遗传算法中英文对照外文翻译文献
(完整word版)外文翻译-遗传算法
What is a genetic algorithm？●Methods of representation●Methods of selection●Methods of change●Other problem—solving techniquesConcisely stated，a genetic algorithm （or GA for short）is a programming technique that mimics biological evolution as a problem-solving strategy。
Given a specific problem to solve, the input to the GA is a set of potential solutions to that problem，encoded in some fashion，and a metric called a fitness function that allows each candidate to be quantitatively evaluated. These candidates may be solutions already known to work，with the aim of the GA being to improve them, but more often they are generated at random.The GA then evaluates each candidate according to the fitness function. In a pool of randomly generated candidates，of course，most will not work at all, and these will be deleted. However，purely by chance, a few may hold promise — they may show activity，even if only weak and imperfect activity，toward solving the problem.These promising candidates are kept and allowed to reproduce. Multiple copies are made of them, but the copies are not perfect；random changes are introduced during the copying process. These digital offspring then go on to the next generation，forming a new pool of candidate solutions，and are subjected to a second round of fitness evaluation。
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。
遗传学英语文献
遗传学英语文献Genetics has been a field of study that has captivated the minds of scientists and laypeople alike for centuries. The intricacies of the genetic code and its influence on the development and behavior of living organisms have been the subject of extensive research and literature. In the realm of English literature, the topic of genetics has been explored in various forms, from scientific treatises to fictional narratives.One of the seminal works in the field of genetics is Charles Darwin's "On the Origin of Species," published in 1859. This groundbreaking publication laid the foundation for the theory of evolution through natural selection, which has had a profound impact on our understanding of genetics and the diversity of life on Earth. Darwin's work not only presented his scientific findings but also engaged in a broader philosophical discourse on the implications of his theory, sparking debates and conversations that continue to this day.Another notable contribution to the literature on genetics is the work of Gregor Mendel, an Augustinian friar whose experiments with peaplants in the mid-19th century laid the groundwork for our understanding of heredity. Mendel's laws of inheritance, which describe the patterns of genetic inheritance, have become a cornerstone of modern genetics. While Mendel's work was not widely recognized during his lifetime, it has since been celebrated as a pivotal moment in the history of science.In the realm of fiction, genetics has been a recurring theme, often used as a tool to explore the ethical and social implications of scientific advancements. One such example is Aldous Huxley's "Brave New World," published in 1932, which presents a dystopian future where human beings are genetically engineered and society is strictly controlled. Huxley's novel raises questions about the potential consequences of genetic manipulation and the impact it could have on individual autonomy and societal structures.Similarly, Mary Shelley's "Frankenstein," published in 1818, can be interpreted as an exploration of the ethical boundaries of scientific experimentation, particularly in the realm of creating life. The story of Victor Frankenstein's creation of a sentient being, and the subsequent consequences of his actions, has become a classic in the science fiction genre and continues to be analyzed and discussed in the context of genetics and the limits of scientific inquiry.In more recent years, the field of genetics has been further exploredin popular fiction, such as Michael Crichton's "Jurassic Park," which explores the potential of genetic engineering to resurrect extinct species. This novel, and the subsequent film adaptations, have captured the public's imagination and sparked discussions about the ethical and practical implications of such advancements.Beyond fiction, the field of genetics has also been the subject of various scientific texts and scholarly works, which have helped to advance our understanding of the genetic mechanisms that govern the development and function of living organisms. These works range from textbooks and research papers to more accessible popular science books, which aim to bridge the gap between the scientific community and the general public.One such example is James Watson and Francis Crick's "The Double Helix," a firsthand account of their groundbreaking discovery of the structure of DNA, which revolutionized our understanding of the genetic code. This book not only presents the scientific findings but also provides insights into the personalities and dynamics of the scientists involved in the research, offering a glimpse into the human side of scientific discovery.Another notable work in the field of genetics literature is "The Selfish Gene" by Richard Dawkins, published in 1976. This book presents a gene-centric view of evolution, which has had a significant impact onour understanding of the mechanisms of natural selection and the role of genetics in shaping the natural world. Dawkins' engaging writing style and thought-provoking ideas have made this book a classic in the field of evolutionary biology and genetics.In conclusion, the field of genetics has been the subject of a rich and diverse body of English literature, spanning from scientific treatisesto imaginative works of fiction. These literary contributions have not only advanced our understanding of the genetic mechanisms that govern living organisms but have also explored the ethical, social, and philosophical implications of our growing knowledge in this field. As the field of genetics continues to evolve, it is likely that we will see new and innovative perspectives emerge in the literature, further enriching our understanding of this captivating and ever-expanding area of study.。
