Genetic Algorithms with Self-Organized Criticality for Dynamic Optimization
Problems
Renato Tin′o s Departamento de F′?sica e Matem′a tica,FFCLRP Universidade de S?a o Paulo(USP)
14040-901,Ribeir?a o Preto,SP,Brazil
rtinos@https://www.doczj.com/doc/7d6717910.html,p.br
Shengxiang Yang
Department of Computer Science
University of Leicester
University Road,Leicester LE17RH,United Kingdom
s.yang@https://www.doczj.com/doc/7d6717910.html,
Abstract-This paper proposes a genetic algorithm (GA)with random immigrants for dynamic optimiza-tion problems where the worst individual and its neigh-bours are replaced every generation.In this GA,the in-dividuals interact with each other and,when their?t-ness is close,as in the case where the diversity level is low,one single replacement can affect a large number of individuals.This simple approach can take the system to a kind of self-organization behavior,known as Self-Organized Criticality(SOC),which is useful to maintain the diversity of the population in dynamic environments and hence allows the GA to escape from local optima when the problem changes.The experimental results show that the proposed GA presents the phenomenon of SOC.
1Introduction
The research in genetic algorithms(GAs)has been mainly focused on stationary optimization problems,in spite of a signi?cant part of optimization problems in real world being dynamic optimization problems(DOPs)[4].In DOPs,the evaluation function(or?tness function)and the constraints of the problem are not?xed[20].When changes occur, the solution given by the optimization procedure may be no longer effective,and a new solution should be found.
The optimization problem can change by several factors, like faults,machine degradation,environmental or climatic modi?cations,and economic factors.In fact,the natural evolution,which is the inspiration for GAs,is always non-stationary.The occurrence of natural cataclysms,geologi-cal modi?cations,competition for natural resources,coevo-lution between species,and climatic modi?cations are only some examples of changes related to natural evolution.
The simplest approach to deal with DOPs is to start a new optimization process whenever a change in the prob-lem is noticed.However,the optimization process gener-ally requires time and substantial computational effort.If the new solution after the change in the problem is,in some sense,related to the previous solution,the knowledge ob-tained during the search for the old solution can be utilized to?nd the new solution[4].In this case,the search for new solutions based on the old solutions can save substan-tial processing time.Evolutionary algorithms are particu-larly attractive to such problems.Individuals representing solutions of the problem before the changes can be trans-ferred into the new optimization process.
However,in GAs,the population of solutions generally converges in the?tness landscape to points close to the best individual of the population.If the?tness landscape changes,the actual population can be trapped in local op-tima located close to the old solution.In fact,the prema-ture convergence of the solution to a local optima is not a problem exclusive to DOPs,but it can be a serious problem in stationary optimization problems too[17].In order to avoid the premature convergence,several approaches where the diversity level is re-introduced or maintained through-out the run have appeared in literature over the past years [4,5,12,20].Typical examples of this solution are the GAs with random immigrants and the use of hypermutation[6].
The random immigrants approach,which is inspired in the?ux of immigrants that wander in and out of a popula-tion between two generations in nature,is very interesting and simple[6].In the GAs with random immigrants,some individuals of the current population are substituted by ran-dom individuals in each generation of the run.A replace-ment strategy,like replacing random or worst individuals of the population,de?nes which individuals are replaced by new ones[21].
However,in some cases,when the number of genes in the individual(parameters in the solution)is high and the lo-cal optimum where the population is found has?tness much higher than the mean?tness of all possible solutions of the search space,the survival probability of the new random in-dividuals is generally very small.This occurs because the selection methods employed in GAs preserve,directly or indirectly,the best individuals of the population,and the probability that the?tness of the new random individuals is higher than(or close to)the?tness of the current individuals is generally small.
In this paper,instead of substituting the worst individu-als or the random individuals in each generation like in the standard random immigrants approach,the worst individual and its next neighbours are replaced.In this way,individu-als start to interact between themselves and,when the?tness of the individuals are close,as in the case where the diver-sity level is small,one single replacement of an individual can affect a great number of individuals of the population in a chain reaction.In order to protect the newly introduced immigrants from being replaced by?tter individuals,they are placed in a subpopulation and are not allowed to be re-placed by individuals of the main population.The number of individuals in the subpopulation is not de?ned by the pro-grammer,but is given by the number of individuals created
in the chain reaction.It is important to observe that this simple approach can take the system to a self-organization behavior,which can be useful in DOPs.
The experimental results suggest that the proposed GA presents a kind of self-organizing behavior,known as Self-Organized Criticality(SOC)[1],which is described in this paper in Section2.The proposed GA is presented in Sec-tion3,and the results of the experiments with DOPs are presented in Section4.Finally,Section5concludes the pa-per with discussions on relevant future work.
2Self-Organized Criticality
Bak,Tang,and Wiesenfeld suggested in[2]that systems consisting of several interacting constituents may present an interesting kind of self-organizing behavior[13].The authors described this interesting behavior as SOC.It was suggested that several diverse phenomena exhibit SOC,like sand piles,earthquakes,forest?res,electric breakdowns, and growing interfaces.
The seductive characteristic of systems that exhibit SOC is that they self-organize into a particular critical state with-out the need of any signi?cant tuning action from outside. The critical state is described by the response of a system to external perturbation.In a system exhibiting noncriti-cal behavior,the distribution of responses to perturbation at different positions and at different times is narrow and well described by an averaged value.In a system exhibiting crit-ical behavior,no single characteristic response exists,i.e. the system exhibits scale invariance.A small perturbation in one given location of the system may generate a small effect on its neighbourhood or a chain reaction that affects all the constituents of the system.
The statistical distributions describing the response of the system exhibiting SOC are given by power laws in the form
P(s)～s?τ(1) and
P(d)～d?α(2) where s is the number of constituents of the system affected by the perturbation,d is the duration of the chain reaction (lifetime),andτandαare constants.As an example,con-sider the sand pile model described in[2],where a single grain is added at a random position in every interval of time ?t.In order to characterize the response of the system,one can measure the number of sand grains(s)involved in each avalanche induced by the addition of a single grain and the duration(d)of each avalanche.In the critical state,the sta-tistical distributions describing the response of the sand pile model to the addition of a single grain are given by Eqs.1 and2,and the addition of a single grain can affect only a grain in its neighbourhood or can affect the whole sand pile.
