Multiobjective evolutionary algorithms Analyzing the state-of-the-art

Multi-Objective Evolutionary Algorithms for Structural

Optimization

C.A.Coello Coello,G.Toscano Pulido,A.Hern′a ndez Aguirre

CINVESTAV-IPN,Secci′o n de Computaci′o n

Av.IPN No.2508,Col.Sn.Pedro Zacatenco

M′e xico,D.F.07300,MEXICO

ccoello@cs.cinvestav.mx

CIMAT,Department of Computer Science

Guanajuato,Gto.36240,MEXICO

artha@cimat.mx

Abstract

In this paper,we propose a multi-objective evolutionary algorithm(MOEA) for structural optimization.The proposed approach emphasizes ef?ciency

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and has been found to be competitive with respect to other MOEAs in cur-

rent use.One example is used to illustrate the way in which the approach

works.

1Introduction

Evolutionary algorithms have become an increasingly popular design and opti-mization tool in the last few years,with a constantly growing development of new algorithms and applications[1].Despite this considerably large volume of re-search,new areas remain to be explored with suf?cient depth.One of them is the use of evolutionary algorithms to solve multiobjective optimization problems.In nature,most problems are multiobjective,but we normally tend to restate them as single-objective optimization in problems by transforming all the objectives,but one into constraints.However,such an assumption keeps us from producing de-signs that represent better trade-offs among the original objectives of the problem and therefore limit the quality of our designs.

Evolutionary algorithms seem also particularly desirable for solving multi-objective optimization problems because they deal simultaneously with a set of possible solutions(the so-called population)which allows us to?nd several mem-bers of the Pareto optimal set in a single run of the algorithm,instead of having to

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perform a series of separate runs as in the case of the traditional mathematical pro-gramming techniques.Additionally,evolutionary algorithms are less susceptible to the shape or continuity of the Pareto front(e.g.,they can easily deal with dis-continuous and concave Pareto fronts),whereas these two issues are a real concern for mathematical programming techniques[3].

In this paper,we propose an evolutionary multiobjective optimization algo-rithm that has been found to be ef?cient and relatively easy to implement.We also present one example to illustrate the way in which our approach works.

2Basic Concepts

We want to solve multiobjective optimization problems(MOPs)of the form:

minimize(1) subject to the inequality constraints:

(2)

and the equality constraints:

3

(3)

where is the number of objective functions.We call

the vector of decision variables.We wish to determine from among the set of all numbers which satisfy(2)and(3)the particular set

which yields the optimum values of all the objective functions.

2.1Pareto optimality

It is rarely the case that there is a single point that simultaneously optimizes all the objective functions.Therefore,we normally look for“trade-offs”,rather than single solutions when dealing with multiobjective optimization problems.The notion of“optimality”is therefore,different in this case.The most commonly adopted notion of optimality is called Pareto optimality.We say that a vector of decision variables is Pareto optimal if there does not exist another such that for all and for at least one.

Unfortunately,the concept of Pareto optimality almost always gives not a sin-gle solution,but rather a set of solutions called the Pareto optimal set.The vectors correspoding to the solutions included in the Pareto optimal set are called non-

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dominated.The plot of the objective functions whose nondominated vectors are in the Pareto optimal set is called the Pareto front.

3Description of our approach

The term micro-genetic algorithm(micro-GA)refers to a small-population genetic algorithm with reinitialization where computational ef?ciency is emphasized.The approach proposed in this paper is the?rst attempt to use a micro-GA for multiob-jective optimization.The proposed technique incorporates concepts that represent the state-of-the-art in evolutionary multiobjective optimization,namely elitism (implemented using an external or secondary memory to retain nondominated individuals found along the evolutionary process)and Pareto ranking(i.e.,non-dominated individuals are favored by the selection process).Despite the various efforts to use evolutionary multiobjective optimization algorithms in structural op-timization problems(see[3]for a survey),few of those efforts have used Pareto ranking.Aggregating functions are still very popular in structural optimization despite their well-known limitations(e.g.,they cannot generate non-convex por-tions of the Pareto front).The main emphasis of the work reported in this paper is precisely to show what can be achieved by using a“true”evolutionary multi-

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objective optimization algorithm(i.e.,an algorithm that uses Pareto ranking and elitism).