【机械类文献翻译】采用遗传算法优化加工夹具定位和加紧位置
附录Machining fixture locating and clamping position optimizationusing genetic algorithmsNecmettin Kaya*Department of Mechanical Engineering, Uludag University, Go¨ru¨kle, Bursa 16059, Turkey Received 8 July 2004; accepted 26 May 2005Available online 6 September 2005AbstractDeformation of the workpiece may cause dimensional problems in machining. Supports and locators are used in order to reduce the error caused by elastic deformation of the workpiece. The optimization of support, locator and cl amp locations is a critical problem to minimize the geometric error in workpiece machining. In this paper, the application of genetic algorithms (GAs) to the fixture layout optimization is presented to handle fixture layout optimization problem. A genetic algorithm based approach is developed to optimise fixture layout through integrating a finite element code running in batch mode to compute the objective function values for each generation. Case studies are given to illustrate the application of proposed approach. Chromosome library approach is used to decrease the total solution time. Developed GA keeps track of previously analyzed designs; therefore the numbers of function evaluations are decreased about 93%. The results of this approach show that the fixture layout optimization problems are multi-modal problems. Optimized designs do not have any apparent similarities although they provide very similar performances. Keywords: Fixture design; Genetic algorithms; Optimization1. IntroductionFixtures are used to locate and constrain a workpiece during a machining operation, minimizing workpiece and fixture tooling deflections due to clamping and cutting forces are critical to ensuring accuracy of the machining operation. Traditionally, machining fixtures are designed and manufactured throughtrial-and-error, which prove to be both expensive and time-consuming to themanufacturing process. To ensure a workpiece is manufactured according to specified dimensions and tolerances, it must be appropriately located and clamped, making it imperative to develop tools that will eliminate costly and time-consuming trial-and-error designs. Proper workpiece location and fixture design are crucial to product quality in terms of precision, accuracy and finish of the machined part.Theoretically, the 3-2-1 locating principle can satisfactorily locate all prismatic shaped workpieces. This method provides the maximum rigidity with the minimum number of fixture elements. To position a part from a kinematic point of view means constraining the six degrees of freedom of a free moving body (three translations and three rotations). Three supports are positioned below the part to establish the location of the workpiece on its vertical axis. Locators are placed on two peripheral edges and intended to establish the location of the workpiece on the x and y horizontal axes. Properly locating the workpiece in the fixture is vital to the overall accuracy and repeatability of the manufacturing process. Locators should be positioned as far apart as possible and should be placed on machined surfaces wherever possible. Supports are usually placed to encompass the center of gravity of a workpiece and positioned as far apart as possible to maintain its stability. The primary responsibility of a clamp in fixture is to secure the part against the locators and supports. Clamps should not be expected to resist the cutting forces generated in the machining operation.For a given number of fixture elements, the machining fixture synthesis problem is the finding optimal layout or positions of the fixture elements around the workpiece. In this paper, a method for fixture layout optimization using genetic algorithms is presented. The optimization objective is to search for a 2D fixture layout that minimizes the maximum elastic deformation at different locations of the workpiece. ANSYS program has been used for calculating the deflection of the part under clamping and cutting forces. Two case studies are given to illustrate the proposed approach.2. Review of related worksFixture design has received considerable attention in recent years. However, little attention has been focused on the optimum fixture layout design. Menassa and DeVries[1]used FEA for calculating deflections using the minimization of the workpiece deflection at selected points as the design criterion. The designproblem was to determine the position of supports. Meyer and Liou[2] presented an approach that uses linear programming technique to synthesize fixtures for dynamic machining conditions. Solution for the minimum clamping forces and locator forces is given. Li and Melkote[3]used a nonlinear programming method to solve the layout optimization problem. The method minimizes workpiece location errors due to localized elastic deformation of the workpiece. Roy andLiao[4]developed a heuristic method to plan for the best supporting and clamping positions. Tao et al.[5]presented a geometrical reasoning methodology for determining the optimal clamping points and clamping sequence for arbitrarily shaped workpieces. Liao and Hu[6]presented a system for fixture configuration analysis based on a dynamic model which analyses the fixture–workpiece system subject to time-varying machining loads. The influence of clamping placement is also investigated. Li and Melkote[7]presented a fixture layout and clamping force optimal synthesis approach that accounts for workpiece dynamics during machining. A combined fixture layout and clamping force optimization procedure presented.They used the contact elasticity modeling method that accounts for the influence of workpiece rigid body dynamics during machining. Amaral et al. [8] used ANSYS to verify fixture design integrity. They employed 3-2-1 method. The optimization analysis is performed in ANSYS. Tan et al. [9] described the modeling, analysis and verification of