Researchers have suggested that SOC occurs in natural evolution too[1].An evidence of SOC in evolution would be the fact that it does take place through bursts of activ-ity intercalated by calm periods,instead of gradually at a slow and constant pace.There are many more small ex-tinction events than large events,such as the Cretaceous ex-tinction of dinosaurs and many other species,and extinction events occur on a large variety of length scales[19].These facts suggested that extinctions propagate through ecosys-tems,such as avalanches in a sand pile,and perturbations of the same size can unleash extinction events of a large vari-ety of sizes.This would occur because species co-evolve to a critical state[14].
Bak and Sneppen[1]proposed a very simple simulation model to study the connection between evolution and SOC. In the one-dimensional version of the model,the individu-als(or species in the authors’terminology)are disposed in a circle,and a random value of?tness is assigned to each one of them.In each generation of the simulation,the val-ues of?tness of the individual with the smallest?tness in the current population,one individual located in its right position,and one located in its left position are replaced by new random values.An analogy of the connection between neighbours in the model is the interaction between species in nature.If,as an example,a prey is extinct,the?tness of its predators will change.The Bak-Sneppen Model can be summarized by Algorithm1.
1:Find the index j of the individual with the smallest?tness 2:Replace the?tness of the individuals with index j,j?1,and j+1by random values drawn with uniform density
In GAs,Krink and Thomsen[15]proposed the use of the sand pile model previously discussed to generate power laws utilized to control the size of spatial extinction zones in a diffusion model.When an individual is extinct,a mutated version of the best individual of the population is created in its place.It is important to observe that,in the algorithm proposed in[15],SOC appears in the sand pile model uti-lized to control the size of the extinctions,and not as a result of the self-organization of the constituents of the system(in-dividuals of the GA).
3Proposed Algorithm
In this paper,we propose the substitution of the worst in-dividual and its two next neighbours for new random indi-viduals in the random immigrants approach.The indexes of the individuals are used to determine the neighbourhood relations.In each generation of the algorithm,the individ-ual with the smallest?tness in the current population(in-dex j),one individual located in its right position(index j+1),and one located in its left position(index j?1)are replaced by new random individuals.We hope that,with this replacement strategy,the system can exhibit SOC in or-der to increase the diversity level of the population in a self-organized way and,then,to avoid the situation where the individuals get trapped in local optima in the?tness land-scape when the problem changes.
However,this simple idea does not guarantee that the system exhibits SOC as the new random individuals added to the current population,which generally have small val-ues of?tness,are very often substituted by individuals with high values of?tness present in the population.As a con-sequence,the statistical distribution describing the response of the system to a single extinction will not be a power law, but a narrow one characterized by an averaged value.
In order to protect the newly introduced individuals from being replaced by individuals with high values of?tness,a second strategy should be adopted.In this strategy,the new individuals created during an extinction event are preserved in a subpopulation,which is not de?ned by the program-mer,but is given by the number of individuals created in the current extinction event.The individuals in the current population that do not belong to the subpopulation are not allowed to replace individuals present in the subpopulation. The individuals that belong to the subpopulation are allowed to evolve,i.e.they are submitted to mutation,crossover, and selection.It is important to observe that selection and crossover are allowed only between individuals that belong to the subpopulation.
In the proposed algorithm,there are two major modi?ca-tions in the standard GA.In the?rst modi?cation,which is presented in Algorithm2,the current size of each extinction event,denoted by ext,is recorded,and the minimum and maximum index values of the replaced individuals(i min?1 and i max+1)are utilized to compute the number of individ-uals affected by the current extinction,i.e.the individuals that belong to the subpopulation.When the chain reaction ceases,i.e.the individual with the smallest?tness do not belong to the subpopulation or is not neighbour of the min-imum and maximum index values of the replaced individu-als,the size of the extinction is set to1.
1:Find the index j of the individual with the smallest?tness 2:Replace the individuals with index j,j?1,and j+1by random individuals
3:if(j≥i min?1)and(j≤i max+1)then
4:ext←ext+1
5:if(j=i min?1)then
6:i min←j
7:end if
8:if(j=i max+1)then
9:i max←j
10:end if
11:else
12:ext←1
13:i min←j
14:i max←j
15:end if
Algorithm3Selection
4Experimental Studies
In order to evaluate the performance of proposed algorithm, two sets of experiments are carried out.In the?rst set of ex-periments,the dynamic test environment for GAs proposed by Yang[22]is employed.In the second set of experiments, evolutionary robots are simulated in dynamic environments. In the experiments,the proposed algorithm is compared to the standard GA,and to two versions of the GA with random immigrants.In the?rst version,three individuals randomly chosen are replaced by new random individuals.In the sec-ond version,the three worst individuals,i.e.the individuals with the smallest?tness,are replaced by new random indi-viduals.
4.1Dynamic Test Environments
In order to evaluate the performance of different GAs in DOPs,Yang [22]proposed an environment generator based on unitation and trap functions.The unitation function u (x )of a binary vector x of length l is given by the number of ones in this vector.A trap function is de?ned as follows
f (x )= a
l ?z (u (x )?z )otherwise (3)
where a is the local and possibly deceptive optimum,b is the
global optimum,and z is the slope-change location which separates the attraction basin sizes of the two optima.A trap function can be a deceptive function for GAs,i.e.a function where there exist low-order schemata that,instead of combining to form high-order schemata,forms schemata resulting in a deceptive solution that is sub-optimal [10].A trap function is deceptive on average if the ratio of the ?tness of the local optimum to that of the global optimum is constrained by the following relation [8].
r =
a
2?1/z
(4)
Deception is not the only element that can generate dif-?culty to a GA.The problem dif?culty can also be caused by exogenous noise and scaling,which arises in functions that consist of several schemata with different worth to the solution [11].A scaling problem can be simulated using additively decomposable functions as follows
f (x )=
m i =1
c i f i (x I i )(5)
where m is the number of schemata that are juxtaposed and
summed together,I i is the set of the ?xed bit positions that form schema i ,and c i is the scaling factor for each sub-function f i .