The way in which our technique works is illustrated in Figure1.First,a ran-dom population is generated.This random population feeds the population mem-ory,which is divided in two parts:a replaceable and a non-replaceable portion. The non-replaceable portion of the population memory will never change during the entire run and is meant to provide the required diversity for the algorithm.In contrast,the replaceable portion will experience changes after each cycle of the micro-GA.The population of the micro-GA at the beginning of each of its cycles is taken(with a certain probability)from both portions of the population memory so that we can have a mixture of randomly generated individuals(non-replaceable portion)and evolved individuals(replaceable portion).During each cycle,the micro-GA undergoes conventional genetic operators(binary representation is used in our implementation):tournament selection,two-point crossover,uniform mu-tation,and elitism(only one nondominated vector is arbitrarily selected at each generation and copied intact to the following one).After the micro-GA?nishes one cycle,we choose two nondominated vectors from the?nal population and compare them with the contents of the external memory(this memory is initially empty).If either of them(or both)remains as nondominated after comparing it

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against the vectors in this external memory,then they are included there(i.e.,in the external memory).This is our historical archive of nondominated vectors.

To keep diversity along the Pareto front,we use a modi?ed version of the adap-tive grid proposed by Knowles&Corne[5](see Figure2).The idea is that once the archive that stores nondominated solutions has reached its limit,we divide the objective search space that this archive covers,assigning a set of coordinates to each solution.Then,each newly generated nondominated solution will be ac-cepted only if the geographical location to where the individual belongs is less populated than the most crowded location.

Note that although our approach requires several parameters that have to be de?ned by the user,we have suggested in previous work default values that can be adopted when nothing is known about the problem to be solved(see[2]for details).

4An Example

We have compared our micro-GA against some of the most competitive multi-objective evolutionary algorithms in current use(i.e.,the NSGA-II[4]and PAES [5]),obtaining very good results(see[2]for details).Due to space limitations,in

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this paper we will only present one engineering design example,and results will be compared with respect to the true Pareto front of the problem(generated by enumeration).Obviously,in more complex problems the true Pareto front cannot be found by enumeration.However,we adopted this methodology just to illustrate that our technique is able to approximate the true Pareto front of a problem with a very good accuracy in a short period of time.

4.1Design of a welded beam

This problem was originally proposed by Reklaitis et al.[6]and was transformed into a bi-objective problem by Wu[7].A beam A is to be welded to a rigid support member B.The welded beam is to consist of1010steel is to support a force of6000lb.The two design objectives are to simultaneously minimize the beam cost and minimize the end de?ection.There are constraints on shear stress, normal stress and buckling load.The independent design variables in this case, which are all continuous,are the dimensions and(see Figure3).The length is assumed to be speci?ed at14inches.The parameters used by our micro-GA are the following:size of the external memory=100,nominal convergence= 2iterations,size of the population memory=50,population size(of the micro-GA)=4,number of subdivisions of the adaptive grid=25,crossover rate=0.8,

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mutation rate=1.0/(=length of the chromosome),replacement cycle=50, percentage of non-replaceable memory=0.3,maximum number of generations= 3500.The true Pareto front of the problem(generated by enumeration)compared to the solution generated by our micro-GA are shown in Figure4.The average running time of the micro-GA for this problem was of1.475seconds(on a PC with an Athlon XP1500+processor,running at1.3GHz and256Mb of RAM). As can bee seen in Figure4,our micro-GA produces a very good approximation of the Pareto front of this problem.

5Conclusions and Future Work

We have presented a multiobjective evolutionary algorithm that has been succes-fully applied to solve structural optimization problems.The algorithm is concep-tually simple and very ef?cient.1The results obtained show that our algorithm can produce reasonably good approximations of the Pareto front of a problem at an affordable computational cost.Our main goal is to encourage engineers to get involved in evolutionary multiobjective optimization and to use this or other algorithms currently available in the specialized literature(see[3]).As part of

our future work,we plan to introduce on-line adaptation of the parameters of our micro-GA so that no parameters?ne-tuning is required.

Acknowledgements

The?rst author acknowledges support from CONACyT project34201-A.The second author acknowledges support from CONACyT through a scholarship to pursue graduate studies at CINVESTA V-IPN.The third author acknowledges par-tial support from CONCyTEG project No.01-02-202-111and CONACyT No. I-39324-A.

References

[1]Thomas B¨a ck,David B.Fogel,and Zbigniew Michalewicz,editors.Hand-

book of Evolutionary Computation.Institute of Physics Publishing and Ox-ford University Press,1997.

