SURVEY OF GENETIC ALGORITHMS AND GENETIC PROGRAMMING
Genetic Algorithms for Multiobjective Optimization Formulation ...
Carlos M.Fonseca†and Peter J.Fleming‡Dept.Automatic Control and Systems Eng.University of SheffieldSheffield S14DU,U.K.AbstractThe paper describes a rank-basedfitness as-signment method for Multiple Objective Ge-netic Algorithms(MOGAs).Conventionalniche formation methods are extended to thisclass of multimodal problems and theory forsetting the niche size is presented.Thefit-ness assignment method is then modified toallow direct intervention of an external deci-sion maker(DM).Finally,the MOGA is gen-eralised further:the genetic algorithm is seenas the optimizing element of a multiobjectiveoptimization loop,which also comprises theDM.It is the interaction between the twothat leads to the determination of a satis-factory solution to the problem.Illustrativeresults of how the DM can interact with thegenetic algorithm are presented.They alsoshow the ability of the MOGA to uniformlysample regions of the trade-offsurface.1INTRODUCTIONWhilst most real world problems require the simulta-neous optimization of multiple,often competing,cri-teria(or objectives),the solution to such problems isusually computed by combining them into a single cri-terion to be optimized,according to some utility func-tion.In many cases,however,the utility function isnot well known prior to the optimization process.Thewhole problem should then be treated as a multiobjec-tive problem with non-commensurable objectives.Inthis way,a number of solutions can be found whichprovide the decision maker(DM)with insight into thecharacteristics of the problem before afinal solution ischosen.2VECTOR EV ALUATED GENETICALGORITHMSBeing aware of the potential GAs have in multiob-jective optimization,Schaffer(1985)proposed an ex-tension of the simple GA(SGA)to accommodate vector-valuedfitness measures,which he called the Vector Evaluated Genetic Algorithm(VEGA).The se-lection step was modified so that,at each generation, a number of sub-populations was generated by per-forming proportional selection according to each ob-jective function in turn.Thus,for a problem with q objectives,q sub-populations of size N/q each would be generated,assuming a population size of N.These would then be shuffled together to obtain a new popu-lation of size N,in order for the algorithm to proceed with the application of crossover and mutation in the usual way.However,as noted by Richardson et al.(1989),shuf-fling all the individuals in the sub-populations together to obtain the new population is equivalent to linearly combining thefitness vector components to obtain a single-valuedfitness function.The weighting coeffi-cients,however,depend on the current population. This means that,in the general case,not only will two non-dominated individuals be sampled at differ-ent rates,but also,in the case of a concave trade-offsurface,the population will tend to split into differ-ent species,each of them particularly strong in one of the objectives.Schaffer anticipated this property of VEGA and called it speciation.Speciation is unde-sirable in that it is opposed to the aim offinding a compromise solution.To avoid combining objectives in any way requires a different approach to selection.The next section de-scribes how the concept of inferiority alone can be used to perform selection.3A RANK-BASED FITNESSASSIGNMENT METHOD FORMOGAsConsider an individual x i at generation t which is dom-inated by p(t)i individuals in the current population.Its current position in the individuals’rank can be given byrank(x i,t)=1+p(t)i.All non-dominated individuals are assigned rank1,see Figure1.This is not unlike a class of selection meth-ods proposed by Fourman(1985)for constrained opti-mization,and correctly establishes that the individual labelled3in thefigure is worse than individual labelled 2,as the latter lies in a region of the trade-offwhich is less well described by the remaining individuals.The13511211f1f2Figure1:Multiobjective Rankingmethod proposed by Goldberg(1989,p.201)would treat these two individuals indifferently. Concerningfitness assignment,one should note that not all ranks will necessarily be represented in the pop-ulation at a particular generation.This is also shown in the example in Figure1,where rank4is absent. The traditional assignment offitness according to rank may be extended as follows:1.Sort population according to rank.2.Assignfitnesses to individuals by interpolatingfrom the best(rank1)to the worst(rank n∗≤N) in the usual way,according to some function,usu-ally linear but not necessarily.3.Average thefitnesses of individuals with the samerank,so that all of them will be sampled at the same rate.Note that this procedure keeps the global populationfitness constant while maintain-ing appropriate selective pressure,as defined by the function used.Thefitness assignment method just described appears as an extension of the standard assignment offitness according to rank,to which it maps back in the case of a single objective,or that of non-competing objectives.4NICHE-FORMATION METHODS FOR MOGAsConventionalfitness sharing techniques(Goldberg and Richardson,1987;Deb and Goldberg,1989)have been shown to be to effective in preventing genetic drift,in multimodal function optimization.However,they in-troduce another GA parameter,the niche sizeσshare, which needs to be set carefully.The existing theory for setting the value ofσshare assumes that the solu-tion set is composed by an a priori knownfinite num-ber of peaks and uniform niche placement.Upon con-vergence,local optima are occupied by a number of individuals proportional to theirfitness values.On the contrary,the global solution of an MO prob-lem isflat in terms of individualfitness,and there is no way of knowing the size of the solution set before-hand,in terms of a phenotypic metric.Also,local optima are generally not interesting to the designer, who will be more concerned with obtaining a set of globally non-dominated solutions,possibly uniformly spaced and illustrative of the global trade-offsurface. The use of ranking already forces the search to concen-trate only on global optima.By implementingfitness sharing in the objective value domain rather than the decision variable domain,and only between pairwise non-dominated individuals,one can expect to be able to evolve a uniformly distributed representation of the global trade-offsurface.Niche counts can be consistently incorporated into the extendedfitness assignment method described in the previous section by using them to scale individualfit-nesses within each rank.The proportion offitness allo-cated to the set of currently non-dominated individuals as a whole will then be independent of their sharing coefficients.4.1CHOOSING THE PARAMETERσshare The sharing parameterσshare establishes how far apart two individuals must be in order for them to decrease each other’sfitness.The exact value which would allow a number of points to sample a trade-offsurface only tangentially interfering with one another obviously de-pends on the area of such a surface.As noted above in this section,the size of the set of so-lutions to a MO problem expressed in the decision vari-able domain is not known,since it depends on the ob-jective function mappings.However,when expressed in the objective value domain,and due to the defini-tion of non-dominance,an upper limit for the size of the solution set can be calculated from the minimum and maximum values each objective assumes within that set.Let S be the solution set in the decision variable domain,f(S)the solution set in the objective domain and y=(y1,...,y q)any objective vector in f(S).Also,letm=(miny y1,...,minyy q)=(m1,...,m q)M=(maxy y1,...,maxyy q)=(M1,...,M q)as illustrated in Figure2.The definition of trade-offsurface implies that any line parallel to any of the axes will have not more than one of its points in f(S),which eliminates the possibility of it being rugged,i.e.,each objective is a single-valued function of the remaining objectives.Therefore,the true area of f(S)will be less than the sum of the areas of its projections according to each of the axes.Since the maximum area of each projection will be at most the area of the correspond-ing face of the hyperparallelogram defined by mand Figure2:An Example of a Trade-offSurface in3-Dimensional SpaceM,the hyperarea of f(S)will be less thanA=qi=1qj=1j=i(M j−m j)which is the sum of the areas of each different face of a hyperparallelogram of edges(M j−m j)(Figure3). In accordance with the objectives being non-commensurable,the use of the∞-norm for measuring the distance between individuals seems to be the most natural one,while also being the simplest to compute. In this case,the user is still required to specify an indi-vidualσshare for each of the objectives.However,the metric itself does not combine objective values in any way.Assuming that objectives are normalized so that all sharing parameters are the same,the maximum num-ber of points that can sample area A without in-terfering with each other can be computed as the number of hypercubes of volumeσqsharethat can be placed over the hyperparallelogram defined by