Using Equations 3and 5,it is possible to create different dynamic environments where the problem dif?culty can be adjusted.In this paper,dynamic environments where the de-ception dif?culty is modi?ed by changing the peak heights of optima are employed [22].In these dynamic environ-ments,the ?tness of an individual x is given by additively decomposable trap functions de?ned as follows
f (x )=m i =1
c i f i (x I i ,t )(6)
f (x I i ,t )=
a i (t )
l i ?z i (u (x I i )?z i )otherwise
(7)
where:i =1,2,3;x T =[x T I 1x T I 2x T I 3];x I 1=[x 1···x 6]T
;x I 2=[x 7···x 12]T ;x I 3=[x 13···x 18]T ;l i =6;b i =b =1.0;z i =z ;the scaling is given by c i =2i ?1;a i switches between A min >0and A max >b i in every 2000genera-tions.The parameter A min is constrained by Eq.4,i.e.it is chosen in order that the trap functions are deceptive on average.In this way,in every 2000generations,the
global optimum changes between b and a i =A max ,and the problem changes between deceptive and non-deceptive.Two environments are utilized to generate the results for all GAs.In the ?rst (Environment 1),z =5,A min =0.6,and A max =1.4.In the second (Environment 2),z =4,A min =0.9,and A max =1.9.4.1.1Experimental Design
For each run of an algorithm in a dynamic environment,the individuals of the initial population of the algorithm are ran-domly chosen.The individuals are selected in each genera-tion according to elitism and the roulette wheel method.The two-point crossover is utilized.For all algorithms,20000generations are executed with the number of individuals in the population equal to 100.
The comparison of the results obtained from different al-gorithms on DOPs is more complex than the same compar-ison for stationary problems [20].For DOPs,it is necessary to evaluate not the ?nal result,but rather the optimization process itself.Here,the measure Adaptability ,proposed in [20]and based on a measure proposed by De Jong [7],is utilized to evaluate the GAs.Adaptability is computed as the difference,averaged over the entire run,between the ?t-ness of the current best individual of each generation and the corresponding optimum value.The best results for the Adaptability measure are those with the smallest values.4.1.2Experimental Results
Table 1presents the measure Adaptability and the mean ?t-ness of all individuals of the population averaged over 20trials for environments 1and 2.The results of three ex-periments of environment 1with different values for the crossover rate (p c )and mutation rate (p m )are presented.The values of p c and p m are indicated in Table 1.The per-centage inside the parentheses indicates the sum,over all generations,of the difference between the current value of the maximum ?tness and the ?tness of the current best indi-vidual.
Hypothesis tests,considering the Student’s t-distribution,with a level of signi?cance equal to 0.01indicate that the measure Adaptability is smaller for the proposed GA in these experiments.4.2Evolutionary Robotics
Robots in which arti?cial evolution is used as a fundamen-tal form of adaptation or design are known as evolutionary robots [18].In the experiments presented in this section,mobile robots are simulated in DOPs using a modi?ed ver-sion of the Evorobot simulator developed by S.Nol?[18].In the simulator utilized in the experiments presented in this section,the robots are controlled by a recurrent arti?cial neural network (Elman Network)with synaptic weights ad-justed by GAs.
The experiments presented here are inspired in the ex-periment proposed by Floreano and Mondada [9],where a Khepera robot with 8infrared distance sensors (six in one side and two in another side of the robot),2ambient light
Table1:Experimental Results of Algorithms in Dynamic Test Environments
Standard0.19454(16.21%)0.19575(16.31%)0.20010(16.67%)0.18764(12.94%) Adaptability Random immigrants0.03559(2.97%)0.02808(2.34%)0.04582(3.82%)0.02320(1.60%) (best individual)Random immigrants(worst)0.03946(3.29%)0.02761(2.30%)0.05689(4.74%)0.02579(1.78%) Proposed algorithm0.02071(1.73%)0.01168(0.97%)0.02591(2.16%)0.01362(0.94%)
Standard0.22700
Mean Fitness Random immigrants0.23038
(all individuals)Random immigrants(worst)0.22360
Proposed algorithm0.26492
a new solution is found,allowing the robot to navigate in
the environment and to return to the battery recharge area
only when the battery level is low.When the environment
changes,the?tness values of the robots become small,and
a new solution is searched.
Hypothesis tests,considering the Student’s t-
distribution,with a level of signi?cance equal to0.07
indicate that the measure Adaptability is smaller for the
proposed GA in the evolutionary robotics experiment.
4.3Analysis of the Results
In the experiments presented here,the mean values of adapt-
ability for the three GAs with random immigrants(includ-
ing the proposed GA)are smaller than the mean values for
the standard GA,indicating that the average?tness of the
best individuals are higher for the GAs with random im-
migrants.These results can be explained by the fact that
the standard GA has dif?culties in escaping from the lo-
cal optima induced by the deceptive problem(e.g.,between
generations0to1999of the dynamic test environments ex-
periments)and by changing the global optima(e.g.between
2000and3999in the same experiments).On the other hand,
random immigrants inserted in every generation provide di-
versity to the populations in the last three GAs,which ex-
plains their better results.
Let us now analyze the results of the three GAs with ran-
dom immigrants.First,let us investigate how the proposed
algorithm works.In the beginning of the experiments,the
individuals of the initial populations generally have small
?tness.In the proposed GA,the new individuals that re-
place the individual with the smallest?tness and its neigh-
bours generally have small values of?tness too.As sev-
eral individuals in the population have small values of?t-
ness,the probability that one of the neighbours of the cur-
rent worst individual becomes the new worst is small.As
a consequence,a single replacement of an individual gener-
ally does not generate large chain reactions of extinctions,
00.20.40.60.8
1
1.2 1.4 1.6 1.8
2
x 10
4
5
10
15
20
generation
d u r a t i o n o f
e x t i n c t i o n e v e n t s
x 10
4
generation
f i t n e s s
Figure 1:Mean ?tness and duration of the extinction events in the forth trial of the experiment in dynamic test environment 1.
i.e.the distribution of the duration of extinction events is narrow and well described by a small average value.As the number of generations increases,the mean ?tness increases too.In this situation,several individuals of the current pop-ulation have values of ?tness higher than the average ?tness of the new random individuals.Then,the probability that one of the two neighbours of the old worst individual,which were replaced in the last generation,becomes the new worst individual increases.When this new worst individual is re-placed with its two next neighbours,a chain reaction can be developed and the extinction events can have,then,a large variety of sizes.In this case,the extinction events can not be characterized by a narrow distribution.