optimal fixturing configurations by the methods of force closure, optimization and finite element modeling.Most of the above studies use linear or nonlinear programming methods which often do not give global optimum solution. All of the fixture layout optimization procedures start with an initial feasible layout. Solutions from these methods are depending on the initial fixture layout. They do not consider the fixture layout optimization on overall workpiece deformation.The GAs has been proven to be useful technique in solving optimization problems in engineering[10–12]. Fixture design has a large solution space and requires a search tool to find the best design. Few researchers have used the GAs for fixture design and fixture layout problems. Kumar et al. [13] have applied both GAs and neural networks for designing a fixture. Marcelin [14]has used GAs to the optimization of support positions. Vallapuzha et al. [15]presented GA based optimization method that uses spatial coordinates to represent the locations offixture elements. Fixture layout optimization procedure was implemented using MATLAB and the genetic algorithm toolbox. HYPERMESH and MSC/NASTRAN were used for FE model. Vallapuzha et al. [16] presented results of an extensive investigation into the relative effectiveness of various optimization methods. They showed that continuous GA yielded the best quality solutions. Li and Shiu [17] determined the optimal fixture configuration design for sheet metal assembly using GA. MSC/NASTRAN has been used for fitness evaluation. Liao[18]presented a method to automatically select the optimal numbers of locators and clamps as well as their optimal positions in sheet metal assembly fixtures. Krishnakumar and Melkote [19]developed a fixture layout optimization technique that uses the GA to find the fixture layout that minimizes the deformation of the machined surface due to clamping and machining forces over the entire tool path. Locator and clamp positions are specified by node numbers. A built-in finite element solver was developed.Some of the studies do not consider the optimization of the layout for entire tool path and chip removal is not taken into account. Some of the studies used node numbers as design parameters.In this study, a GA tool has been developed to find the optimal locator and clamp positions in 2D workpiece. Distances from the reference edges as design parameters are used rather than FEA node numbers. Fitness values of real encoded GA chromosomes are obtained from the results of FEA. ANSYS has been used for FEA calculations. A chromosome library approach is used in order to decrease the solution time. Developed GA tool is tested on two test problems. Two case studies are given to illustrate the developed approach. Main contributions of this paper can be summarized as follows:(1) developed a GA code integrated with a commercial finite element solver;(2) GA uses chromosome library in order to decrease the computation time;(3) real design parameters are used rather than FEA node numbers;(4) chip removal is taken into account while tool forces moving on the workpiece.3. Genetic algorithm conceptsGenetic algorithms were first developed by John Holland. Goldberg [10] published a book explaining the theory and application examples of genetic algorithm in details. A genetic algorithm is a random search technique thatmimics some mechanisms of natural evolution. The algorithm works on a population of designs. The population evolves from generation to generation, gradually improving its adaptation to the environment through natural selection; fitter individuals have better chances of transmitting their characteristics to later generations.In the algorithm, the selection of the natural environment is replaced by artificial selection based on a computed fitness for each design. The term fitness is used to designate the chromosome’s chances of survival and it is essentially the objective function of the optimization problem. The chromosomes that define characteristics of biological beings are replaced by strings of numerical values representing the design variables.GA is recognized to be different than traditional gradient based optimization techniques in the following four major ways [10]:1. GAs work with a coding of the design variables and parameters in the problem, rather than with the actual parameters themselves.2. GAs makes use of population-type search. Many different design points are evaluated during each iteration instead of sequentially moving from one point to the next.3. GAs needs only a fitness or objective function value. No derivatives or gradients are necessary.4. GAs use probabilistic transition rules to find new design points for exploration rather than using deterministic rules based on gradient information to find these new points.4. Approach4.1. Fixture positioning principlesIn machining process, fixtures are used to keep workpieces in a desirable position for operations. The most important criteria for fixturing ar e workpiece position accuracy and workpiece deformation. A good fixture design minimizes workpiece geometric and machining accuracy errors. Another fixturing requirement is that the fixture must limit deformation of the workpiece. It is important to consider the cutting forces as well as the clamping forces. Without adequate fixture support, machining operations do not conform to designed tolerances. Finite element analysis is a powerful tool in the resolution of some of these problems [22].Common locating method for prismatic parts is 3-2-1 method. This method provides the maximum rigidity with the minimum number of fixture elements. A workpiece in 3D may be positively located by means of six points positioned so that they restrict nine degrees of freedom of the workpiece. The other three degrees of freedom are removed by clamp elements. An example layout for 2D workpiece based 3-2-1 locating principle is shown in Fig. 4.Fig. 4. 