A(Fig-ure4).This can be computed as the difference in vol-ume between two hyperparallelograms,one with edges (M i−m i+σshare)and the other with edges(M i−m i), divided by the volume of a hypercube of edgeσshare, i.e.N=qi=1(M i−m i+σshare)−qi=1(M i−m i)Figure3:Upper Bound for the Area of a Trade-offSurface limited by the Parallelogram defined by (m1,m2,m3)and(M1,M2,M3)(q−1)-order polynomial equationNσq−1share −qi=1(M i−m i+σshare)−qi=1(M i−m i)Pareto set of interest to the DM by providing external information to the selection algorithm.Thefitness assignment method described earlier was modified in order to accept such information in the form of goals to be attained,in a similar way to that used by the conventional goal attainment method(Gembicki,1974),which will now be briefly introduced.5.1THE GOAL ATTAINMENT METHOD The goal attainment method solves the multiobjective optimization problem defined asminx∈Ωf(x)where x is the design parameter vector,Ωthe feasible parameter space and f the vector objective function, by converting it into the following nonlinear program-ming problem:minλ,x∈Ωλsuch thatf i−w iλ≤g iHere,g i are goals for the design objectives f i,and w i≥0are weights,all of them specified by the de-signer beforehand.The minimization of the scalarλleads to thefinding of a non-dominated solution which under-or over-attains the specified goals to a degree represented by the quantities w iλ.5.2A MODIFIED MO RANKINGSCHEME TO INCLUDE GOALINFORMATIONThe MO ranking procedure previously described was extended to accommodate goal information by altering the way in which individuals are compared with one another.In fact,degradation in vector components which meet their goals is now acceptable provided it results in the improvement of other components which do not satisfy their goals and it does not go beyond the goal boundaries.This makes it possible for one to prefer one individual to another even though they are both non-dominated.The algorithm will then identify and evolve the relevant region of the trade-offsurface. Still assuming a minimization problem,consider two q-dimensional objective vectors,y a=(y a,1,...,y a,q) and y b=(y b,1,...,y b,q),and the goal vector g= (g1,...,g q).Also consider that y a is such that it meets a number,q−k,of the specified goals.Without loss of generality,one can write∃k=1,...,q−1:∀i=1,...,k,∀j=k+1,...,q,(y a,i>g i)∧(y a,j≤g j)(A) which assumes a convenient permutation of the objec-tives.Eventually,y a will meet none of the goals,i.e.,∀i=1,...,q,(y a,i>g i)(B)or even all of them,and one can write∀j=1,...,q,(y a,j≤g j)(C) In thefirst case(A),y a meets goals k+1,...,q and, therefore,will be preferable to y b simply if it domi-nates y b with respect to itsfirst k components.For the case where all of thefirst k components of y a are equal to those of y b,y a will still be preferable to y b if it dominates y b with respect to the remaining com-ponents,or if the remaining components of y b do not meet all their goals.Formally,y a will be preferable to y b,if and only ify a,(1,...,k)p<y b,(1,...,k) ∨y a,(1,...,k)=y b,(1,...,k) ∧y a,(k+1,...,q)p<y b,(k+1,...,q) ∨∼ y b,(k+1,...,q)≤g(k+1,...,q)In the second case(B),y a satisfies none of the goals. Then,y a is preferable to y b if and only if it dominates y b,i.e.,y a p<y bFinally,in the third case(C)y a meets all of the goals, which means that it is a satisfactory,though not nec-essarily optimal,solution.In this case,y a is preferable to y b,if and only if it dominates y b or y b is not satis-factory,i.e.,(y a p<y b)∨∼(y b≤g)The use of the relation preferable to as just described, instead of the simpler relation partially less than,im-plies that the solution set be delimited by those non-dominated points which tangentially achieve one or more goals.Setting all the goals to±∞will make the algorithm try to evolve a discretized description of the whole Pareto set.Such a description,inaccurate though it may be,can guide the DM in refining its requirements.When goals can be supplied interactively at each GA generation, the decision maker can reduce the size of the solution set gradually while learning about the trade-offbe-tween objectives.The variability of the goals acts as a changing environment to the GA,and does not im-pose any constraints on the search space.Note that appropriate sharing coefficients can still be calculated as before,since the size of the solution set changes in a way which is known to the DM.This strategy of progressively articulating the DM preferences,while the algorithm runs,to guide the search,is not new in operations research.The main disadvantage of the method is that it demands a higher effort from the DM.On the other hand,it potentially reduces the number of function evaluations required when compared to a method for a posteriori articula-tion of preferences,as well as providing less alternativeddddDM a priori knowledgeGAobjective function values fitnesses(acquired knowledge)resultsFigure 5:A General Multiobjective Genetic Optimizerpoints at each iteration,which are certainly easier for the DM to discriminate between than the whole Pareto set at once.6THE MOGA AS A METHOD FOR PROGRESSIVE ARTICULATION OF PREFERENCESThe MOGA can be generalized one step further.The DM action can be described as the consecutive evalu-ation of some not necessarily well defined utility func-tion .The utility function expresses the way in which the DM combines objectives in order to prefer one point to another and,ultimately,is the function which establishes the basis for the GA population to evolve.Linearly combining objectives to obtain a scalar fit-ness,on the one hand,and simply ranking individuals according to non-dominance,on the other,both corre-spond to two different attitudes of the DM.In the first case,it is assumed that the DM knows exactly what to optimize,for example,financial cost.In the second case,the DM is making no decision at all apart from letting the optimizer use the broadest definition of MO optimality.Providing goal information,or using shar-ing techniques,simply means a more elaborated atti-tude of the DM,that is,a less straightforward utility function,which may even vary during the GA process,but still just another utility function.A multiobjective genetic optimizer would,in general,consist of a standard genetic algorithm presenting the DM at each generation with a set of points to be as-sessed.The DM makes use of the concept of Pareto optimality and of any a priori information available to express its preferences,and communicates them to the GA,which in turn replies with the next generation.At the same time,the DM learns from the data it is presented with and eventually refines its requirements until a suitable solution has been found (Figure 5).In the case of a human DM,such a set up may require reasonable interaction times for it to become attrac-tive.The natural solution would consist of speedingup the process by running the GA on a parallel ar-chitecture.The most appealing of all,however,would be the use of an automated DM,such as an expert system.7INITIAL RESULTSThe MOGA is currently being applied to the step response optimization of a Pegasus gas turbine en-gine.A full non-linear model of the engine (Han-cock,1992),implemented in Simulink (MathWorks,1992b),is used to simulate the system,given a num-ber of initial conditions and the controller parameter settings.The GA is implemented in Matlab (Math-Works,1992a;Fleming et al.,1993),which means that all the code actually runs in the same computation en-vironment.The logarithm of each controller parameter was Gray encoded as a 14-bit string,leading to 70-bit long chro-mosomes.A random initial population of size 80and standard two-point reduced surrogate crossover and binary mutation were used.The initial goal values were set according to a number of performance require-ments for the engine.Four objectives were used:t r The time taken to reach 70%of the final output change.Goal:t r ≤0.59s.t s The time taken to settle within ±10%of the final output change.Goal:t s ≤1.08s.os Overshoot,measured relatively to the final output change.Goal:os ≤10%.err A measure of the output error 4seconds after thestep,relative to the final output change.Goal:err ≤10%.During the GA run,the DM stores all non-dominated points evaluated up to the current generation.This constitutes acquired knowledge about the trade-offs available in the problem.From these,the relevant points are identified,the size of the trade-offsurface estimated and σshare set.At any time in the optimiza-trts ov err 00.20.40.60.81N o r m a l i z e d o b j e c t i v e v a l u e s Objective functions0.59s 1.08s 10% 10%Figure 6:Trade-offGraph for the Pegasus Gas Turbine Engine after 40Generations (Initial Goals)tion process,the goal values can be changed,in order to zoom in on the region of interest.A typical trade-offgraph,obtained after 40genera-tions with the initial goals,is presented in Figure 6and represents the accumulated set of satisfactory non-dominated points.At this stage,the setting of a much tighter goal for the output error (err ≤0.1%)reveals the graph in Figure 7,which contains a subset of the points in Figure 6.Continuing to run the GA,more definition