This situation can be observed in Figure 1,where the mean ?tness and the duration of the extinction events in the forth trial of the experiment in dynamic test environment 1(p c =0.2and p m =0.01)are plotted.One can observe that,when the global optimum changes from a smaller to a higher value,the mean ?tness of the population increased,resulting in higher mean values for the duration of the ex-tinction events and,as a consequence,increasing the diver-sity of the population.Such interesting behavior is reached by self-organization,and not by a rule imposed by the pro-grammer.
Figure 2presents the three ?rst steps of an extinction event for a version of the experiment in dynamic test envi-ronment 2with only 10individuals.The ?gure respectively shows the ?tness of all individuals in the current popula-tion in generations 6195,6196,and 6197.In generation 6195,the individual 3has the smallest ?tness of the popu-lation (index j in Algorithm 2).In this way,this individual and its two next neighbours (individuals 2and 4)are re-placed by new random individuals.The individual 4(index j )has now the smallest ?tness in generation 6196,and it
Figure 2:Fitness of the individuals of the current popula-tion in generations 6195,6196,and 6197for a version of the experiment in dynamic test environment 2with 10indi-viduals.
and its two next neighbours (individuals 3and 5)are then replaced.In generation 6197,the individual 5(index j )has the smallest ?tness.Observe that the chain reaction was propagated because the remaining individuals have values of ?tness higher than the individuals in the subpopulation de?ned by the limits i min ?1and i max +1(see Algorithms 2and 3).The individuals that do not belong to this sub-population are not allowed to replace an individual of this subpopulation.
The better results of the proposed GA when compared to the other GAs with random immigrants in the experiments presented here can be explained by two major factors.First, the number of different individuals that are replaced in a ?xed period of generations is generally higher for the pro-posed GA.One can observe in Figure2that the subpopu-lation in generation6197is formed by5individuals(with indexes from i min?1to i max+1).In the GA with random immigrants where the worst individuals are replaced,it is common that new individuals replace individuals with the same index in next generation,because the new individuals generally have small values of?tness.In this way,the num-ber of different individuals that are replaced in a?xed pe-riod of generations is generally smaller in comparison to the proposed GA,and,as a result,the diversity becomes smaller too.This fact can be observed by analyzing the results pre-sented in Table1,where the mean?tness of the population is smaller in the proposed GA,even though its higher val-ues of?tness of the best individuals(i.e.the adaptability is smaller).
The second major fact that explains the better results for the proposed GA is that the survival probability of a new random individual,which can be evolved to become a solu-tion of the problem,is generally smaller in the standard GAs with random immigrants.This is explained because the val-ues of?tness for the current individuals,whose locations are generally located in(or close to)local maxima after sev-eral generations,are generally much higher than the mean ?tness of the search space,i.e.the mean?tness of all possi-ble individuals.This occurs because the selection methods employed in GA preserves,directly or indirectly,the best individuals of the population.An immigrant generally sur-vives during the evolution only if its?tness is close to the mean?tness of the population,which is a rare event when the number of parameters in the solution is high or when the local optimum where the population is found has values of?tness much higher than the mean?tness of the search space.On the other hand,the proposed GA preserves a new potential solution in a subpopulation and allows it to evolve while the current extinction event is in progress.When the extinction event ends,evolved versions of possible new so-lutions given by fair immigrants are generally present in the current population and can be combined with the individu-als of the main population to generate new solutions.
In the investigated experiments,like in the fossil recorded data for the extinction events in nature[19],there are more small than large extinction events,and the ex-tinction events occur on a large variety of length scales. In Figure3,the distribution of the number of extinction events against each size is plotted in a log-log scale for the forth trial of the experiment on dynamic test environment1 (p c=0.2and p m=0.01).From Figure3it can be ob-served that the result exhibits power laws(see Section2), even without any apparent tuning,indicating the presence of SOC.This kind of self-organization behavior arises in systems where many degrees of freedom are interacting and the dynamics of the system is dominated by the interaction between these degrees of freedom,rather than by the intrin-
Figure3:Number of occurrences for each size of the extinc-tion events in the forth trial of the experiment in dynamic test environment1.
sic dynamics of the individual degrees of freedom[13].In the proposed GA,the population self-organizes in order to allow the occurrence of extinction events with a large vari-ety of length https://www.doczj.com/doc/7d6717910.html,rge extinction events generally occur when the mean?tness of the population is high,and,as a consequence,the diversity level of the population is small. In this way,the diversity of the population is controlled by self-organization,allowing the GA to escape from local op-tima when the problem changes.
5Conclusions and Future Work
In this work,a GA with random immigrants where the worst individual and its next neighbours are replaced in every gen-eration is proposed.In the proposed GA,the individual starts to interact between themselves and,when the?tness of the individuals are high and close,as in the case where the diversity level is small,one single replacement can affect a large number of individuals in an extinction event.In order to avoid that the individuals with the best?tness replaces the newly introduced individuals,these ones are preserved in a subpopulation.The number of individuals in the subpopu-lation is not de?ned by the programmer,but is given by the number of individuals created in the extinction event.It is important to observe that this simple approach can take the system to a self-organization behavior,which can be use-ful in DOPs to maintain the diversity of the solutions and, then,to allow the GA to escape from local optima when the problem changes.In this way,the proposed algorithm is in-teresting in problems where the new solution is located in a peak that is hardly reached from the location of the old solution by traditional GA operators.