3-2-1 locating layout for 2D prismatic workpieceThe number of locating faces must not exceed two so as to avoid a redundant location. Based on the 3-2-1 fixturing principle there are two locating planes for accurate location containing two and one locators. Therefore, there are maximum of two side clampings against each locating plane. Clamping forces are always directed towards the locators in order to force the workpiece to contact all locators. The clamping point should be positioned opposite the positioning points to prevent the workpiece from being distorted by the clamping force.Since the machining forces travel along the machining area, it is necessary to ensure that the reaction forces at locators are positive for all the time. Any negative reaction force indicates that the workpiece is free from fixture elements. In other words, loss of contact or the separation between the workpiece and fixture element might happen when the reaction force is negative. Positive reaction forces at the locators ensure that the workpiece maintains contact with all the locators from the beginning of the cut to the end. The clamping forces should be just sufficient to constrain and locate the workpiece without causing distortion or damage to the workpiece. Clamping force optimization is not considered in this paper.4.2. Genetic algorithm based fixture layout optimization approachIn real design problems, the number of design parameters can be very large and their influence on the objective function can be very complicated. The objective function must be smooth and a procedure is needed to compute gradients. Genetic algorithms strongly differ in conception from other search methods, including traditional optimization methods and other stochastic methods [23]. By applying GAs to fixture layout optimization, an optimal or group of sub-optimal solutions can be obtained.In this study, optimum locator and clamp positions are determined using genetic algorithms. They are ideally suited for the fixture layout optimization problem since no direct analytical relationship exists between the machining error and the fixture layout. Since the GA deals with only the design variables and objective function value for a particular fixture layout, no gradient or auxiliary information is needed [19].The flowchart of the proposed approach is given in Fig. 5.Fixture layout optimization is implemented using developed software written in Delphi language named GenFix. Displacement values are calculated in ANSYS software [24]. The execution of ANSYS in GenFix is simply done by WinExec function in Delphi. The interaction between GenFix and ANSYS is implemented in four steps:(1) Locator and clamp positions are extracted from binary string as real parameters.(2) These parameters and ANSYS input batch file (modeling, solution and post processing commands) are sent to ANSYS using WinExec function.(3) Displacement values are written to a text file after solution.(4) GenFix reads this file and computes fitness value for current locator and clamp positions.In order to reduce the computation time, chromosomes and fitness values are stored in a library for further evaluation. GenFix first checks if current chromosome’s fitness value has been calculated before. If not, locator positions are sent to ANSYS, otherwise fitness values are taken from the library. During generating of the initial population, every chromosome is checked whether it is feasible or not. If the constraint is violated, it is eliminated and new chromosome is created. This process creates entirely feasible initial population. This ensures that workpiece is stable under the action of clamping and cutting forces for everychromosome in the initial population.The written GA program was validated using two test cases. The first test case uses Himmelblau function [21]. In the second test case, the GA program was used to optimise the support positions of a beam under uniform loading.5. Fixture layout optimization case studiesThe fixture layout optimization problem is defined as: finding the positions of the locators and clamps, so that workpiece deformation at specific region is minimized. Note that number of locators and clamps are not design parameter, since they are known and fixed for the 3-2-1 locating scheme. Hence, the design parameters are selected as locator and clamp positions. Friction is not considered in this paper. Two case studies are given to illustrate the proposed approach.6. ConclusionIn this paper, an evolutionary optimization technique of fixture layout optimization is presented. ANSYS has been used for FE calculation of fitness values. It is seen that the combined genetic algorithm and FE method approach seems to be a powerful approach for present type problems. GA approach is particularly suited for problems where there does not exist a well-defined mathematical relationship between the objective function and the design variables. The results prove the success of the application of GAs for the fixture layout optimization problems.In this study, the major obstacle for GA application in fixture layout optimization is the high computation cost. Re-meshing of the workpiece is required for every chromosome in the population. But, usages of chromosome library, the number of FE evaluations are decreased from 6000 to 415. This results in a tremendous gain in computational efficiency. The other way to decrease the solution time is to use distributed computation in a local area network.The results of this approach show that the fixture layout optimization problems are multi-modal problems. Optimized designs do not have any apparent similarities although they provide very similar performances. It is shown that fixture layout problems are multi-modal therefore heuristic rules for fixture design should be used in GA to select best design among others.Fig. 5. The flowchart of the proposed methodology and ANSYS interface.采用遗传算法优化加工夹具定位和加紧位置摘要：工件变形的问题可能导致机械加工中的空间问题。
遗传算法简介 英文版
of steepest gradient. Simple to implement, guaranteed convergence. Must know something about the derivative. Can easily get stuck in a local minimum.