can be obtained in this area (Figure 8).Fig-ure 9presents an alternative view of these solutions,illustrating the arising step responses.8CONCLUDING REMARKSGenetic algorithms,searching from a population of points,seem particularly suited to multiobjective opti-mization.Their ability to find global optima while be-ing able to cope with discontinuous and noisy functions has motivatedan increasing number of applications in engineering and related fields.The development of the MOGA is one expression of our wish to bring decision making into engineering design,in general,and control system design,in particular.An important problem arising from the simple Pareto-based fitness assignment method is that of the global size of the solution plex problems can be expected to exhibit a large and complex trade-offsur-face which,to be sampled accurately,would ultimately overload the DM with virtually useless information.Small regions of the trade-offsurface,however,can still be sampled in a Pareto-based fashion,while the deci-sion maker learns and refines its requirements.Niche formation methods are transferred to the objective value domain in order to take advantage of the prop-erties of the Paretoset.Figure 7:Trade-offGraph for the Pegasus Gas Turbine Engine after 40Generations (New Goals)Figure 8:Trade-offGraph for the Pegasus Gas Turbine Engine after 60Generations (New Goals)Figure 9:Satisfactory Step Responses after 60Gener-ations (New Goals)Initial results,obtained from a real world engineering problem,show the ability of the MOGA to evolve uni-formly sampled versions of trade-offsurface regions. They also illustrate how the goals can be changed dur-ing the GA run.Chromosome coding,and the genetic operators them-selves,constitute areas for further study.Redundant codings would eventually allow the selection of the ap-propriate representation while evolving the trade-offsurface,as suggested in(Chipperfield et al.,1992). The direct use of real variables to represent an indi-vidual together with correlated mutations(B¨a ck et al., 1991)and some clever recombination operator(s)may also be interesting.In fact,correlated mutations should be able to identify how decision variables re-late to each other within the Pareto set.AcknowledgementsThefirst author gratefully acknowledges support by Programa CIENCIA,Junta Nacional de Investiga¸c˜a o Cient´ıfica e Tecnol´o gica,Portugal.ReferencesB¨a ck,T.,Hoffmeister,F.,and Schwefel,H.-P.(1991).A survey of evolution strategies.In Belew,R.,editor,Proc.Fourth Int.Conf.on Genetic Algo-rithms,pp.2–9.Morgan Kaufmann.Chipperfield, A.J.,Fonseca, C.M.,and Fleming, P.J.(1992).Development of genetic optimiza-tion tools for multi-objective optimization prob-lems in CACSD.In IEE Colloq.on Genetic Algo-rithms for Control Systems Engineering,pp.3/1–3/6.The Institution of Electrical Engineers.Di-gest No.1992/106.Deb,K.and Goldberg,D.E.(1989).An investigation of niche and species formation in genetic func-tion optimization.In Schaffer,J.D.,editor,Proc.Third Int.Conf.on Genetic Algorithms,pp.42–50.Morgan Kaufmann.Farshadnia,R.(1991).CACSD using Multi-Objective Optimization.PhD thesis,University of Wales, Bangor,UK.Fleming,P.J.(1985).Computer aided design of regulators using multiobjective optimization.In Proc.5th IFAC Workshop on Control Applica-tions of Nonlinear Programming and Optimiza-tion,pp.47–52,Capri.Pergamon Press. Fleming,P.J.,Crummey,T.P.,and Chipperfield,A.J.(1992).Computer assisted control systemdesign and multiobjective optimization.In Proc.ISA Conf.on Industrial Automation,pp.7.23–7.26,Montreal,Canada.Fleming,P.J.,Fonseca,C.M.,and Crummey,T.P.(1993).Matlab:Its toolboxes and open struc-ture.In Linkens,D.A.,editor,CAD for Control Systems,chapter11,pp.271–286.Marcel-Dekker. Fourman,M.P.(1985).Compaction of symbolic lay-out using genetic algorithms.In Grefenstette, J.J.,editor,Proc.First Int.Conf.on Genetic Algorithms,pp.141–wrence Erlbaum. Gembicki,F.W.(1974).Vector Optimization for Con-trol with Performance and Parameter Sensitivity Indices.PhD thesis,Case Western Reserve Uni-versity,Cleveland,Ohio,USA.Goldberg,D.E.(1989).Genetic Algorithms in Search, Optimization and Machine Learning.Addison-Wesley,Reading,Massachusetts.Goldberg,D.E.and Richardson,J.(1987).Genetic algorithms with sharing for multimodal function optimization.In Grefenstette,J.J.,editor,Proc.Second Int.Conf.on Genetic Algorithms,pp.41–wrence Erlbaum.Hancock,S.D.(1992).Gas Turbine Engine Controller Design Using Multi-Objective Optimization Tech-niques.PhD thesis,University of Wales,Bangor, UK.MathWorks(1992a).Matlab Reference Guide.The MathWorks,Inc.MathWorks(1992b).Simulink User’s Guide.The MathWorks,Inc.Richardson,J.T.,Palmer,M.R.,Liepins,G.,and Hilliard,M.(1989).Some guidelines for genetic algorithms with penalty functions.In Schaffer, J.D.,editor,Proc.Third Int.Conf.on Genetic Algorithms,pp.191–197.Morgan Kaufmann. Schaffer,J.D.(1985).Multiple objective optimiza-tion with vector evaluated genetic algorithms.In Grefenstette,J.J.,editor,Proc.First Int.Conf.on Genetic Algorithms,pp.93–wrence Erl-baum.Wienke,D.,Lucasius,C.,and Kateman,G.(1992).Multicriteria target vector optimization of analyt-ical procedures using a genetic algorithm.Part I.Theory,numerical simulations and application to atomic emission spectroscopy.Analytica Chimica Acta,265(2):211–225.。
Genetic Algorithms A Tutorial
The GA Cycle of Reproduction
reproduction
parents
children
modification
modified children
population
deleted members
evaluation
evaluated children
discard
Wendy Williams Metaheuristic Algorithms 7 Genetic Algorithms: A Tutorial
Reproduction
reproduction
parents children
population
Parents are selected at random with selection chances biased in relation to chromosome evaluations.
Wendy Williams Metaheuristic Algorithms 5 Genetic Algorithms: A Tutorial
Simple Genetic Algorithm
{
initialize population; evaluate population; while TerminationCriteriaNotSatisfied
After:
(1.38 -67.5 326.44 0.1)
Causes movement in the search space (local or global) Restores lost information to the population
11 Genetic Algorithms: A Tutorial
人工智能 遗传算法
人工智能遗传算法英文回答：Genetic Algorithms for Artificial Intelligence.Genetic algorithms (GAs) are a class of evolutionary algorithms that are inspired by the process of natural selection. They are used to solve optimization problems by iteratively improving a population of candidate solutions.How GAs Work.GAs work by simulating the process of natural selection. In each iteration, the fittest individuals in thepopulation are selected to reproduce. Their offspring are then combined and mutated to create a new population. This process is repeated until a satisfactory solution is found.Components of a GA.A GA consists of the following components:Population: A set of candidate solutions.Fitness function: A function that evaluates thequality of each candidate solution.Selection: The process of choosing the fittest individuals to reproduce.Reproduction: The process of creating new individuals from the selected parents.Mutation: The process of introducing random changes into the new individuals.Applications of GAs.GAs have been used to solve a wide variety of problems, including:Optimization problems.Machine learning.Scheduling.Design.Robotics.Advantages of GAs.GAs offer several advantages over traditional optimization methods, including:They can find near-optimal solutions to complex problems.They are not easily trapped in local optima.They can be used to solve problems with multiple objectives.Disadvantages of GAs.GAs also have some disadvantages, including:They can be computationally expensive.They can be sensitive to the choice of parameters.They can be difficult to terminate.中文回答：人工智能中的遗传算法。
Genetic Algorithms(遗传算法)PPT课件
Encoding
{0,1}L
(representation)
010001001
011101001 Decoding (inverse representation)
A.E. Eiben and J.E. Smith, Introduction to Evolutionary Computing Genetic Algorithms
Holland’s original GA is now known as the simple genetic algorithm (SGA)
Other GAs use different:
– Representations – Mutations – Crossovers – Selection mechanisms
probability pc , otherwise copy parents 4. For each offspring apply mutation (bit-flip with
probability pm independently for each bit) 5. Replace the whole population with the resulting
Main idea: better individuals get higher chance
– Chances proportional to fitness
– Implementation: roulette wheel technique
– many variants, e.g., reproduction models, operators
A.E. Eiben and J.E. Smith, Introduction to Evolutionary Computing Genetic Algorithms
遗传算法(GeneticAlgorithm)..
2018/10/7
选择(Selection)
选择(复制)操作把当前种群的染色体按与适应值成正比例 的概率复制到新的种群中 主要思想: 适应值较高的染色体体有较大的选择(复制)机 会 实现1：”轮盘赌”选择(Roulette wheel selection) 将种群中所有染色体的适应值相加求总和，染色体适应 值按其比例转化为选择概率Ps 产生一个在0与总和之间的的随机数m 从种群中编号为1的染色体开始，将其适应值与后续染色 体的适应值相加，直到累加和等于或大于m
2018/10/7
选择(Selection)
染色体的适应值和所占的比例
轮盘赌选择
2018/10/7
选择(Selection)
染色体被选的概率
染色体编号
1
2
3
4
5
6
染色体
适应度 被选概率 适应度累计
01110
8
0.16 8
11000
15
0.3 23
00100
2
0.04 25
10010
5
0.1 30
适者生存(Survival of the Fittest)
GA主要采用的进化规则是“适者生存” 较好的解保留，较差的解淘汰
2018/10/7
生物进化与遗传算法对应关系
生物进化
环境
适者生存 个体 染色体 基因 群体 种群 交叉 变异
2018/10/7
遗传算法
适应函数
适应函数值最大的解被保留的概率最大 问题的一个解 解的编码 编码的元素 被选定的一组解 根据适应函数选择的一组解 以一定的方式由双亲产生后代的过程 编码的某些分量发生变化的过程
遗传算法的基本操作
遗传算法(GeneticAlgorithm)..