In the proposed algorithm,the old solutions generated by the standard genetic operators can be combined with the solutions created during an extinction event.In this way,the proposed GA can save considerable computation time when compared to a standard GA where a new optimization pro-cess with random individuals is started whenever a change in the problem is noticed.
Studying and combining self-organizing behaviors,such as the self-organized criticality studied in this paper,into GAs have shown to be bene?cial for their performance un-der dynamic environments.Much work can be further done in this area.In this paper a simple neighbourhood scheme is used for indexing individuals for the extinction event.That is,individuals in the population are randomly arranged, where neighbouring individuals may not have certain rela-tionship.This is not always true for natural or evolutionary systems.Developing other neighbouring schemes that as-sign certain relationship between neighbours instead of the random scheme for extinction events in the proposed GA may further improve its performance for DOPs,which is now under investigation by the authors.Another relevant future work is to compare the self-organizing property with other properties,such as the speciation schemes,for GAs under more comprehensive dynamic environments. Acknowledgments
The authors would like to thank FAPESP(Proc.04/04289-6)for the?nancial support.
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With的用法全解 with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。 一、 with结构的构成 它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词； 2. with或without-名词/代词+副词； 3. with或without-名词/代词+介词短语； 4. with或without-名词/代词 +动词不定式； 5. with或without-名词/代词 +分词。 下面分别举例： 1、 She came into the room，with her nose red because of cold.（with+名词+形容词，作伴随状语）
2、 With the meal over ， we all went home.（with+名词+副词，作时间状语） 3、The master was walking up and down with the ruler under his arm。（with+名词+介词短语，作伴随状语。） The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.（with+名词+不定式，作伴随状语）He could not finish it without me to help him.（without+代词 +不定式，作条件状语） 5、She fell asleep with the light burning.（with+名词+现在分词，作伴随状语） Without anything left in the with结构是许多英 语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。 二、with结构的用法 with是介词，其意义颇多，一时难掌握。为帮助大家理清头绪，以教材中的句子为例，进行分类，并配以简单的解释。在句子中with结构多数充当状语，表示行为方式，伴随情况、时间、原因或条件（详见上述例句）。 1.带着，牵着…… (表动作特征)。如： Run with the kite like this.
with复合结构专项练习（二） 一请选择最佳答案 1）With nothing_______to burn，the fire became weak and finally died out. A.leaving B.left C.leave D.to leave 2）The girl sat there quite silent and still with her eyes_______on the wall. A.fixing B.fixed C.to be fixing D.to be fixed 3）I live in the house with its door_________to the south.（这里with结构作定语） A.facing B.faces C.faced D.being faced 4）They pretended to be working hard all night with their lights____. A.burn B.burnt C.burning D.to burn 二：用with复合结构完成下列句子 1）_____________（有很多工作要做），I couldn't go to see the doctor. 2）She sat__________（低着头）。 3）The day was bright_____.（微风吹拂） 4）_________________________，（心存梦想）he went to Hollywood. 三把下列句子中的划线部分改写成with复合结构。 1）Because our lessons were over，we went to play football. _____________________________. 2）The children came running towards us and held some flowers in their hands. _____________________________. 3）My mother is ill，so I won't be able to go on holiday. _____________________________. 4）An exam will be held tomorrow，so I couldn't go to the cinema tonight. _____________________________.
1. with+宾语+形容词。比如：. The boy wore a shirt with the neck open, showing his bare chest. 那男孩儿穿着一件衬衫，颈部敞开，露出光光的胸膛。Don’t talk with your mouth full. 嘴里有食物时不要讲话。 2. with+宾语+副词。比如：She followed the guide with her head down. 她低着头，跟在导游之后。 What a lonely world it will be with you away. 你不在，多没劲儿呀！ 3. with+宾语+过去分词。比如：He was listening to the music with his eyes half closed. 他眼睛半闭着听音乐。She sat with her head bent. 她低着头坐着。 4. with+宾语+现在分词。比如：With winter coming, it’s time to buy warm clothes. 冬天到了，该买些保暖的衣服了。 He soon fell asleep with the light still burning. 他很快就睡着了，（可）灯还亮着。 5. with+宾语+介词短语。比如：He was asleep with his head on his arms. 他的头枕在臂膀上睡着了。 The young lady came in, with her two- year-old son in her arms. 那位年轻的女士进来了，怀里抱着两岁的孩子。 6. with+宾语+动词不定式。比如： With nothing to do in the afternoon, I went to see a film. 下午无事可做，我就去看了场电影。Sorry, I can’t go out with all these dishes to wash. 很抱歉，有这么多盘子要洗，我不能出去。 7. with+宾语+名词。比如： He died with his daughter yet a school-girl.他去逝时，女儿还是个小学生。 He lived a luxurious life, with his old father a beggar . 他过着奢侈的生活，而他的老父亲却沿街乞讨。(8)With so much work to do ,I can't go swimming with you. (9)She stood at the door,with her back towards us. (10)He entered the room,with his nose red with cold. with复合结构与分词做状语有啥区别 [ 标签：with, 复合结构, 分词状语] Ciro Ferrara 2009-10-18 16:17 主要是分词形式与主语的关系 满意答案好评率：100%
with的用法大全----四级专项训练with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。 一、 with结构的构成 它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词; 2. with或without-名词/代词+副词; 3. with或without-名词/代词+介词短语; 4. with或without-名词/代词+动词不定式; 5. with或without-名词/代词+分词。 下面分别举例：
1、 She came into the room，with her nose red because of cold.(with+名词+形容词，作伴随状语) 2、 With the meal over ， we all went home.(with+名词+副词，作时间状语) 3、The master was walking up and down with the ruler under his arm。(with+名词+介词短语，作伴随状语。) The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.(with+名词+不定式，作伴随状语) He could not finish it without me to help him.(without+代词 +不定式，作条件状语) 5、She fell asleep with the light burning.(with+名词+现在分词，作伴随状语) 6、Without anything left in the cupboard， she went out to get something to eat.(without+代词+过去分词，作为原因状语) 二、with结构的用法 在句子中with结构多数充当状语，表示行为方式，伴随情况、时间、原因或条件(详见上述例句)。
