Differential evolution with hybrid linkage crossover
Differential evolution with hybrid linkage
crossover
Yiqiao Cai a ,?,Jiahai Wang b
a College of Computer Science and Technology,Huaqiao University,Xiamen 361021,China b
Department of Computer Science,Sun Yat-sen University,Guangzhou 510006,China
a r t i c l e i n f o Article history:
Received 2March 2014
Received in revised form 5February 2015Accepted 15May 2015
Available online 27May 2015Keywords:
Differential evolution Linkage learning Crossover Grouping
Numerical optimization
a b s t r a c t
In the ?eld of evolutionary algorithms (EAs),differential evolution (DE)has been the sub-ject of much attention due to its strong global optimization capability and simple imple-mentation.However,in most DE algorithms,crossover operator often ignores the consideration of interactions between pairs of variables.That is,DE is linkage-blind,and the problem-speci?c linkages are not utilized effectively to guide the search process.Furthermore,linkage learning techniques have been veri?ed to play an important role in EA optimization.Therefore,to alleviate the drawback of linkage-blind in DE and enhance its performance,a novel linkage utilization technique,called hybrid linkage crossover (HLX),is proposed in this study.HLX utilizes the perturbation-based method to automat-ically extract the linkage information of a speci?c problem and then uses the linkage infor-mation to guide the crossover process.By incorporating HLX into DE,the resulting algorithm,named HLXDE,is presented.In order to evaluate the effectiveness of HLXDE,HLX is incorporated into six original DE algorithms,as well as several advanced DE vari-ants.Experimental results demonstrate the high performance of HLX for the DE algorithms studied.
ó2015Elsevier Inc.All rights reserved.
1.Introduction
Differential evolution (DE),proposed by Storn and Price [55],is a simple and powerful evolutionary algorithm (EA)for global optimization over continuous space.In the ?eld of EA,DE has been the subject of much attention due to its attractive characteristics,such as its compact structure,ease of use,speediness and robustness.In the last few years,DE has been extended for handling multiobjective,constrained,large scale,dynamic and uncertain optimization problems [11,40]and is now successfully used in various scienti?c and engineering ?elds [47,66,19,85],such as chemical engineering,engineering design,and pattern recognition.
When DE is applied to a given optimization problem,there are two main factors which signi?cantly affect the behavior of DE:control parameters (i.e.,population size NP ,mutation scaling factor F and crossover rate Cr )and evolutionary operators (i.e.,mutation,crossover and selection).During the last decade,many researchers have worked to improve DE by adopting self-adaptive strategies for the control parameters [48,30,13],devising new mutation operators [23,5,67],developing ensem-ble strategies [68,25,6],and proposing a hybrid DE with other optimization algorithms [73,46,64],etc.Many studies related to the evolutionary operators of DE have focused on the mutation operator [48,30,23,5,68,25].In contrast,there have been few studies on the crossover operator of DE [43,24,69].https://www.sodocs.net/doc/0f10426551.html,/10.1016/j.ins.2015.05.026
0020-0255/ó2015Elsevier Inc.All rights reserved.
?Corresponding author.
E-mail addresses:caiyq@https://www.sodocs.net/doc/0f10426551.html, (Y.Cai),wjiahai@https://www.sodocs.net/doc/0f10426551.html, (J.Wang).
Y.Cai,J.Wang/Information Sciences320(2015)244–287245 Linkages or inter-dependencies between pairs of variables have been studied and utilized in genetic algorithm(GA)and EAs to improve performance on dif?cult problems[8,65].From the perspective of GA,tight linkage refers to the identi?ed building blocks(BBs)on a chromosome,and the genes belonging to the same BB should be inherited together by the off-spring at a higher probability.According to the existing work,linkage identi?cation or recognition of BBs plays an important role in GA optimization[8,65].Many linkage learning techniques have been proposed for combinatorial optimization [8,65,17],while techniques for global numerical optimization have been rarely discussed[84,7].In addition,to the best of our knowledge,studies explicitly using linkage information to enhance the performance of DE are scarce.Therefore,most DE algorithms are not able to effectively utilize problem-speci?c linkages for guiding the search.
Based on these considerations,we present a novel linkage utilization technique,called hybrid linkage crossover(HLX),to utilize the problem-speci?c linkages to guide the crossover process of DE.First,HLX uses a perturbation-based method,an improved differential grouping(DG)method[44],to adaptively extract the linkage information between pairs of variables. The linkage information is stored in a linkage matrix(LM).In LM,each element stands for‘‘linkage strength’’which measures the likelihood of a pair of variables being tightly linked.Then,with LM,the BBs are identi?ed by automatically decomposing the problem variables into different groups without overlaps.Here,BB is a group of tightly interactive variables.Finally,two group-wise crossover operators are designed to explicitly use the identi?ed BBs for guiding the crossover process.One is named group-wise binomial crossover(GbinX).Different from the conventional binomial crossover of DE,GbinX exchanges the variables based on the detected groups.The second one is referred to as group-wise orthogonal crossover(GorthX), which combines the orthogonal design[27,38]and the identi?ed BBs to make a systematic search in a region de?ned by a pair of the target and mutant vectors.In this way,both GbinX and GorthX can avoid the disruption of BBs during crossover. By incorporating HLX into DE,the resulting algorithm,named HLXDE,is proposed.In HLXDE,the conventional binomial crossover operator and the two group-wise crossover operators are implemented together in a cooperative manner.