被选定的一组解 根据适应函数选择的一组解 以一定的方式由双亲产生后代的过程 编码的某些分量发生变化的过程
遗传算法的基本操作
➢选择(selection):
根据各个个体的适应值，按照一定的规则或方法，从 第t代群体P(t)中选择出一些优良的个体遗传到下一代 群体P(t+1)中。
等到达一定程度时，值0会从整个群体中那个位上消失，然而全局最 优解可能在染色体中那个位上为0。如果搜索范围缩小到实际包含全局 最优解的那部分搜索空间，在那个位上的值0就可能正好是到达全局最 优解所需要的。
2023/10/31
适应函数(Fitness Function)
➢ GA在搜索中不依靠外部信息，仅以适应函数为依据，利 用群体中每个染色体(个体)的适应值来进行搜索。以染 色体适应值的大小来确定该染色体被遗传到下一代群体 中的概率。染色体适应值越大，该染色体被遗传到下一 代的概率也越大；反之，染色体的适应值越小，该染色 体被遗传到下一代的概率也越小。因此适应函数的选取 至关重要，直接影响到GA的收敛速度以及能否找到最优 解。
2023/10/31
如何设计遗传算法
➢如何进行编码？ ➢如何产生初始种群？ ➢如何定义适应函数？ ➢如何进行遗传操作(复制、交叉、变异)？ ➢如何产生下一代种群？ ➢如何定义停止准则？
2023/10/31
编码(Coding)
表现型空间
基因型空间 = {0,1}L
编码(Coding)
10010001
父代
111111111111
000000000000
交叉点位置
子代
2023/10/31
111100000000 000011111111
基因算法 文献综述
文献综述1遗传算法的起源当前科学技术正进入多学科互相交叉、互相渗透、互相影响的时代，生命科学与工程科学的交叉、渗透和相互促进是其中一个典型例子，也是近代科学技术发展的一个显著特点。
遗传算法的蓬勃发展正体现了科学发展的这一特点和趋势。
1967年，Holland的学生在博士论文中首次提出“遗传算法”（Genetic Algorithms）一词。
此后，Holland指导学生完成了多篇有关遗传算法研究的论文。
1971年，R.B.Hollstien在他的博士论文中首次把遗传算法用于函数优化。
1975年Holland出版了他的著名专著《自然系统和人工系统的自适应》（Adaptation in Natural and Artificial Systems），这是第一本系统论述遗传算法的专著，因此有人把1975年作为遗传算法的诞生年。
Holland在该书中系统地阐述了遗传算法的基本理论和方法，并提出了对遗传算法的理论研究和发展极其重要的模式理论（schema theory）。
该理论首次确认了结构重组遗传操作对于获得并行性的重要性。
同年，K.A.De Jong完成了他的博士论文《一类遗传自适应系统的行为分析》（An Analysis of the Behavior of a Class of Genetic Adaptive System）。
该论文所做的研究工作，可看作是遗传算法发展进程中的一个里程碑，这是因为，他把Holland的模式理论与他的计算实验结合起来。
尽管De Jong和Hollstien 一样主要侧重于函数优化的应用研究，但他将选择、交叉和变异操作进一步完善和系统化，同时又提出了诸如代沟（generation gap）等新的遗传操作技术。
可以认为，De Jong的研究工作为遗传算法及其应用打下了坚实的基础，他所得出的许多结论，迄今仍具有普遍的指导意义。
进入八十年代，遗传算法迎来了兴盛发展时期，无论是理论研究还是应用研究都成了十分热门的课题。
遗传算法原理(英文)
Soft Computing Lab.
WASEDA UNIVERSITY , IPS
2
Evolutionary Algorithms and Optimization:
Theory and its Applications
Part 2: Network Design
Network Design Problems Minimum Spanning Tree Logistics Network Design Communication Network and LAN Design
Book Info
Provides a comprehensive survey of selection strategies, penalty techniques, and genetic operators used for constrained and combinatorial problems. Shows how to use genetic algorithms to make production schedules and enhance system reliability.
Soft Computing Lab.
WASEDA UNIVERSITY , IPS
4
Evolutionary Algorithms and Optimization:
Theory and its Applications
Part 4: Scheduling
Machine Scheduling and Multi-processor Scheduling Flow-shop Scheduling and Job-shop Scheduling Resource-constrained Project Scheduling Advanced Planning and Scheduling Multimedia Real-time Task Scheduling
遗传算法综述
遗传算法综述尘本是心摘要：遗传算法是一种借鉴生物界自然选择和进化机制发展起来的高度有效的随机搜索算法。
近年来，由于遗传算法求解复杂优化问题的巨大潜力及其在工业工程领域的成功应用，这种算法受到了国内外学者的广泛关注。
本文介绍了遗传算法的基本原理和特点，以及在各个领域的应用情况。
关键词：遗传算法，综述，最优化。
A Review of Genetic AlgorithmsChen BenshixinAbstract:Genetic algorithms are considered as a search used in computing to find exact or a approximate solution for optimization and search problems.This article has a review of the genetic algorithm basic principle and the characteristic and its applications.Keywords:genetic algorithm,review,Optimization0前言在人工智能领域中，有不少问题需要在复杂而庞大的搜索空间中寻找最优解或准最优解。
在计算此类问题时，若不能利用问题的固有知识来缩小搜索空间则会产生搜索的组合爆炸。
因此，研究能在搜索过程中自动获取和积累有关搜索空间的知识并自适应地控制搜索过程从而得到最优解的通用搜索算法一直是令人瞩目的课题。
遗传算是这类特别有效的算法之一，它(GeneticAlgorithm,GA)是一类借鉴生物界的进化规律(适者生存,优胜劣汰遗传机制)演化而来的随机搜索算法。
是由美国Michigan大学的J.Holland教授1975年首先提出，它尤其适用于处理传统搜索方法难以解决的复杂的和非线性的问题。
如著名的TSP、背包问题、排课问题等1遗传算法基本原理遗传算法是建立在自然选择和群众遗传学机理基础上的，具有广泛适应性的搜索方法。
遗传算法及其应用
选择-复制 通常做法是：对于一个规模为N 的种群S,按每个染色体xi∈S的选择概率P(xi)所决 定的选中机会, 分N次从S中随机选定N个染色体, 并进行复制。
这里的选择概率P(xi)的计算公式为
P(xi )
f (xi )
N
f (xj)
j 1
交叉 就是互换两个染色体某些位上的基因。 例如, 设染色体 s1=01001011, s2=10010101, 交换其后4位基因, 即
U1 U2 U3 U4 U5 U6 U7 U8 U9 U10
适应度值eval 4.3701 3.7654 4.9184 4.5556 2.5802 3.4671 3.6203 3.6203 1.0000 3.6203
选择概率P 0.1230 0.1060 0.1385 0.1283 0.0727 0.0976 0.1019 0.1019 0.0282 0.1019
➢ 若下述关系成立，则选择第k个染色体。
Qk1 r Qk ,Q0 0, (1 k pop size)
伪随机数表示指针 大小表示位置 所指向的染色体就是 待选择的染色体
针对本例题，首先计算适值之和
10
F eval(Uk ) 35.5178 k 1
计算各染色体选择概率、积累概率
序号NO.
对一个染色体串的适应度评价由下列三个步骤组成：
（1）将染色体进行反编码，转换成真实值。在本例中，意 味着将二进制串转为实际值：
xk (x2k ), k 1, 2,
（2）评价目标函数f（xk）。 （3）将目标函数值转为适应度值。对于极小值问题，适应 度就等于目标函数值，即
eval(Uk ) f (xk ), k 1, 2,
• 适应度函数(fitness function)就是问题中的 全体个体与其适应度之间的一个对应关。 它一般是一个实值函数。该函数就是遗传 算法中指导搜索的评价函数。
关于遗传算法的研究毕业论文
摘要：在本篇论文主要讨论的是通过介绍生物的遗传问题，什么是遗传算法（genetic Algorithm），遗传算法的性质，应用，传统遗传算法的基本步骤和遗传算法的目前的发展趋向等等内容，使大家得到关于遗传算法的比较深厚的了解。
中文关键词：遗传；遗传算法；染色体；基因；基因地点；基因特征值；适应度英文关键词：Genetic；Genetic Algorithm；Chronmosome；Gene；Locus；Gene Feature；Fitness1、生物的遗传问题与自然选择：众所周知，生命的出现，变化以及其消亡是必然的。
在地球上最早的生命出现以来，在自然界中多种多样的生物一起存在着并且生命的形式与物种不断发生着变化。
由于不同原因，一些物种相继消亡，有一些物种得以生存到现在且还有一些生物改变到另一种生物。
那么到底是什么原因导致这种情况呢？我们先看一下达尔文的自然选择学说的主要内容。
达尔文的自然选择学说是一种被人们广泛接受的生物进化学说。
这种学说认为，生物要生存下去，就必须进行生存斗争。
生存斗争包括种内斗争、种间斗争以及生物跟无机环境之间的斗争三个方面。
在生存斗争中，具有有利变异的个体容易存活下来，并且有更多的机会将有利变异传给后代；具有不利变异的个体就容易被淘汰，产生后代的机会也少的多。
因此，凡是在生存斗争中获胜的个体都是对环境适应性比较强的。
达尔文把这种在生存斗争中适者生存，不适者淘汰的过程叫做自然选择。
它表明，遗传和变异是决定生物进化的内在因素。
自然界中的多种生物之所以能够适应环境而得以生存进化，是和遗传和变异生命现象分不开的。
总之，在这个问题中，我们把主要原因概括在下列两个方面：一个是自然界为生命存在方式所提供的条件即有些生物由于对自然界的适应能力比较强，它们都能适应自然环境的各种变化，反而，还有一些生物的适应能力比较弱，所以它们不能适应自然环境和资源的变化并且很容易就被自然界淘汰。
原因之二是生物自身的遗传与变异功能。
Genetic Algorithm-遗传算法
Travelling salesman problem
Continue.