基本用法 它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语或非谓语动词充当 一、with或without+名词/代词+形容词 例句:1.I like to sleep with the windows open. 我喜欢把窗户开着睡觉。(伴随情况) 2.With the weather so close and stuffy, ten to one it'll rain presently. 大气这样闷，十之八九要下雨(原因状语) 二、with或without+名词/代词+副词 例句:1.She left the room with all the lights on. 她离开了房间，灯还亮着。(伴随情况) 2.The boy stood there with his head down. 这个男孩低头站在那儿。(伴随情况) 三、with或without+名词/代词+介词短语 例句:1.He walked into the dark street with a stick in his hand. 他走进黑暗的街道时手里拿着根棍子。(伴随情况) 2. With the children at school, we can't take our vacation when we want to. 由于孩子们在上学，所以当我们想度假时而不能去度假。(原因状语) 四、with或without+名词/代词+非谓语动词 1、with或without+名词/代词+动词不定式，此时，不定式表示将发生的动作。 例句: 1.With no one to talk to, John felt miserable. 由于没人可以说话的人，约翰感到很悲哀。(原因状语)
with用法归纳 （1）“用……”表示使用工具，手段等。例如： ①We can walk with our legs and feet. 我们用腿脚行走。 ②He writes with a pencil. 他用铅笔写。 （2）“和……在一起”，表示伴随。例如： ①Can you go to a movie with me? 你能和我一起去看电影'>电影吗？ ②He often goes to the library with Jenny. 他常和詹妮一起去图书馆。 （3）“与……”。例如： I’d like to have a talk with you. 我很想和你说句话。 （4）“关于，对于”，表示一种关系或适应范围。例如： What’s wrong with your watch? 你的手表怎么了？ （5）“带有，具有”。例如： ①He’s a tall kid with short hair. 他是个长着一头短发的高个子小孩。 ②They have no money with them. 他们没带钱。 （6）“在……方面”。例如： Kate helps me with my English. 凯特帮我学英语。 （7）“随着，与……同时”。例如： With these words, he left the room. 说完这些话，他离开了房间。 [解题过程] with结构也称为with复合结构。是由with+复合宾语组成。常在句中做状语，表示谓语动作发生的伴随情况、时间、原因、方式等。其构成有下列几种情形： 1.with+名词(或代词)+现在分词 此时，现在分词和前面的名词或代词是逻辑上的主谓关系。 例如:1)With prices going up so fast, we can't afford luxuries. 由于物价上涨很快，我们买不起高档商品。（原因状语） 2)With the crowds cheering, they drove to the palace. 在人群的欢呼声中，他们驱车来到皇宫。（伴随情况） 2.with+名词(或代词)+过去分词 此时，过去分词和前面的名词或代词是逻辑上的动宾关系。
With的复合结构 介词with without +宾语+宾语的补足语可以构成独立主格结构，上面讨论过的独立主格结构的几种情况在此结构中都能体现。 1. with+名词代词+形容词 He doesn’t like to sleep with the windows open. = He doesn’t like to sleep when the windows are open. He stood in the rain, with his clothes wet. = He stood in the rain, and his clothes were wet. With his father well-known, the boy didn’t want to study. 2. with+名词代词+副词 Our school looks even more beautiful with all the lights on. = Our school looks even more beautiful if when all the lights are on. The boy was walking, with his father ahead. = The boy was walking and his father was ahead. 3. with+名词代词+介词短语 He stood at the door, with a computer in his hand. He stood at the door, computer in hand. = He stood at the door, and a computer was in his hand. Vincent sat at the desk, with a pen in his mouth. Vincent sat at the desk, pen in mouth. = Vincent sat at the desk, and he had a pen in his mouth. 4. with+名词代词+动词的-ed形式 With his homework done, Peter went out to play. = When his homework was done, Peter went out to play. With the signal given, the train started. = After the signal was given, the train started. I wouldn’t dare go home without the job finished. = I wouldn’t dare go home because the job was not finish ed. 5. with+名词代词+动词的-ing形式 The girl hid her box without anyone knowing where it was. = The girl hid her box and no one knew where it was. Without anyone noticing, he slipped through the window. = When no one was noticing, he slipped through the window. 6. with+名词代词+动词不定式 The little boy looks sad, with so much homework to do. = The little boy looks sad because he has so much homework to do. with the window closed with the light on with a book in her hand with a cat lying in her arms with the problem solved with the new term to begin
with用法小结 一、with表拥有某物 Mary married a man with a lot of money . 马莉嫁给了一个有着很多钱的男人。 I often dream of a big house with a nice garden . 我经常梦想有一个带花园的大房子。 The old man lived with a little dog on the lonely island . 这个老人和一条小狗住在荒岛上。 二、with表用某种工具或手段 I cut the apple with a sharp knife . 我用一把锋利的刀削平果。 Tom drew the picture with a pencil . 汤母用铅笔画画。 三、with表人与人之间的协同关系 make friends with sb talk with sb quarrel with sb struggle with sb fight with sb play with sb work with sb cooperate with sb I have been friends with Tom for ten years since we worked with each other, and I have never quarreled with him . 自从我们一起工作以来，我和汤姆已经是十年的朋友了，我们从没有吵过架。 四、with 表原因或理由 John was in bed with high fever . 约翰因发烧卧床。 He jumped up with joy . 他因高兴跳起来。 Father is often excited with wine . 父亲常因白酒变的兴奋。 五、with 表“带来”，或“带有,具有”，在…身上，在…身边之意
with+复合宾语的用法 一、with的复合结构的构成 二、所谓"with的复合结构”即是"with+复合宾语”也即"with +宾语+宾语补足语” 的结构。其中的宾语一般由名词充当（有时也可由代词充当）；而宾语补足语则是根据 具体的需要由形容词，副词、介词短语，分词短语（包括现在分词和过去分词）及不定式短语充当。下面结合例句就这一结构加以具体的说明。 三、1、with +宾语+形容词作宾补 四、①He slept well with all the windows open.（82 年高考题） 上面句子中形容词open作with的宾词all the windows的补足语， ②It' s impolite to talk with your mouth full of food. 形容词短语full of food 作宾补。Don't sleep with the window ope n in win ter 2、with+宾语+副词作宾补 with Joh n away, we have got more room. He was lying in bed with all his clothes on. ③Her baby is used to sleeping with the light on.句中的on 是副词，作宾语the light 的补足语。 ④The boy can t play with his father in.句中的副词in 作宾补。 3、with+宾语+介词短语。 we sat on the grass with our backs to the wall. his wife came dow n the stairs,with her baby in her arms. They stood with their arms round each other. With tears of joy in her eyes ,she saw her daughter married. ⑤She saw a brook with red flowers and green grass on both sides. 句中介词短语on both sides 作宾语red flowersandgreen grass 的宾补， ⑥There were rows of white houses with trees in front of them.，介词短语in front of them 作宾补。 4、with+宾词+分词（短语 这一结构中作宾补用的分词有两种，一是现在分词，二是过去分词，一般来说，当分词所表 示的动作跟其前面的宾语之间存在主动关系则用现在分词，若是被动关系，则用过去分词。 ⑦In parts of Asia you must not sit with your feet pointing at another person.（高一第十课），句中用现在分词pointing at…作宾语your feet的补足语，是因它们之间存在主动关系，或者说point 这一动作是your feet发出的。 All the after noon he worked with the door locked. She sat with her head bent. She did not an swer, with her eyes still fixed on the wall. The day was bright,with a fresh breeze（微风）blowing. I won't be able to go on holiday with my mother being ill. With win ter coming on ,it is time to buy warm clothes. He soon fell asleep with the light still bur ning. ⑧From space the earth looks like ahuge water covered globe,with a few patches of land stuk ing out above the water而在下面句子中因with的宾语跟其宾补之间存在被动关系，故用过去分词作宾补：