Difficult Problems
Appeared in Jan/Feb 2002
SIAM News in the 100Dollar, 100-Digit Challenge.
exp(sin(50*x)) + sin(60*exp(y)) + sin(70*sin(x)) + sin(sin(80*y)) sin(10*(x+y)) + 0.25*(x^2 + y^2)
Time Share Evaluation Function
function [assignment, soln] = local_min(assignment, options)
global family_info
cost = 0; occupancy = zeros(16,1); for i = 1:64 if ceil(assignment(i)/4) == family_info(i,2) cost = cost + 0; elseif ceil(assignment(i)/4) == family_info(i,3) cost = cost + 2*family_info(i,1); elseif ceil(assignment(i)/4) == family_info(i,4) cost = cost + 4*family_info(i,1); else cost = cost + 50 + 7*family_info(i,1); end building = ceil(assignment(i)/4); occupancy(building) = occupancy(building) + family_info(i,1); end for i = 1:16 if occupancy(building) > 22 cost = cost + 1000; end end soln = -cost; % first choice % second choice % third choice % didn't get any choice
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()2GMNO的计算复杂度或者需要更多的处理时间（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。
立体仓库中英文对照外文翻译文献
立体仓库中英文对照外文翻译文献(文档含英文原文和中文翻译)由一个单一的存储/检索机服务的多巷道自动化立体仓库存在的拣选分拣问题摘要随着现代化科技的发展，仓库式存储系统在设计与运行方面出现了巨大的改革。
自动化立体仓库（AS / RS）嵌入计算机驱动正变得越来越普遍。
由于AS / RS 使用的增加对计算机控制的需要与支持也在提高。
这项研究解决了在多巷道立体仓库的拣选问题，在这种存储/检索（S / R）操作中，每种货物可以在多个存储位置被寻址到。
提出运算方法的目标是，通过S/R系统拣选货物来最大限度的减少行程时间。
我们开发的遗传式和启发式算法，以及通过比较从大量的问题中得到一个最佳的解决方案。
关键词：自动化立体仓库，AS / RS系统，拣选，遗传算法。
1.言在现今的生产环境中，库存等级保持低于过去。
那是因为这种较小的存储系统不仅降低库存量还增加了拣选货物的速度。
自动化立体仓库（AS / RS），一方面通过提供快速响应，来达到高操作效率；另一方面它还有助于运作方面的系统响应时间，减少的拣选完成的总行程时间。
因此，它常被用于制造业、储存仓库和分配设备等行业中。
拣选是仓库检索功能的基本组成部分。
它的主要目的是，在预先指定的地点中选择适当数量的货物以满足客户拣选要求。
虽然拣选操作仅仅是物体在仓储中装卸操作之一，但它却是“最耗时间和花费最大的仓储功能。
许多情形下，仓储盈利的高低就在于是否能将拣选操作运行处理好”。
（Bozer和White）Ratliff和Rosenthal，他们关于自动化立体仓库系统（AS/RS）的拣选问题进行的研究，发明了基图算法，在阶梯式布局中选取最短的访问路径。
Roodbergen 和de Koster 拓展了Ratliff 和Rosenthal算法。
他们认为，在平行巷道拣选问题上，应该穿越巷道末端和中间端进行拣选，就此他们发明了一种动态的规划算法解决这问题。
就此Van den Berg 和Gademann发明了一种运输模型(TP)，它是对于指定的存储和卸载进行测算的仪器。
一种新的改进遗传算法及其性能分析外文翻译、中英文翻译、外文文献翻译
一种新的改进遗传算法及其性能分析外文翻译@中英文翻译@外文文献翻译摘要：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。
本文根据几个基本定理，提出了一种使用变异染色体长度和交叉变异概率的改进遗传算法，它的主要思想是：在进化的开始阶段，我们使用短一些的变异染色体长度和高一些的交叉变异概率来解决，在全局最优解附近，使用长一些的变异染色体长度和低一些的交叉变异概率。
最后，一些关键功能的测试表明，我们的解决方案可以显著提高遗传算法的收敛速度，其综合性能优于只保留最佳个体的遗传算法。
关键字：编译染色体长度；变异概率；遗传算法；在线离线性能遗传算法是一种以自然界进化中的选择和繁殖机制为基础的自适应的搜索技术，它是由Holland 1975年首先提出的。
它以其全局搜索、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。
然而它也有一些缺点，如本地搜索不佳，过早收敛，以及收敛速度慢。
近些年，这个问题被广泛地进行了研究。
本文提出了一种使用变异染色体长度和交叉变异概率的改进遗传算法。
一些关键功能的测试表明，我们的解决方案可以显著提高遗传算法的收敛速度，其综合性能优于只保留最佳个体的遗传算法。
在第一部分，提出了我们的新算法。
第二部分，通过几个优化例子，将该算法和只保留最佳个体的遗传算法进行了效率的比较。
第三部分，就是所得出的结论。
最后，相关定理的证明过程可见附录。