• This application is an attempt to solve the Traveling Salesman Problem with a genetic algorithm. This algorithm creates a number of full solutions, measures their comparative finesses, and selects the best ones for a new generation of solutions, while also featuring genetic mutation, and immigration features. In this way, the algorithm borrows from the process of biological evolution in order to "evolve" a very good solution for the Traveling Salesman Problem in a short timeframe.
PROBLEM DOMAINS
• Problems which appear to be particularly appropriate for solution by genetic algorithms include timetabling and scheduling problems, and many scheduling software packages are based on GAs. GAs have also been applied to engineering Genetic algorithms are often applied as an approach to solve global optimization problems. • As a general rule of thumb genetic algorithms might be useful in problem domains that have a complex fitness landscape as recombination is designed to move the population away from local optima that a traditional hill climbing algorithm might get stuck in.
基因和遗传学的应用的英语作文
基因和遗传学的应用的英语作文The Applications of Genetics and Genetics in Modern Society.Genetics, the study of genes and their functions in heredity, has revolutionized our understanding of life and its processes. The field of genetics, coupled with advancements in biotechnology, has led to remarkable applications that span from medicine to agriculture, and beyond.Medical Applications.One of the most significant applications of genetics in medicine is the diagnosis and treatment of genetic diseases. Genetic testing allows doctors to identify mutations in genes that cause diseases like cystic fibrosis, sickle cell anemia, and Huntington's disease. With this knowledge, individuals can make informed decisions about their health, such as planning their families or seeking earlyintervention.Gene therapy, a relatively new field, aims to correct genetic defects by inserting healthy genes into patient cells. This innovative approach has shown promise in treating inherited diseases like hemophilia and some forms of blindness. Although still in its early stages, gene therapy offers hope for patients with otherwise incurable conditions.Personalized Medicine.Genetics also plays a crucial role in personalized medicine, which tailors medical treatments to theindividual's genetic profile. By analyzing a patient's genome, doctors can predict their response to certain drugs or therapies, enabling more effective and safer treatment. This approach has been particularly beneficial in cancer treatment, where patients' tumor genomes can guide targeted therapies and reduce the risk of drug resistance.Agricultural Applications.Genetics has revolutionized agriculture, leading to the development of crop varieties that are more resistant to diseases, pests, and environmental stress. Genetic engineering has allowed scientists to transfer desirable traits from one species to another, creating crops with improved yields, nutritional content, and shelf life. For example, genetically modified (GM) cotton varieties have significantly reduced the need for pesticides, while GM corn and soybeans have enhanced nutritional value.Environmental Applications.Genetics also plays a role in environmental conservation and restoration. By understanding the genetic makeup of plant and animal species, scientists can develop strategies to protect endangered species from extinction. Genetic resources can be used to restore damaged ecosystems by reintroducing genetically diverse populations of plants and animals.Biotechnology Applications.The field of biotechnology has been greatly influenced by genetics. Biotechnology uses genetic principles to create new products and processes, such as enzymes for industrial applications, vaccines for disease prevention, and biofuels for renewable energy. Genetically modified organisms (GMOs) have also been used in the production of pharmaceuticals, biopesticides, and other valuable compounds.Ethical and Social Considerations.While the applications of genetics and genetics have brought remarkable benefits, they also raise ethical and social concerns. Issues such as genetic privacy, informed consent, and the potential for genetic discrimination need to be addressed. Additionally, the ethical implications of genetic engineering, particularly in human germline gene editing, are hotly debated and require careful consideration.Conclusion.The applications of genetics and genetics have transformed our world, offering new solutions to complex problems in medicine, agriculture, environmental conservation, and biotechnology. As we continue to harness the power of genetics, it is crucial to balance thebenefits with ethical and social responsibilities. By doing so, we can ensure that the applications of genetics and genetics continue to benefit society while respecting the dignity and rights of all.。
调查报告性氏研究英语作文
调查报告性氏研究英语作文## Genetic Genealogy: Uncovering Ancestral Roots through DNA Analysis.Introduction.Genetic genealogy is a rapidly evolving field that utilizes DNA analysis to trace ancestral lineages and uncover family histories. By comparing DNA samples from individuals, researchers can identify shared genetic markers that indicate common ancestry. This information can be used to construct family trees, identify unknown relatives, and shed light on historical events.DNA Analysis and Genetic Markers.DNA analysis plays a crucial role in genetic genealogy. DNA is the genetic material found in all living organisms, and it carries information about an individual's traits and ancestry. Genetic markers are specific regions of DNA thatvary from person to person. By comparing these markers, researchers can identify patterns that suggest a shared genetic heritage.Commonly used genetic markers for genealogy include:Autosomal DNA (atDNA): Inherited from both parents, atDNA can be used to trace ancestry from any line.Y-DNA (Y-chromosome DNA): Passed down from father to son, Y-DNA is used to trace paternal ancestry.Mitochondrial DNA (mtDNA): Inherited solely from the mother, mtDNA is used to trace maternal ancestry.Types of Genetic Genealogy Tests.Various genetic genealogy tests are available, each providing different levels of information:Ancestry tests: These tests provide an overview of a person's genetic heritage, including ethnic breakdown andpotential regions of ancestry.Family reconciliation tests: These tests match individuals with potential relatives based on shared DNA.Y-DNA and mtDNA tests: These tests focus on specific ancestral lines and can be used to determine haplogroups (genetic lineages) and identify distant relatives.Applications of Genetic Genealogy.Genetic genealogy has numerous applications, including:Historical research: Identifying genetic markers associated with specific historical events or migrations.Adoption and family reunification: Searching for unknown biological relatives and resolving adoption mysteries.Genealogical research: Confirming family tree information, discovering new relatives, and extendingancestral lineages.Forensic investigation: Assisting in crime-solving and identifying missing persons.Medical research: Identifying genetic risk factors and developing personalized treatments.Ethical Considerations.Ethical considerations are essential in genetic genealogy:Informed consent: Individuals must be fully informed about the implications of genetic testing before providing consent.Data privacy and security: Genetic information is highly sensitive and must be protected from unauthorized access or misuse.Genetic discrimination: Genetic information should notbe used to discriminate against individuals based on their genetic makeup.Interpretation of results: Results from genetic genealogy tests should be interpreted cautiously and in consultation with experts.Conclusion.Genetic genealogy has revolutionized the field of genealogy, providing unprecedented insights into our ancestral roots. Through DNA analysis, researchers can uncover hidden family connections, explore historical migrations, and make groundbreaking discoveries. As the technology continues to advance, genetic genealogy will become an even more powerful tool for understanding our past and shaping our future. However, it is crucial to approach genetic genealogy with ethical considerations and a deep respect for the sensitive nature of genetic information.。
遗传算法
遗传算法(Genetic Algorithms)简介
遗传算法（Genetic Algorithms）是基于生物进化理论的原理发展起来的一种广为应用的、高效的随机搜索与优化的方法。
其主要特点是群体搜索策略和群体中个体之间的信息交换，搜索不依赖于梯度信息。
它是在70年代初期由美国密执根（Michigan）大学的霍兰（Holland）教授发展起来的。
1975年霍兰教授发表了第一本比较系统论述遗传算法的专著《自然系统与人工系统中的适应性》（《Adaptation in Natural and Artificial Systems》）。
遗传算法最初被研究的出发点不是为专门解决最优化问题而设计的，它与进化策略、进化规划共同构成了进化算法的主要框架，都是为当时人工智能的发展服务的。
迄今为止，遗传算法是进化算法中最广为人知的算法。
近几年来，遗传算法主要在复杂优化问题求解和工业工程领域应用，取得了一些令人信服的结果，所以引起了很多人的关注，而且在发展过程中，进化策略、进化规划和遗传算法之间差异越来越小。
遗传算法成功的应用包括：作业调度与排序、可靠性设计、车辆路径选择与调度、成组技术、设备布置与分配、交通问题等等。
寻找遗传基因的方法
寻找遗传基因的方法Finding genetic genes is a complex process that requires a combination of scientific methods and technology. 寻找遗传基因是一个复杂的过程，需要结合科学方法和技术。
One method used to find genetic genes is whole genome sequencing, which involves mapping out an individual’s entire genetic code. This process allows researchers to identify specific genes or mutations that may be associated with certain traits or diseases. 通过对整个基因组的测序，研究人员可以识别与特定特征或疾病相关的特定基因或突变。
Another method is gene mapping, which involves identifying the location of specific genes on a chromosome. This can be done through various techniques such as linkage analysis or association studies, and can help pinpoint the genetic basis of certain traits or diseases. 另一种方法是基因映射，它涉及识别染色体上特定基因的位置。
这可以通过各种技术来实现，比如连锁分析或关联研究，可以帮助确定某些特征或疾病的遗传基础。
Furthermore, gene expression analysis can also be used to find genetic genes, as it involves studying how genes are turned on or off in different cells or tissues. This can provide valuable insights into how certain genes may be associated with particular traits or diseases. 此外，基因表达分析也可以用来寻找遗传基因，因为它涉及研究基因在不同细胞或组织中的开启或关闭方式。
遗传算法在生物信息学中的应用
遗传算法在生物信息学中的应用在当今时代，生物信息学逐渐得到广泛关注，已经成为了现代生命科学的重要分支之一。
在生物信息学中，遗传算法已经被广泛应用，并取得了很多有意义的成果。
本文将着重探讨遗传算法在生物信息学中的应用。
一、遗传算法简介遗传算法（GA，Genetic Algorithm）是应用生物进化思想（遗传学、进化论）来解决优化问题的一种搜索算法。
遗传算法首先将种群进行初始化，然后通过选择、交叉、变异等操作，不断优化种群的适应性，最终找到最优解或最优逼近解。
遗传算法的优点在于其具有快速性、自适应性和高可靠性等特点。
在许多复杂问题的解决中，遗传算法已经成为了最有效的方法之一。
二、遗传算法在基因序列比对中的应用基因序列比对是生物信息学的重要研究方向之一。
在进行基因序列比对时，遗传算法被广泛应用。
传统的基因序列比对算法包括Smith-Waterman算法和Needleman-Wunsch算法等。
这些算法在精度方面表现很好，但时间复杂度比较高。
对于大量数据的比对，传统算法已经无法满足需求。
遗传算法通过不断调整基因序列的适应度，从而得到基因的最优匹配。
这种方法可以大大减少比对时间和资源耗费。
目前已经有很多基于遗传算法的基因序列比对软件，例如BLAST、FASTA等。
三、遗传算法在蛋白质结构预测中的应用蛋白质结构预测是生物信息学中的重要问题之一。
在蛋白质结构预测中，遗传算法也被广泛应用。
蛋白质结构预测的难点在于蛋白质的复杂性和多样性。