with复合结构 一. with复合结构的常见形式 1.“with+名词/代词+介词短语”。 The man was walking on the street, with a book under his arm. 那人在街上走着，腋下夹着一本书。 2. “with+名词/代词+形容词”。 With the weather so close and stuffy, ten to one it’ll rain presently. 天气这么闷热，十之八九要下雨。 3. “with+名词/代词+副词”。 The square looks more beautiful than even with all the light on. 所有的灯亮起来，广场看起来更美。 4. “with+名词/代词+名词”。 He left home, with his wife a hopeless soul. 他走了，妻子十分伤心。 5. “with+名词/代词+done”。此结构过去分词和宾语是被动关系，表示动作已经完成。 With this problem solved, neomycin 1 is now in regular production. 随着这个问题的解决，新霉素一号现在已经正式产生。 6. “with+名词/代词+-ing分词”。此结构强调名词是-ing分词的动作的发出者或某动作、状态正在进行。 He felt more uneasy with the whole class staring at him. 全班同学看着他，他感到更不自然了。 7. “with+宾语+to do”。此结构中，不定式和宾语是被动关系，表示尚未发生的动作。 So in the afternoon, with nothing to do, I went on a round of the bookshops. 由于下午无事可做，我就去书店转了转。 二. with复合结构的句法功能 1. with 复合结构，在句中表状态或说明背景情况，常做伴随、方式、原因、条件等状语。With machinery to do all the work, they will soon have got in the crops. 由于所有的工作都是由机器进行，他们将很快收完庄稼。（原因状语） The boy always sleeps with his head on the arm. 这个孩子总是头枕着胳膊睡觉。（伴随状语）The soldier had him stand with his back to his father. 士兵要他背对着他父亲站着。（方式状语）With spring coming on, trees turn green. 春天到了，树变绿了。（时间状语） 2. with 复合结构可以作定语 Anyone with its eyes in his head can see it’s exactly like a rope. 任何一个头上长着眼睛的人都能看出它完全像一条绳子。 【高考链接】 1. ___two exams to worry about, I have to work really hard this weekend.（04北京） A. With B. Besides C. As for D. Because of 【解析】A。“with+宾语+不定式”作状语，表示原因。 2. It was a pity that the great writer died, ______his works unfinished. (04福建) A. for B. with C. from D.of 【解析】B。“with+宾语+过去分词”在句中作状语，表示状态。 3._____production up by 60%, the company has had another excellent year. (NMET) A. As B.For C. With D.Through 【解析】C。“with+宾语+副词”在句中作状语，表示程度。
With复合结构的用法小结 with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。 一、with结构的构成 它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二 部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词； 2. with或without-名词/代词+副词； 3. with或without-名词/代词+介词短语； 4. with或without-名词/代词+动词不定式； 5. with或without-名词/代词+分词。 下面分别举例： 1、She came into the room，with her nose red because of cold.（with+名词+形容词，作伴随状语） 2、With the meal over ，we all went home.（with+名词+副词，作时间状语） 3、The master was walking up and down with the ruler under his arm。（with+名词+介词短语，作伴随状语。）The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.（with+名词+不定式，作伴随状语）He could not finish it without me to help him.（without+代词+不定式，作条件状语） 5、She fell asleep with the light burning.（with+名词+现在分词，作伴随状语）Without anything left in the cupboard，shewent out to get something to eat.（without+代词+过去分词，作为原因状语） 二、with结构的用法 在句子中with结构多数充当状语，表示行为方式，伴随情况、时间、原因或条件（详见上述例句）。 With结构在句中也可以作定语。例如： 1.I like eating the mooncakes with eggs. 2.From space the earth looks like a huge water-covered globe with a few patches of land sticking out above the water. 3.A little boy with two of his front teeth missing ran into the house. 三、with结构的特点 1. with结构由介词with或without+复合结构构成。复合结构中第一部分与第二部分语法上是宾语和宾语补足语关系，而在逻辑上，却具有主谓关系，也就是说，可以用第一部分作主语，第二部分作谓语，构成一个句子。例如：With him taken care of，we felt quite relieved.（欣慰）→（He was taken good care of.）She fell asleep with the light burning. →（The light was burning.）With her hair gone，there could be no use for them. →（Her hair was gone.） 2. 在with结构中，第一部分为人称代词时，则该用宾格代词。例如：He could not finish it without me to help him. 四、几点说明： 1. with结构在句子中的位置：with 结构在句中作状语，表示时间、条件、原因时一般放在
介词with的用法大全 With是个介词，基本的意思是“用”，但它也可以协助构成一个极为多采多姿的句型，在句子中起两种作用；副词与形容词。 with在下列结构中起副词作用： 1.“with+宾语+现在分词或短语”，如： (1) This article deals with common social ills, with particular attention being paid to vandalism. 2.“with+宾语+过去分词或短语”，如： (2) With different techniques used, different results can be obtained. (3) The TV mechanic entered the factory with tools carried in both hands. 3.“with+宾语+形容词或短语”，如： (4) With so much water vapour present in the room, some iron-made utensils have become rusty easily. (5) Every night, Helen sleeps with all the windows open. 4.“with+宾语＋介词短语”，如： (6) With the school badge on his shirt, he looks all the more serious. (7) With the security guard near the gate no bad character could do any thing illegal. 5.“with+宾语＋副词虚词”，如： (8) You cannot leave the machine there with electric power on. (9) How can you lock the door with your guests in? 上面五种“with”结构的副词功能，相当普遍，尤其是在科技英语中。 接着谈“with”结构的形容词功能，有下列五种： 一、“with+宾语+现在分词或短语”，如： (10) The body with a constant force acting on it. moves at constant pace. (11) Can you see the huge box with a long handle attaching to it ? 二、“with+宾语+过去分词或短语” (12) Throw away the container with its cover sealed. (13) Atoms with the outer layer filled with electrons do not form compounds. 三、“with+宾语+形容词或短语”，如： (14) Put the documents in the filing container with all the drawers open.
