisfied, stop; otherwise go to Step 2.2 Test and analysisWe adopt the following two critical functions to test our approach, and compare it with the genetic algorithm which only reserves the best individual:sin 2 弋 x2 + y2 - 0.5 [1 + 0.01( 2 + y 2)]x, y G [-5,5]f (x, y) = 4 - (x2 + 2y2 - 0.3cos(3n x) - 0.4cos(4n y))x, y G [-1,1]22. 1 Analysis of convergenceDuring 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 respectively. And we randomly select four genetic algorithms reserving best individual with various fixed chromosome length and probability of crossover and mutation to compare with our approach. Tab. 1 gives the average converging generation in 100 tests.In our approach, we adopt initial parameter l0= 10, Pc0= 0.3, Pm0= 0.1 and k= 1.2, when changing parameter condition is satisfied, we adjust parameters to l= 30, Pc= 0.1, Pm= 0.01.From Tab. 1, we know that our approach improves convergence speed of genetic algorithm significantly and it accords with above analysis.2.2 Analysis of online and offline performanceQuantitative evaluation methods of genetic algorithm are proposed by Dejong, including online and offline performance. The former tests dynamic performance; and the latter evaluates convergence performance. To better analyze online and offline performance of testing function, w e multiply fitness of each individual by 10, and we give a curve of 4 000 and 1 000 generations for fl and f2, respectively.(a) onlineFig. 1 Online and offline performance of fl(a) online (b) onlineFig. 2 Online and offline performance of f2From Fig. 1 and Fig. 2, we know that online performance of our approach is just little worse than that of the fourth case, but it is much better than that of the second, third and fifth case, whose online performances are nearly the same. At the same time, offline performance of our approach is better than that of other four cases.3 ConclusionIn this paper, based on some general theorems, an improved genetic algorithmusing variant chromosome length and probability of crossover and mutation is proposed. Testing with some critical functions shows that it can improve convergence speed of genetic algorithm significantly, and its comprehensive performance is better than that of the genetic algorithm which only reserves the best individual.AppendixWith the supposed conditions of section 1, we know that the validation of Theorem 1 and Theorem 2 are obvious.Theorem 3 Mathematical expectation Ec(x) of chromosome searching step with one point crossover isb - a PEc(x) = 21 cwhere Pc is the probability of crossover.Proof As shown in Fig. A1, we assume that crossover happens on the kth locus, i. e. parent,s locus from k to l do not change, and genes on the locus from 1 to k are exchanged.During crossover, change probability of genes on the locus from 1 to k is 2 (“1” to “0” or “0” to “1”). So, after crossover, mathematical expectation of chromosome searching step on locus from 1 to k is1 chromosome is equal, namely l Pc. Therefore, after crossover, mathematical expectation of chromosome searching step isE (x ) = T 1 -• P • E (x ) c l c ckk =1Substituting Eq. ( A1) into Eq. ( A2) , we obtain 尸 11 b - a p b - a p • (b - a ) 1 E (x ) = T • P • — •• (2k -1) = 7c • • [(2z -1) ― l ] = ——— (1 一 )c l c 2 21 — 121 21 — 1 21 21 —1 k =1 lb - a _where l is large,-——-口 0, so E (x ) 口 -——P2l — 1 c 21 c 遗传算法中英文对照外文翻译文献 厂 / 、 T 1 T 1 b — a - 1E (x )="—w ="一• ---------- • 2 j -1 二 •ck2 j 2 21 -1 2j =1 j =1 Furthermore, probability of taking • (2k -1) place crossover on each locus ofFig. A1 One point crossoverTheorem 4 Mathematical expectation E m(")of chromosome searching step with bit mutation E m (x)—(b a)* P m, where Pm is the probability of mutation.Proof Mutation probability of genes on each locus of chromosome is equal, say Pm, therefore, mathematical expectation of mutation searching step is一i i - b —a b b- aE (x) = P w = P•—a«2i-1 = P•—a q2，-1)= (b- a) •m m i m 21 -1 m 2 i -1 mi=1 i=1一种新的改进遗传算法及其性能分析摘要：虽然遗传算法以其全局搜索、并行计算、更好的健壮性以及在进化过程中不需要求导而著称，但是它仍然有一定的缺陷，比如收敛速度慢。
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英文翻译2011 届电气工程及其自动化专业 0706073 班级题目遗传算法在非线性模型中的应用姓名学号070607313英语原文：Application of Genetic Programming to NonlinearModelingIntroductionIdentification of nonlinear models which are based in part at least on the underlying physics of the real system presents many problems since both the structure and parameters of the model may need to be determined. Many methods exist for the estimation of parameters from measures response data but structural identification is more difficult. Often a trial and error approach involving a combination of expert knowledge and experimental investigation is adopted to choose between a number of candidate models. Possible structures are deduced from engineering knowledge of the system and the parameters of these models are estimated from available experimental data. This procedure is time consuming and sub-optimal. Automation of this process would mean that a much larger range of potential model structure could be investigated more quickly.Genetic programming (GP) is an optimization method which can be used to optimize the nonlinear structure of a dynamic system by automatically selecting model structure elements from a database and combining them optimally to form a complete mathematical model. Genetic programming works by emulating natural evolution to generate a model structure that maximizes (or minimizes) some objective function involving an appropriate measure of the level of agreement between the model and system response. A population of model structures evolves through many generations towards a solution using certain evolutionary operators and a “survival-of-the-fittest”selection scheme. The parameters of these models may be estimated in a separate and more conventional phase of the complete identification process.ApplicationGenetic programming is an established technique which has been applied to several nonlinear modeling tasks including the development of signal processing algorithms and the identification of chemical processes. In the identification of continuous time system models, the application of a block diagram oriented simulation approach to GP optimization is discussed by Marenbach, Bettenhausen and Gray, and the issues involved in the application of GP to nonlinear system identification are discussed in Gray ‟s another paper. In this paper, Genetic programming is applied to the identification of model structures from experimental data. The systems under investigation are to be represented as nonlinear time domain continuous dynamic models.The model structure evolves as the GP algorithm minimizes some objective function involving an appropriate measure of the level of agreement between the model and system responses. One examples is∑==n i e J 121 (1)Where 1e is the error between model output and experimental data for each of N data points. The GP algorithm constructs and reconstructs model structures from the function library. Simplex and simulated annealing method and the fitness of that model is evaluated using a fitness function such as that in Eq.