传统的蛋白质结构预测算法需要大量的时间和资源，而且精度也难以保证。
遗传算法通过不断优化蛋白质的结构，从而得到最优的蛋白质结构，具有极高的准确性和快速性。
目前已经有很多基于遗传算法的蛋白质结构预测软件，例如Rosetta、SwissModel等。
这些软件已经被广泛应用于生命科学研究和临床治疗中。
四、遗传算法在基因表达数据分析中的应用基因表达数据分析是生物信息学中的一个热门领域。
在基因表达数据分析中，遗传算法也得到了广泛应用。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
SURVEY OF GENETIC ALGORITHMS AND GENETIC PROGRAMMINGJohn R. KozaComputer Science DepartmentMargaret Jacks HallStanford UniversityStanford, California 94305Koza@ 415-941-0336/~koza/ABSTRACTThis paper provides an introduction to geneticalgorithms and genetic programming and lists sourcesof additional information, including books andconferences as well as e-mail lists and software that isavailable over the Internet.1. GENETIC ALGORITHMSJohn Holland's pioneering book Adaptation in Natural and Artificial Systems (1975, 1992) showed how the evolutionary process can be applied to solve a wide variety of problems using a highly parallel technique that is now called the genetic algorithm.The genetic algorithm (GA) transforms a population (set)of individual objects, each with an associated fitness value, into a new generation of the population using the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring genetic operations such as crossover (sexual recombination) and mutation.Each individual in the population represents a possible solution to a given problem. The genetic algorithm attempts to find a very good (or best) solution to the problem by genetically breeding the population of individuals over a series of generations.Before applying the genetic algorithm to the problem, the user designs an artificial chromosome of a certain fixed size and then defines a mapping (encoding) between the points in the search space of the problem and instances of the artificial chromosome. For example, in applying the genetic algorithm to a multidimensional optimization problem (where the goal is to find the global optimum of an unknown multidimensional function), the artificial chromosome may be a linear character string (modeled directly after the linear string of information found in DNA). A specific location (a gene) along this artificial chromosome is associated with each of the variables of the problem. Character(s) appearing at a particular location along the chromosome denote the value of a particular variable (i.e., the gene value or allele). Each individual in the population has a fitness value (which, for a multidimensional optimization problem, is the value of the unknown function). The genetic algorithm then manipulates a population of such artificial chromosomes (usually starting from a randomly-created initial population of strings) using the operations of reproduction, crossover, and mutation. Individuals are probabilistically selected to participate in these genetic operations based on their fitness. The goal of the genetic algorithm in a multidimensional optimization problem is to find an artificial chromosome which, when decoded and mapped back into the search space of the problem, corresponds to a globally optimum (or near-optimum) point in the original search space of the problem.In preparing to use the conventional genetic algorithm operating on fixed-length character strings to solve a problem, the user must(1) determine the representation scheme,(2) determine the fitness measure,(3) determine the parameters and variables for controllingthe algorithm, and(4) determine a way of designating the result and a criterionfor terminating a run.In the conventional genetic algorithm, the individuals in the population are usually fixed-length character strings patterned after chromosome strings. Thus, specification of the representation scheme in the conventional genetic algorithm starts with a selection of the string length L and the alphabet size K. Often the alphabet is binary, so K equals 2. The most important part of the representation scheme is the mapping that expresses each possible point in the search space of the problem as a fixed-length character string (i.e., as a chromosome) and each chromosome as a point in the search space of the problem. Selecting a representation scheme that facilitates solution of the problem by the genetic algorithm often requires considerable insight into the problem and good judgment.The evolutionary process is driven by the fitness measure. The fitness measure assigns a fitness value to each possible fixed-length character string in the population.The primary parameters for controlling the genetic algorithm are the population size, M, and the maximum number of generations to be run, G. Populations can consist of hundreds, thousands, tens of thousands or more individuals. There can be dozens, hundreds, thousands, or more generations in a run of the genetic algorithm.Each run of the genetic algorithm requires specification of a termination criterion for deciding when to terminate a run and a method of result designation. One frequently used method of result designation for a run of the genetic algorithm is to designate the best individual obtained in any generation of the population during the run (i.e., the best-so-far individual) as the result of the run.Once the four preparatory steps for setting up the genetic algorithm have been completed, the genetic algorithm can be run.The evolutionary process described above indicates how a globally optimum combination of alleles (gene values) within a fixed-size chromosome can be evolved.The three steps in executing the genetic algorithm operating on fixed-length character strings are as follows:(1) Randomly create an initial population of individual fixed-length character strings.(2) Iteratively perform the following substeps on thepopulation of strings until the termination criterion has been satisfied:(A) Assign a fitness value to each individual in thepopulation using the fitness measure.(C) Create a new population of strings by applying thefollowing three genetic operations. The geneticoperations are applied to individual string(s) in thepopulation chosen with a probability based on fitness.(i) Reproduce an existing individual string by copyingit into the new population.(ii) Create two new strings from two existing strings by genetically recombining substrings using thecrossover operation (described below) at arandomly chosen crossover point.(iii) Create a new string from an existing string byrandomly mutating the character at one randomlychosen position in the string.(3) The string that is identified by the method of resultdesignation (e.g., the best-so-far individual) is designated as the result of the genetic algorithm for the run. This result may represent a solution (or an approximate solution) to the problem.The genetic operation of reproduction is based on the Darwinian principle of reproduction and survival of the fittest. In the reproduction operation, an individual is probabilistically selected from the population based on its fitness (with reselection allowed) and then the individual is copied, without change, into the next generation of the population. The selection is done in such a way that the better an individual's fitness, the more likely it is to be selected. An important aspect of this probabilistic selection is that every individual, however poor its fitness, has some probability of selection.The genetic operation of crossover (sexual recombination) allows new individuals (i.e., new points in the search space) to be created and tested. The operation of crossover starts with two parents independently selected probabilistically from the population based on their fitness (with reselection allowed). As before, the selection is done in such a way that the better an individual's fitness, the more likely it is to be selected. The crossover operation produces two offspring. Each offspring contains some genetic material from each of its parents.Suppose that the crossover operation is to be applied to the two parental strings 10110 and 01101 of length L = 5 over an alphabet of size K = 2. The crossover operation begins by randomly selecting a number between 1 and L–1 using a uniform probability distribution. Suppose that the third interstitial location is selected. This location becomes the crossover point. Each parent is then split at this crossover point into a crossover fragment and a remainder. The crossover operation then recombines remainder 1 (i.e., – – – 1 0) with crossover fragment 2 (i.e., 011 – –) to create offspring 2 (i.e., 01110). The crossover operation similarly recombines remainder 2 (i.e., – – – 01) with crossover fragment 1 (i.e., 101 – –) to create offspring 1 (i.e., 10101).The operation of mutation allows new individuals to be created. It begins by selecting an individual from the population based on its fitness (with reselection allowed). A point along the string is selected at random and the character at that point is randomly changed. The altered individual is then copied intothe next generation of the population. Mutation is used very sparingly in genetic algorithm work.The genetic algorithm works in a domain-independent wayon the fixed-length character strings in the population. The genetic algorithm searches the space of possible character strings in an attempt to find high-fitness strings. The fitness landscape may be very rugged and nonlinear. To guide this search, the genetic algorithm uses only the numerical fitnessvalues associated with the explicitly tested strings in the population. Regardless of the particular problem domain, the genetic algorithm carries out its search by performing the same disarmingly simple operations of copying, recombining, and occasionally randomly mutating the strings.In practice, the genetic algorithm is surprisingly rapid in effectively searching complex, highly nonlinear, multidimensional search spaces. This is all the more surprising because the genetic algorithm does not know anything about the problem domain or the internal workings of the fitness measurebeing used.1.1 Sources of Additional InformationDavid Goldberg's Genetic Algorithms in Search, Optimization,and Machine Learning (1989) is the leading textbook and bestsingle source of additional information about the field of genetic algorithms.Additional information on genetic algorithms can be foundin Davis (1987, 1991), Michalewicz (1992), and Buckles andPetry (1992). The proceedings of the International Conferenceon Genetic Algorithms provide an overview of research activityin the genetic algorithms field. See Eshelman (1995), Forrest (1993), Belew and Booker (1991), Schaffer (1989), and Grefenstette (1985, 1987).Also see the proceedings of the IEEE International Conference on Evolutionary Computation {IEEE 1994, 1995).The proceedings of the Foundations of Genetic Algorithms workshops cover