[2]Carlos A.Coello Coello and Gregorio Toscano Pulido.Multiobjective Opti-

mization using a Micro-Genetic Algorithm.In Lee Spector,Erik D.Good-man,Annie Wu,https://www.wendangku.net/doc/8113576766.html,ngdon,Hans-Michael V oigt,Mitsuo Gen,Sandip Sen,Marco Dorigo,Shahram Pezeshk,Max H.Garzon,and Edmund Burke,

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editors,Proceedings of the Genetic and Evolutionary Computation Confer-ence(GECCO’2001),pages274–282,San Francisco,California,2001.Mor-gan Kaufmann Publishers.

[3]Carlos A.Coello Coello,David A.Van Veldhuizen,and Gary https://www.wendangku.net/doc/8113576766.html,mont.

Evolutionary Algorithms for Solving Multi-Objective Problems.Kluwer Aca-demic Publishers,New York,May2002.ISBN0-3064-6762-3.

[4]Kalyanmoy Deb,Amrit Pratap,Sameer Agarwal,and T.Meyarivan.A Fast

and Elitist Multiobjective Genetic Algorithm:NSGA–II.IEEE Transactions on Evolutionary Computation,6(2):182–197,April2002.

[5]Joshua D.Knowles and David W.Corne.Approximating the Nondominated

Front Using the Pareto Archived Evolution Strategy.Evolutionary Computa-tion,8(2):149–172,2000.

[6]G.V.Reklaitis,A.Ravindran,and K.M.Ragsdell.Engineering Optimization

Methods and Applications.Wiley-Interscience,1985.

[7]Jin Wu.Quality Assisted Multiobjective and Multidisciplinary Genetic Al-

gorithms.PhD thesis,Department of Mechanical Engineering,University of Maryland at College Park,College Park,Maryland,2001.

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12

Population

Nominal Selection

Crossover

Mutation

Elitism

New Population Convergence?

Filter

External Memory

cycle

micro?GA N

Y Non?Replaceable Replaceable Population Memory

Random Population

Fill in both parts of the population memory Initial Figure 1:Diagram that illustrates the way in which our micro-GA works.

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0 1 2 3 4 5

435

21

Space covered by the grid for objective 1

S p a c e c o v e r e d b y t h e g r i d f o r o b j e c t i v e 2The lowest fit individual for objective 2and the fittest individual for objective 1Figure 2:The adaptive grid used to hadle the external memory of the micro-GA.

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Figure3:Welded beam used for the second example.

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0 0.005

0.01

0.015

0.02

0.025 6 8 10 12 14 16

18 20 22 24 26 28

F 2

F1Pareto Front Micro-GA

Figure 4:Pareto front of the example.The true Pareto front is shown as a contin-uous line and the solutions found by our micro-GA are displayed as crosses.

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进化计算综述

进化计算综述 1.什么是进化计算 在计算机科学领域，进化计算（Evolutionary Computation）是人工智能（Artificial Intelligence），进一步说是智能计算（Computational Intelligence）中涉及到组合优化问题的一个子域。其算法是受生物进化过程中“优胜劣汰”的自然选择机制和遗传信息的传递规律的影响，通过程序迭代模拟这一过程，把要解决的问题看作环境，在一些可能的解组成的种群中，通过自然演化寻求最优解。 2.进化计算的起源 运用达尔文理论解决问题的思想起源于20世纪50年代。 20世纪60年代，这一想法在三个地方分别被发展起来。美国的Lawrence J. Fogel提出了进化编程（Evolutionary programming），而来自美国Michigan 大学的John Henry Holland则借鉴了达尔文的生物进化论和孟德尔的遗传定律的基本思想，并将其进行提取、简化与抽象提出了遗传算法（Genetic algorithms）。在德国，Ingo Rechenberg 和Hans-Paul Schwefel提出了进化策略（Evolution strategies）。 这些理论大约独自发展了15年。在80年代之前，并没有引起人们太大的关注，因为它本身还不够成熟，而且受到了当时计算机容量小、运算速度慢的限制，并没有发展出实际的应用成果。