With 复合结构用法小结 “With + 复合结构”又称为“with结构”，在句中表状态或说明背景情况，常做伴随，方式，原因，条件等状语。具体结构如下： 1. With + 名词 + 介词短语? (1) He was asleep with his head on his arm. ? (2) The man came in with a whip in his hand. ? 在书面语中。上句也可以说成：The man came in, whip in hand. 2．with + 名词 + 形容词（强调名词的特性或状态）? (1)With the weather so close and stuffy, ten to one it'll rain presently.天气这么闷热，十之八九要下雨。? (2)He used to sleep with the windows open. 3. With + 名词 + 副词? (1)With John away, we've got more room. 约翰走了，我们的地方大了一些。? (2)The square looks more beautiful than ever with all the light on. 4. With + 名词 + -ed 分词（强调名词是 -ed分词动作的承受者或动作已经发生） ?(1)With this problem solved, neopenicillin 1 is now in regular production. 随着这个问题的解决，新霉素一号现在已正式生产。 ?(2)All the afternoon he worked with the door locked. 5. with + 名词 + -ing分词（强调名词是 -ing分词的动作的发出者或某动作，状态正在进行）? (1)I won’t be able to go on holiday with my mother being ill. ? (2)He felt more uneasy with the whole class staring at him. ? (3)With the field leveled and irrigation channels controlling the volume of water(水量), no such problem arose again. 6. with + 名词 + to do （不定式动作尚未发生）? (1)So in the afternoon, with nothing to do, I went on a round of the bookshops. 由于下午无事可做，我就去书店转了转。 ?(2)I can't go out with all these dishes to wash. 一、 with结构的构成 它是由介词with或without+复合结构构成，复合结构作介词with或without 的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词； 2. with或without-名词/代词+副词； 3. with或without-名词/代词+介词短语； 4. with或without-名词/代词 +动词不定式； 5. with或without-名词/代词 +分词。 下面分别举例： 1、 She came into the room，with her nose red because of cold.（with+名词+形容词，作伴随状语） 2、 With the meal over ， we all went home.（with+名词+副词，作时间状语） 3、The master was walking up and down with the ruler under his arm。（with+名词+介词短语，作伴随状语。） The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.（with+名词+不定式，作伴随状语） He could not finish it without me to help him.（without+代词 +不定式，作条件状语） 5、She fell asleep with the light burning.（with+名词+现在分词，作伴随状语） Without anything left in the with结构是许多英语复合结构中最
with without 引导的独立主格结构 介词with without +宾语+宾语的补足语可以构成独立主格结构，上面讨论过的独立主格结构的几种情况在此结构中都能体现。 A．with+名词代词+形容词 He doesn’t like to sleep with the windows open. 他不喜欢开着窗子睡觉。 = He doesn’t like to sleep when the windows are open. He stood in the rain, with his clothes wet. 他站在雨中，衣服湿透了。 = He stood in the rain, and his clothes were wet. 注意： 在“with+名词代词+形容词”构成的独立主格结构中，也可用已形容词化的-ing 形式或-ed形式。 With his son so disappointing，the old man felt unhappy. 由于儿子如此令人失望,老人感到很不快乐。 With his father well-known, the boy didn’t want to study. 父亲如此出名，儿子不想读书。 B．with+名词代词+副词 Our school looks even more beautiful with all the lights on. 所有的灯都打开时，我们的学校看上去更美。 = Our school looks even more beautiful if when all the lights are on. The boy was walking, with his father ahead. 父亲在前，小孩在后走着。 = The boy was walking and his father was ahead. C．with+名词代词+介词短语 He stood at the door, with a computer in his hand. 或 He stood at the door, computer in hand. 他站在门口，手里拿着一部电脑。 = He stood at the door, and a computer was in his hand. Vincent sat at the desk, with a pen in his mouth. 或 Vincent sat at the desk, pen in mouth. 文森特坐在课桌前，嘴里衔着一支笔。 = Vincent sat at the desk, and he had a pen in his mouth. D．with+名词代词+动词的-ed形式 With his homework done, Peter went out to play. 作业做好了，彼得出去玩了。 = When his homework was done, Peter went out to play. With the signal given, the train started. 信号发出了，火车开始起动了。 = After the signal was given, the train started. I wouldn’t dare go home without the job finished. 工作还没完成，我不敢回家。 = I wouldn’t dare go home because the job was not finished.