(1). The general fitness of the population improves until the GP eventually converges to a model description of the system.The Genetic programming algorithmFor this research, a steady-state Genetic-programming algorithm was used. At each generation, two parents are selected from the population and the offspring resulting from their crossover operation replace an existing member of the same population. The number of crossover operations is equal to the size of the population i.e. the crossover rate is 100℅. The crossover algorithm used was a subtree crossover with a limit on the depth of the resulting tree.Genetic programming parameters such as mutation rate and population sizevaried according to the application. More difficult problems where the expected model structure is complex or where the data are noisy generally require larger population sizes. Mutation rate did not appear to have a significant effect for the systems investigated during this research. Typically, a value of about 2℅was chosen.The function library varied according to application rate and what type of nonlinearity might be expected in the system being identified. A core of linear blocks was always available. It was found that specific nonlinearity such as look-up tables which represented a physical phenomenon would only be selected by the Genetic Programming algorithm if that nonlinearity actually existed in the dynamic system.This allows the system to be tested for specific nonlinearities.Programming model structure identificationEach member of the Genetic Programming population represents a candidate model for the system. It is necessary to evaluate each model and assign to it some fitness value. Each candidate is integrated using a numerical integration routine to produce a time response. This simulation time response is compared with experimental data to give a fitness value for that model. A sum of squared error function (Eq.(1)) is used in all the work described in this paper, although many other fitness functions could be used.The simulation routine must be robust. Inevitably, some of the candidate models will be unstable and therefore, the simulation program must protect against overflow error. Also, all system must return a fitness value if the GP algorithm is to work properly even if those systems are unstable.Parameter estimationMany of the nodes of the GP trees contain numerical parameters. These could be the coefficients of the transfer functions, a gain value or in the case of a time delay, the delay itself. It is necessary to identify the numerical parameters of each nonlinear model before evaluating its fitness. The models are randomly generated and cantherefore contain linearly dependent parameters and parameters which have no effect on the output. Because of this, gradient based methods cannot be used. Genetic Programming can be used to identify numerical parameters but it is less efficient than other methods. The approach chosen involves a combination of the Nelder-Simplex and simulated annealing methods. Simulated annealing optimizes by a method which is analogous to the cooling process of a metal. As a metal cools, the atoms organize themselves into an ordered minimum energy structure. The amount of vibration or movement in the atoms is dependent on temperature. As the temperature decreases, the movement, though still random, become smaller in amplitude and as long as the temperature decreases slowly enough, the atoms order themselves slowly enough, the atoms order themselves into the minimum energy structure. In simulated annealing, the parameters start off at some random value and they are allowed to change their values within the search space by an amount related to a quantity defined as system …temperature‟. If a parameter change improves overall fitness, it is accepted, if it reduces fitness it is accepted with a certain probability. The temperature decreases according to some predetermined …cooling‟ schedule and the parameter values should converge to some solution as the temperature drops. Simulated annealing has proved particularly effective when combines with other numerical optimization techniques.One such combination is simulated annealing with Nelder-simplex is an (n+1) dimensional shape where n is the number of parameters. This simples explores the search space slowly by changing its shape around the optimum solution .The simulated annealing adds a random component and the temperature scheduling to the simplex algorithm thus improving the robustness of the method .This has been found to be a robust and reasonably efficient numerical optimization algorithm. The parameter estimation phase can also be used to identify other numerical parameters in part of the model where the structure is known but where there are uncertainties about parameter values.Representation of a GP candidate modelNonlinear time domain continuous dynamic models can take a number of different forms. Two common representations involve sets of differential equations or block diagrams. Both these forms of model are well known and relatively easy to simulate .Each has advantages and disadvantages for simulation, visualization and implementation in a Genetic Programming algorithm. Block diagram and equation based representations are considered in this paper along with a third hybrid representation incorporating integral and differential operators into an equation based representation.Choice of experimental data set——experimental design The identification of nonlinear systems presents particular problems regarding experimental design. The system must be excited across the frequency range of interest as with a linear system, but it must also cover the range of any nonlinearities in the system. This could mean ensuring that the input shape is sufficiently varied to excite different modes of the system and that the data covers the operational range of the system state space.A large training data set will be required to identify an accurate model. However the simulation time will be proportional to the number of data points, so optimization time must be balanced against quantity of data. A recommendation on how to select efficient step and PRBS signals to cover the entire frequency rage of interest may be found in Godfrey and Ljung‟s texts.Model validationAn important part of any modeling procedure is model validation. The new model structure must be validated with a different data set from that used for the optimization. There are many techniques for validation of nonlinear models, the simplest of which is analogue matching where the time response of the model is compared with available response data from the real system. The model validationresults can be used to refine the Genetic Programming algorithm as part of an iterative model development process.Selected from “Control Engineering Practice, Elsevier Science Ltd. ,1998”中文翻译：遗传算法在非线性模型中的应用导言：非线性模型的辨识，至少是部分基于真实系统的基层物理学，自从可能需要同时决定模型的结构和参数以来，就出现了很多问题。