到了20世纪90年代初，遗传编程（Genetic programming）这一分支也被提出，进化计算作为一个学科开始正式出现。四个分支交流频繁，取长补短，并融合出了新的进化算法，促进了进化计算的巨大发展。 Nils Aall Barricelli在20世纪六十年代开始进行用进化算法和人工生命模拟进化的工作。Alex Fraser发表的一系列关于模拟人工选择的论文大大发展了这一工作。 [1]Ingo Rechenberg在上世纪60 年代和70 年代初用进化策略来解决复杂的工程问题的工作使人工进化成为广泛认可的优化方法。[2]特别是John Holland的作品让遗传算法变得流行起来。[3]随着学术研究兴趣的增长，计算机能力的急剧增加使包括自动演化的计算机程序等实际的应用程序成为现实。[4]比起人类设计的软件，进化算法可以更有效地解决多维的问题，优化系统的设计。[5] 3.进化计算的分支 进化计算的主要分支有：遗传算法GA ，遗传编程GP、进化策略ES、进化编程EP。下面将对这4个分支依次做简要的介绍。 1遗传算法（Genetic Algorithms）： 遗传算法是一类通过模拟生物界自然选择和自然遗传机制的随机化搜索算法，由美国John HenryHoland教授于1975年在他的专著《Adaptation in Natural and Artificial Systems》中首次提出。[6]它是利用某种编码技术作用于称为染色体的二进制数串，其基本思想是模拟由这些串组成的种群的进化过程，通过有组织地然而是随机地信息交换来重新组合那些适应性好的串。遗传算法对求解问题的本身一无所知，它所需要的仅是对算法所产生的每个染

高一生物：基因突变及其他变异(教学设计)

( 生物教案 ) 学校：_________________________ 年级：_________________________ 教师：_________________________ 教案设计 / 精品文档 / 文字可改 高一生物：基因突变及其他变异 (教学设计) Biology is a discipline that studies the species, structure, development and origin of the evolutionary system at all levels of biology.

高一生物：基因突变及其他变异(教学设 计) 一、染色体变异的种类 1.染色体结构的变异 包括⑴缺失、⑵重复、⑶倒位、⑷易位四种类型。 染色体结构的改变，都会使排列在染色体上的基因数目或排列顺序发生改变，从而使性状的改变。如猫叫综合征，是5号染色体缺失造成的。 2.染色体数目的变异 有两种类型：⑴个别染色体的增加或减少如人类的21三体综合症，是由于21号染色体有3条造成的。⑵以染色体组的形式成倍的增加或减少如单倍体、多倍体的形成等。

巩固训练1.已知某物种的一条染色体上依次排列着a、b、c、d、e五个基因，其中基因在染色体上的状况为：ab cde 。则下面列出的若干种变化中，未发生染色体结构变化的是（） a.ab c b.ab cdef c.ab ccde d.ab cde 二、染色体组的概念及判断 1.染色体组的概念 染色体组是指细胞中的一组非同源染色体，它们在形态和功能上各不相同，但是携带着控制一种生物生长发育、遗传和变异的全部信息的一组染色体。 要构成一个染色体组，应具备以下条件：①一个染色体组中不含同源染色体；②一个染色体组中所含的染色体形态、大小和功能各不相同；③一个染色体组中含有控制生物性状的一整套基因，但不能重复。 2.染色体组数目的判别 ①根据染色体形态判断细胞内形态相同的染色体有几条，则含有几个染色体组。

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

//F1函数 Sphere double calculation(double *sol) { int i; double result=0; fit++; //标记评估次数 for (i=0; i

{ tmp1+=sol[j]; } tmp2+=tmp1*tmp1; } result=tmp2; return result; } //*********************************** //F4函ˉ数簓 double calculation(double *sol) { int i,j; double result=fabs(sol[0]); fit++; for(i=1;i