1. 算法的描述1.1 一些定理在提出我们的算法之前，先给出一个一般性的定理（见附件），如下：我们假设有一个变量（多变量可以拆分成多个部分，每一部分是一个变量）x ∈[ a, b ] , x ∈R，二进制的染色体编码是1.定理1 染色体的最小分辨率是s =定理2 染色体的第i位的权重值是w i = ( i = 1,2,…l )定理3 单点交叉的染色体搜索步骤的数学期望E c(x)是E c (x) = P c其中P c是交叉概率定理4位变异的染色体搜索步骤的数学期望E m(x)是E m ( x ) = ( b- a) P m其中P m是变异概率1.2 算法机制在进化过程中，我们假设变量的值域是固定的，交叉的概率是一个常数，所以从定理1 和定理3我们知道，较长的染色体长度有着较少的染色体搜索步骤和较高的分辨率；反之亦然。
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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 Analysis Abstract: 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,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 and variant 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, in section 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 is s =12l --a b Theorem 2 Weight value of the ith bit of chromosome isw i =12l --a b 12-i ( i = 1,2,…l ) Theorem 3 Mathematical expectation Ec(x) of chromosome searching step with one-point crossover isE c (x) = la b 2-P c where 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 m1. 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) .1. 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 as X(t) = G 1∑=G t avg f1(t)where G is the current evolutionary generation,avg f is individual averagefitness. 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, whichcan 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 fitness0avg f ,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 generationavg f ;Step 3 If 0avg avgf f ≥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: ()]01.01[5.0sin 5.0),(2222221y x y x y x f ++-+-= ]5,5[ ∈,-y x))4cos(4.0)3cos(3.02(4),(222y x y x y x f ππ--+-= ]1,1[ ∈,-y x2. 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 f1 and f2, respectively.(a) online (b) onlineFig. 1 Online and offline performance of f1(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 is Ec(x) = c P l a b 2-where 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 21(“1” to “0” or “0” to “1”). So, after crossover, mathematical expectation of chromosome searching step on locus from 1 to k is)12(12212122121)(111-•--•=•--•==-==∑∑k l j k j l j kj ck a b a b w x E Furthermore, probability of taking place crossover on each locus of chromosome is equal, namely l 1Pc. Therefore, after crossover, mathematical expectation of chromosome searching step is)(1)(11x E P lx E ck c l k c ••=∑-= Substituting Eq. ( A1) into Eq. ( A2) , we obtain )1211(2)(])12[(122)12(12211)(11---•=--•--•=-•--•••=∑-=l c i l c k l c l k c l a b P l a b l P a b P lx E where l is large, 012≈-l l , so )(x E c c P l a b 2-≈Fig. A1 One point crossoverTheorem 4 Mathematical expectation)(x E m of chromosome searching step with bit mutation m m P a b x E •-=)()(, 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 isE m (x )=P m ·w i =i =1l åP m ·b -a 2l -1·2i -1=i =1l åP m ·b -a 2i -1·(2i -1)=(b -a )·P m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。