theoretical aspects of the field. See Whitleyand Vose (1995), Whitley (1992), and Rawlins (1991).Fogel and Atmar (1992, 1993), Sebald and Fogel (1994), andSebald and Fogel (1995) emphasizes recent work on evolutionary programming (EP).The proceedings of the Parallel Problem Solving from Nature conferences emphasize work on evolution strategies (ES). See Schwefel and Maenner (1991), Maenner and Manderick (1992), and Davidor, Schwefel, and Maenner (1994).Stender (1993) describes parallelization of genetic algorithms. Also see Koza and Andre 1995. Davidor (1992) describes application of genetic algorithms to robotics. Schafferand Whitley (1992) and Albrecht, Reeves, and Steele (1993) describe work on combinations of genetic algorithms and neural networks. Forrest (1991) describes application of genetic classifier systems to semantic nets.Additional information about genetic algorithms may be obtained from the GA-LIST electronic mailing list to which youmay subscribe, at no charge, by sending a subscription request toGA-List-Request@. Issues of theGA-LIST provide instructions for accessing the genetic algorithms archive, which contains software that may be obtained over the Internet. The archive may be accessed overthe World Wide Web at /galist/ or through anonymous ftp at (192.26.18.68)in /pub/galist.2. GENETIC PROGRAMMINGGenetic programming is an attempt to deal with one of the central questions in computer science (posed by Arthur Samuel in 1959), namelyHow can computers learn to solve problems withoutbeing explicitly programmed? In other words, how cancomputers be made to do what needs to be done, withoutbeing told exactly how to do it?All computer programs – whether they are written in FORTRAN, PASCAL, C, assembly code, or any other programming language – can be viewed as a sequence of applications of functions (operations) to arguments (values). Compilers use this fact by first internally translating a given program into a parse tree and then converting the parse tree into the more elementary assembly code instructions that actually run on the computer. However this important commonality underlying all computer programs is usually obscured by the large variety of different types of statements, operations, instructions, syntactic constructions, and grammatical restrictions found in most popular programming languages.Any computer program can be graphically depicted as a rooted point-labeled tree with ordered branches.Genetic programming is an extension of the conventional genetic algorithm in which each individual in the population is a computer program.The search space in genetic programming is the space of all possible computer programs composed of functions and terminals appropriate to the problem domain. The functions may be standard arithmetic operations, standard programming operations, standard mathematical functions, logical functions, or domain-specific functions.The book Genetic Programming: On the Programming of Computers by Means of Natural Selection (Koza 1992) demonstrated a result that many found surprising and counterintuitive, namely that an automatic, domain-independent method can genetically breed computer programs capable of solving, or approximately solving, a wide variety of problems from a wide variety of fields.In applying genetic programming to a problem, there are five major preparatory steps. These five steps involve determining(1) the set of terminals,(2) the set of primitive functions,(3) the fitness measure,(4) the parameters for controlling the run, and(5) the method for designating a result and the criterion forterminating a run.The first major step in preparing to use genetic programmingis to identify the set of terminals. The terminals can be viewed as the inputs to the as-yet-undiscovered computer program. The set of terminals (along with the set of functions) are the ingredients from which genetic programming attempts to construct a computer program to solve, or approximately solve, the problem.The second major step in preparing to use genetic programming is to identify the set of functions that are to be used to generate the mathematical expression that attempts to fit the given finite sample of data.Each computer program (i.e., mathematical expression, LISPS-expression, parse tree) is a composition of functions from the function set F and terminals from the terminal set T.Each of the functions in the function set should be able to accept, as its arguments, any value and data type that may possibly be returned by any function in the function set and any value and data type that may possibly be assumed by any terminal in the terminal set. That is, the function set and terminal set selected should have the closure property.These first two major steps correspond to the step of specifying the representation scheme for the conventional genetic algorithm. The remaining three major steps for genetic programming correspond to the last three major preparatory steps for the conventional genetic algorithm.In genetic programming, populations of hundreds, thousands, or millions of computer programs are genetically bred. This breeding is done using the Darwinian principle of survival and reproduction of the fittest along with a genetic crossover operation appropriate for mating computer programs.A computer program that solves (or approximately solves) a given problem often emerges from this combination of Darwinian natural selection and genetic operations.Genetic programming starts with an initial population (generation 0) of randomly generated computer programs composed of functions and terminals appropriate to the problem domain. The creation of this initial random population is, in effect, a blind random search of the search space of the problem represented as computer programs.Each individual computer program in the population is measured in terms of how well it performs in the particular problem environment. This measure is called the fitness measure. The nature of the fitness measure varies with the problem.For many problems, fitness is naturally measured by the error produced by the computer program. The closer this error is to zero, the better the computer program. In a problem of optimal control, the fitness of a computer program may be the amount of time (or fuel, or money, etc.) it takes to bring the system to a desired target state. The smaller the amount of time (or fuel, or money, etc.), the better. If one is trying to recognize patterns or classify examples, the fitness of a particular program may be measured by some combination of the number of instances handled correctly (i.e., true positive and true negatives) and the number of instances handled incorrectly (i.e., false positives and false negatives). Correlation is often used as a fitness measure. On the other hand, if one is trying to find a good randomizer, the fitness of a given computer program might be measured by means of entropy, satisfaction of the gap test, satisfaction of the run test, or some combination of these factors. For electronic circuit design problems, the fitness measure may involve a convolution. For some problems, it may be appropriate to use a multiobjective fitness measure incorporating a combination of factors such as correctness, parsimony (smallness of the evolved program), or efficiency (of execution).Typically, each computer program in the population is run over a number of different fitness cases so that its fitness is measured as a sum or an average over a variety of representative different situations. These fitness cases sometimes represent a sampling of different values of an independent variable or a sampling of different initial conditions of a system. For example, the fitness of an individual computer program in the population may be measured in terms of the sum of the absolute value of the differences between the output produced by the program and the correct answer to the problem (i.e., the Minkowski distance) or the square root of the sum of thesquares (i.e., Euclidean distance). These sums are taken over a sampling of different inputs (fitness cases) to the program. The fitness cases may be chosen at random or may be chosen in some structured way (e.g., at regular intervals or over a regular grid). It is also common for fitness cases to represent initial conditions of a system (as in a control problem). In economic forecasting problems, the fitness cases may be the daily closing price of some financial instrument.The computer programs in generation 0 of a run of genetic programming will almost always have exceedingly poor fitness. Nonetheless, some individuals in the population will turn out to be somewhat more fit than others. These differences in performance are then exploited.The Darwinian principle of reproduction and survival of the fittest and the genetic operation of crossover are used to create a new offspring population of individual computer programs from the current population of programs.The reproduction operation involves selecting a computer program from the current population of programs based on fit-ness (i.e., the better the fitness, the more likely the individual is to be selected) and allowing it to survive by copying it into the new population.The crossover operation is used to create new offspring computer programs from two parental programs selected based on fitness. The parental programs in genetic programming are typically of different sizes and shapes. The offspring programs are composed of subexpressions (subtrees, subprograms, subroutines, building blocks) from their parents. These offspring programs are typically of different sizes and shapes than their parents.The mutation operation may also be used in genetic programming.After the genetic operations are performed on the current population, the population of offspring (i.e., the new generation) replaces the old population (i.e., the old generation). Each individual in the new population of programs is then measured for fitness, and the process is repeated over many generations.At each stage of this highly parallel, locally controlled, decentralized process, the state of the process will consist only of the current population of individuals.The force driving this process consists only of the observed fitness of the individuals in the current population in grappling with the problem environment.As will be seen, this algorithm will produce populations of programs which, over many generations, tend to exhibit increasing average fitness in dealing with their environment. In addition, these populations of computer programs can rapidly and effectively adapt to changes in the environment.The best individual appearing in any generation of a run (i.e., the