动态演化经典论文Evolutionary dynamics on graphs

Received 24September;accepted 16November 2004;doi:10.1038/nature03211. 1.MacArthur,R.H.&Wilson,E.O.The Theory of Island Biogeography (Princeton Univ.Press,Princeton,1969). 2.Fisher,R.A.,Corbet,A.S.&Williams,C.B.The relation between the number of species and the number of individuals in a random sample of an animal population.J.Anim.Ecol.12,42–58(1943). 3.Preston,F.W.The commonness,and rarity,of species.Ecology 41,611–627(1948). 4.Brown,J.H.Macroecology (Univ.Chicago Press,Chicago,1995). 5.Hubbell,S.P .A uni?ed theory of biogeography and relative species abundance and its application to tropical rain forests and coral reefs.Coral Reefs 16,S9–S21(1997). 6.Hubbell,S.P .The Uni?ed Theory of Biodiversity and Biogeography (Princeton Univ.Press,Princeton,2001). 7.Caswell,https://www.wendangku.net/doc/8113576766.html,munity structure:a neutral model analysis.Ecol.Monogr.46,327–354(1976).8.Bell,G.Neutral macroecology.Science 293,2413–2418(2001).9.Elton,C.S.Animal Ecology (Sidgwick and Jackson,London,1927).10.Gause,G.F.The Struggle for Existence (Hafner,New York,1934). 11.Hutchinson,G.E.Homage to Santa Rosalia or why are there so many kinds of animals?Am.Nat.93,145–159(1959). 12.Huffaker,C.B.Experimental studies on predation:dispersion factors and predator-prey oscillations.Hilgardia 27,343–383(1958). 13.Paine,R.T.Food web complexity and species diversity.Am.Nat.100,65–75(1966).14.MacArthur,R.H.Geographical Ecology (Harper &Row,New York,1972). https://www.wendangku.net/doc/8113576766.html,ska,M.S.&Wootton,J.T.Theoretical concepts and empirical approaches to measuring interaction strength.Ecology 79,461–476(1998). 16.McGill,B.J.Strong and weak tests of macroecological theory.Oikos 102,679–685(2003). 17.Adler,P .B.Neutral models fail to reproduce observed species-area and species-time relationships in Kansas grasslands.Ecology 85,1265–1272(2004). 18.Connell,J.H.The in?uence of interspeci?c competition and other factors on the distribution of the barnacle Chthamalus stellatus .Ecology 42,710–723(1961). 19.Paine,R.T.Ecological determinism in the competition for space.Ecology 65,1339–1348(1984).20.Wootton,J.T.Prediction in complex communities:analysis of empirically-derived Markov models.Ecology 82,580–598(2001). 21.Wootton,J.T.Markov chain models predict the consequences of experimental extinctions.Ecol.Lett.7,653–660(2004). 22.Paine,R.T.Food-web analysis through ?eld measurements of per capita interaction strength.Nature 355,73–75(1992). 23.Moore,J.C.,de Ruiter,P .C.&Hunt,H.W.The in?uence of productivity on the stability of real and model ecosystems.Science 261,906–908(1993). 24.Rafaelli,D.G.&Hall,S.J.in Food Webs:Integration of Pattern and Dynamics (eds Polis,G.&Winemiller,K.)185–191(Chapman and Hall,New York,1996). 25.Wootton,J.T.Estimates and tests of per-capita interaction strength:diet,abundance,and impact of intertidally foraging birds.Ecol.Monogr.67,45–64(1997). 26.Kokkoris,G.D.,Troumbis,A.Y.&Lawton,J.H.Patterns of species interaction strength in assembled theoretical competition communities.Ecol.Lett.2,70–74(1999). 27.Drossel,B.,McKane,A.&Quince,C.The impact of nonlinear functional responses on the long-term evolution of food web structure.J.Theor.Biol.229,539–548(2004). Acknowledgements I thank the Makah Tribal Council for providing access to Tatoosh Island;J.Sheridan,J.Salamunovitch,F.Stevens,https://www.wendangku.net/doc/8113576766.html,ler,B.Scott,J.Chase,J.Shurin,K.Rose,L.Weis,R.Kordas,K.Edwards,M.Novak,J.Duke,J.Orcutt,K.Barnes,C.Neufeld and L.Weintraub for ?eld assistance;and NSF,EPA (CISES)and the Andrew W.Mellon foundation for partial ?nancial support. Competing interests statement The author declares that he has no competing ?nancial interests.Correspondence and requests for materials should be addressed to J.T.W.(twootton@https://www.wendangku.net/doc/8113576766.html,). .............................................................. Evolutionary dynamics on graphs Erez Lieberman 1,2,Christoph Hauert 1,3&Martin A.Nowak 1 1 Program for Evolutionary Dynamics,Departments of Organismic and Evolutionary Biology,Mathematics,and Applied Mathematics,Harvard University,Cambridge,Massachusetts 02138,USA 2 Harvard-MIT Division of Health Sciences and Technology,Massachusetts Institute of Technology,Cambridge,Massachusetts,USA 3 Department of Zoology,University of British Columbia,Vancouver,British Columbia V6T 1Z4,Canada ............................................................................................................................................................................. Evolutionary dynamics have been traditionally studied in the context of homogeneous or spatially extended populations 1–4.Here we generalize population structure by arranging individ-uals on a graph.Each vertex represents an individual.The weighted edges denote reproductive rates which govern how often individuals place offspring into adjacent vertices.The homogeneous population,described by the Moran process 3,is the special case of a fully connected graph with evenly weighted edges.Spatial structures are described by graphs where vertices are connected with their nearest neighbours.We also explore evolution on random and scale-free networks 5–7.We determine the ?xation probability of mutants,and characterize those graphs for which ?xation behaviour is identical to that of a homogeneous population 7.Furthermore,some graphs act as suppressors and others as ampli?ers of selection.It is even possible to ?nd graphs that guarantee the ?xation of any advantageous mutant.We also study frequency-dependent selec-tion and show that the outcome of evolutionary games can depend entirely on the structure of the underlying graph.Evolu-tionary graph theory has many fascinating applications ranging from ecology to multi-cellular organization and economics.Evolutionary dynamics act on populations.Neither genes,nor cells,nor individuals evolve;only populations evolve.In small populations,random drift dominates,whereas large populations Figure 1Models of evolution.a ,The Moran process describes stochastic evolution of a ?nite population of constant size.In each time step,an individual is chosen for reproduction with a probability proportional to its ?tness;a second individual is chosen for death.The offspring of the ?rst individual replaces the second.b ,In the setting of evolutionary graph theory,individuals occupy the vertices of a graph.In each time step,an individual is selected with a probability proportional to its ?tness;the weights of the outgoing edges determine the probabilities that the corresponding neighbour will be replaced by the offspring.The process is described by a stochastic matrix W ,where w ij denotes the probability that an offspring of individual i will replace individual j .In a more general setting,at each time step,an edge ij is selected with a probability proportional to its weight and the ?tness of the individual at its tail.The Moran process is the special case of a complete graph with identical weights. letters to nature NATURE |VOL 433|20JANUARY 2005|https://www.wendangku.net/doc/8113576766.html,/nature 312 ? 2005 Nature Publishing Group

MEGA6 Molecular Evolutionary Genetics Analysis version 6.0

MBE Brief Communication MEGA6: Molecular Evolutionary Genetics Analysis version 6.0 Koichiro Tamura 1, 2, Glen Stecher 3, Daniel Peterson 3, Alan Filipski 3, and Sudhir Kumar 3,4,5* 1Research Center for Genomics and Bioinformatics, Tokyo Metropolitan University, Hachioji, Tokyo, Japan 2 Department of Biological Sciences, Tokyo Metropolitan University, Hachioji, Tokyo, Japan 3Center for Evolutionary Medicine and Informatics, Biodesign Institute, Arizona State University, Tempe, Arizona, USA 4School of Life Sciences, Arizona State University, Tempe, Arizona, USA 5Center of Excellence in Genomic Medicine Research, King Abdulaziz University, Jeddah, Saudi Arabia *Correspondence to: Sudhir Kumar, Ph.D. Center for Evolutionary Medicine and Informatics Biodesign Institute @ Arizona State University Tempe, Arizona 85287, USA Email: s.kumar@https://www.wendangku.net/doc/8113576766.html, ? The Author 2013. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, please e-mail: journals.permissions@https://www.wendangku.net/doc/8113576766.html, MBE Advance Access published October 16, 2013 at Zhejiang University on October 30, 2013 https://www.wendangku.net/doc/8113576766.html,/Downloaded from

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2012年12月第二篇细节题分析 提问方式：62.Why do doctors recommend routine cancer screening for elderly people? 参考答案：D).The elderly are in greater danger of tumor growth. 答案来源：Our risk of cancer rises dramatically as we age. So it makes sense that the elderly should be routinely screened for new tumors. 提问方式：63.How do some researchers now look at routine cancer screening for the elderly? 参考答案：C).They are doubtful about necessity. 答案来源：While such vigilant tracking of cancer is a good thing in general, researchers are increasingly questioning whether all of this testing is necessary for the elderly. 提问方式：64.What is the conventional view about women screening for breast cancer? 参考答案：B).It is a must for adult women. 答案来源：But the message that everyone must screen for cancer has become so deep-rooted that when health care experts recommended that women under 50 and over 74 stop screening for breast cancer, it caused a riotous reaction among doctors, patients and advocacy groups.