best-so-far individual) is typically designated as the result produced by the run of genetic programming.The hierarchical character of the computer programs that are produced is an important feature of genetic programming. The results of genetic programming are inherently hierarchical. In many cases the results produced by genetic programming are default hierarchies, prioritized hierarchies of tasks, or hierarchies in which one behavior subsumes or suppresses another.The dynamic variability of the computer programs that are developed along the way to a solution is also an important feature of genetic programming. It is often difficult and unnatural to try to specify or restrict the size and shape of the eventual solution in advance. Moreover, advance specification or restriction of the size and shape of the solution to a problem narrows the window by which the system views the world and might well preclude finding the solution to the problem at all.Another important feature of genetic programming is the absence or relatively minor role of preprocessing of inputs and postprocessing of outputs. The inputs, intermediate results, and outputs are typically expressed directly in terms of the natural terminology of the problem domain. The programs produced by genetic programming consist of functions that are natural for the problem domain. The postprocessing of the output of a program, if any, is done by a wrapper (output interface).Finally, another important feature of genetic programming is that the structures undergoing adaptation in genetic programming are active. They are not passive encodings (i.e., chromosomes) of the solution to the problem. Instead, given a computer on which to run, the structures in genetic programming are active structures that are capable of being executed in their current form.The genetic crossover (sexual recombination) operation operates on two parental computer programs selected with a probability based on fitness and produces two new offspring programs consisting of parts of each parent.For example, consider the following computer program (presented here as a LISP S-expression):(+ (* 0.234 Z) (- X 0.789)),which we would ordinarily write as0.234 Z + X – 0.789.This program takes two inputs (X and Z) and produces a floating point output.Also, consider a second program:(* (* Z Y) (+ Y (* 0.314 Z))).Suppose that the crossover points are the * in the first parent and the + in the second parent. These two crossover fragments correspond to the underlined sub-programs (sub-lists) in the two parental computer programs.The two offspring resulting from crossover are as follows:(+ (+ Y (* 0.314 Z)) (- X 0.789))(* (* Z Y) (* 0.234 Z)).Thus, crossover creates new computer programs using parts of existing parental programs. Because entire sub-trees are swapped, the crossover operation always produces syntactically and semantically valid programs as offspring regardless of the choice of the two crossover points. Because programs are selected to participate in the crossover operation with a probability based on fitness, crossover allocates future trials to regions of the search space whose programs contains parts from promising programs.The videotape Genetic Programming: The Movie (Koza and Rice 1992) provides a visualization of the genetic programming process and of solutions to various problems.2.2 Automatically Defined FunctionsI believe that no approach to automated programming is likely to be successful on non-trivial problems unless it provides some hierarchical mechanism to exploit, by reuse and parameterization, the regularities, symmetries, homogeneities, similarities, patterns, and modularities inherent in problem environments. Subroutines do this in ordinary computer programs.Accordingly, Genetic Programming II: Automatic Discovery of Reusable Programs (Koza 1994) describes how to evolve multi-part programs consisting of a main program and one or more reusable, parameterized, hierarchically-called subprograms (called automatically defined functions or ADF s). A visualization of the solution to numerous example problems using automatically defined functions can be found in the videotape Genetic Programming II Videotape: The Next Generation (Koza 1994).Automatically defined functions can be implemented within the context of genetic programming by establishing a constrained syntactic structure for the individual programs in the population. Each multi-part program in the population contains one (or more) function-defining branches and one (or more) main result-producing branches. The result-producing branch usually has the ability to call one or more of the automatically defined functions. A function-defining branch may have the ability to refer hierarchically to other already-defined automatically defined functions.Genetic programming evolves a population of programs, each consisting of an automatically defined function in the function-defining branch and a result-producing branch. The structures of both the function-defining branches and the result-producing branch are determined by the combined effect, over many generations, of the selective pressure exerted by the fitness measure and by the effects of the operations of Darwinian fitness-based reproduction and crossover. The function defined by the function-defining branch is available for use by the result-producing branch. Whether or not the defined function will be actually called is not predetermined, but instead, determined by the evolutionary process.Since each individual program in the population of this example consists of function-defining branch(es) and result-producing branch(es), the initial random generation must be created so that every individual program in the population has this particular constrained syntactic structure. Since a constrained syntactic structure is involved, crossover must be performed so as to preserve this syntactic structure in all offspring.Genetic programming with automatically defined functions has been shown to be capable of solving numerous problems (Koza 1994a). More importantly, the evidence so far indicates that, for many problems, genetic programming requires less computational effort (i.e., fewer fitness evaluations to yield a solution with, say, a 99% probability) with automatically defined functions than without them (provided the difficulty of the problem is above a certain relatively low break-even point).Also, genetic programming usually yields solutions with smaller average overall size with automatically defined functions than without them (provided, again, that the problem is not too simple). That is, both learning efficiency and parsimony appear to be properties of genetic programming with automatically defined functions.Moreover, there is evidence that genetic programming with automatically defined functions is scalable. For several problems for which a progression of scaled-up versions was studied, the computational effort increases as a function of problem size at a slower rate with automatically defined functions than without them. Also, the average size of solutions similarly increases as a function of problem size at a slower rate with automatically defined functions than without them. This observed scalability results from the profitable reuse of hierarchically-callable, parameterized subprograms within the overall program.When single-part programs are involved, genetic programming automatically determines the size and shape of the solution (i.e., the size and shape of the program tree) as well as the sequence of work-performing primitive functions that can solve the problem. However, when multi-part programs and automatically defined functions are being used, the question arises as to how to determine the architecture of the programs that are being evolved. The architecture of a multi-part program consists of the number of function-defining branches (automatically defined functions) and the number of arguments (if any) possessed by each function-defining branch.2.3 Evolutionary Selection of ArchitectureOne technique for creating the architecture of the overall program for solving a problem during the course of a run of genetic programming is to evolutionarily select the architecture dynamically during a run of genetic programming. This technique is described in chapters 21 – 25 of Genetic Programming II: Automatic Discovery of Reusable Programs (Koza 1994a). The technique of evolutionary selection starts with an architecturally diverse initial random population. As the evolutionary process proceeds, individuals with certain architectures may prove to be more fit than others at solving the problem. The more fit architectures will tend to prosper, while the less fit architectures will tend to wither away.The architecturally diverse populations used with the technique of evolutionary selection require a modification of both the method of creating the initial random population and the two-offspring subtree-swapping crossover operation previously used in genetic programming. Specifically, the architecturally diverse population is created at generation 0 so as to contain randomly-created representatives of a broad range of different architectures. Structure-preserving crossover with point typing is a one-offspring crossover operation that permits robust recombination while guaranteeing that any pair of architecturally different parents will produce syntactically and semantically valid offspring.2.4 Architecture-AlteringOperationsA second technique for creating the architecture of the overall program for solving a problem during the course of a run of genetic programming is to evolve the architecture using architecture-altering (Koza 1995).2.8 Sources of Additional InformationIn addition to the author's books (Koza 1992, 1994) and accompanying videotapes (Koza and Rice 1992, Koza 1994), the first Advances in Genetic Programming book (Kinnear 1994) and the upcoming second book in this series (Angeline and Kinnear 1996) contain about two dozen articles each on various applications and aspects of genetic programming.In addition to the conferences mentioned in the earlier section on genetic algorithms, the conferences of artificial life {Brooks and Maes 1994) and simulation of adaptive behavior (Cliff et al. 1994) and have articles on genetic programming.Additional information about genetic programming may be obtained from the GP-LIST electronic mailing list to which you may subscribe, at no charge, by sending a subscription request to genetic-programming-request@.Information about obtaining software in C, C++, LISP, and other programming languages for genetic programming, information about upcoming conferences, and links to various。