In order to evaluate the effectiveness of HLXDE,HLX is incorporated into six original DE algorithms,as well as several advanced DE variants.Experimental studies are carried out on a suite of benchmark problems,including the classical func-tions[74],the functions from the IEEE congress on evolutionary computation(CEC)2005special session on real-parameter optimization[56]and the functions from the IEEE CEC2012special session on large-scale global optimization[60].The results indicate that HLX can effectively enhance the performance of most DE algorithms studied.
The major contributions of this study include the following:
An improved differential grouping technique is presented to address the linkage learning problem for global numer-ical optimization.It provides some insights on how the idea of grouping variables can be extended beyond the coop-erative coevolution framework.
Two group-wise crossover operators,GbinX and GorthX,are designed to explicitly utilize the identi?ed BBs to guide the crossover process of DE.
HLXDE effectively combines two group-wise crossover operators with the binomial crossover in a cooperative man-ner,which effectively maintains the advantages of the binomial crossover and utilizes the BBs of good or promising individuals.
HLX can be easily applied to other advanced DE variants and cooperated with different kinds of modi?cations in the advanced DE variants.It provides a new promising approach for optimization.
The rest of this paper is organized as follows.Section2brie?y describes the original DE algorithm,the related work to the crossover operator of DE and the linkage learning techniques.Then,HLX and HLXDE are presented in detail in Section3.In Section4,the experimental results for a suite of benchmark functions are reported and analyzed.Finally,the conclusions are drawn in Section5.
2.Related work
In this section,the original DE algorithm is introduced?rst.Then,the related work to the crossover operator of DE and the linkage learning techniques are reviewed.
2.1.DE
DE is for solving the numerical optimization problem.Without loss of generality,we consider the following optimization problem:Minimize feXT;X2S,where S#R D and D is the dimension of the decision variables.DE evolves a population of vec-tors,and each vector is denoted as X i;G?ex1;i;G;x2;i;G;...;x D;i;GT,where i?1;2;...;NP;NP is the size of the population and G is the number of current iteration.Here,the initial value of the j th parameter of X i;G can be generated by:
x j;i;G?L jtrndreale0;1TáeU jàL jTe1T
where rndreale0;1Trepresents a uniformly distributed random variable within the range[0,1]and L j(U j)represents the lower(upper)bound of the j th variable.
During each generation,DE uses three main operators for population reproduction:mutation,crossover and selection.
(1)Mutation:DE employs the mutation strategy to generate a mutant vector V i;G with respect to each individual X i;G (called the target vector)in the current population.The general notation for mutation strategy is‘‘DE/x/y’’,where DE stands for differential evolution algorithm,x represents the vector to be perturbed and y represents the number of difference vec-tors considered for perturbation of x.Two commonly used strategies are as follows:
‘‘DE/rand/1’’
V i;G?X r1;GtFáeX r2;GàX r3;GTe2T ‘‘DE/best/1’’
V i;G?X best;GtFáeX r2;GàX r3;GTe3Twhere F is called the mutation scaling factor,and r1;r2and r3are distinct integers randomly selected from the range[1,NP] and are different from i.There are various well-known and widely used mutation strategies in the literature,such as ‘‘DE/rand/2’’,‘‘DE/current-to-best/1’’,‘‘DE/rand-to-best/1’’and‘‘DE/best/2’’.More details of them can be found in[55,11].
(2)Crossover:The crossover operator is applied to each pair of X i;G and the corresponding V i;G to generate a trial vector U i;G. There are two types of crossover scheme:binomial and exponential.Here,only the binomial crossover(BinX)is outlined,as it is more widely used.BinX is shown as follows:
u j;i;G?
v j;i;G if rndreale0;1T6Cr or j?j
rand
x j;i;G otherwise
e4T
where Cr2?0;1 is called the crossover rate,and j
rand
is an integer randomly selected from the range[1,D].In this study,if u j;i;G is out of the boundary,it will be reinitialized within the range[L j;U j].
(3)Selection:DE uses a one-to-one selection operator to select the better one between X i;G and U i;G to survive into the next generation.The selection operator is described as follows:
X i;Gt1?
U i;G if feU i;GT6feX i;GT
X i;G otherwise
e5T
2.2.Crossover operator in DE
DE has drawn many researchers’attention,which has resulted in many variants with improved performance[11,41]. According to[41],these DE variants can be divided into two categories:DE with an extra component and DE with modi?ed structures.In the existing work of DE,the mutation operator has been studied in various ways.In contrast,there are few studies on the crossover operator of DE[11,41].In this section,we focus on the work related to the crossover operator in the context of DE.Table1provides a list of some previous studies on the crossover operator in DE along with different facets (i.e.,tuning Cr value,parameter adaption technique and crossover scheme).
Many researchers focus on tuning Cr to improve the performance of DE.From Table1,we can?nd that these empirical suggestions for setting Cr are different and lack suf?cient experimental justi?cations.However,some interesting observa-tions can be obtained from these?ndings.A small Cr value(e.g.,Cr60:2)is more appropriate for the separable functions, and a large Cr value(e.g.,Cr>0:9)is the best for non-separable functions.For the role of Cr in optimizing functions with interacting parameters,the greater the number of interacting parameters,the higher Cr must be.In addition,from the anal-ysis in[39],DE with low values of Cr(near0)results in very small exploratory moves that are orthogonal to the current axes, while DE with high values of Cr(near1)makes large exploratory moves that are at angles to the search space’s axes.That is, both extremes are able to produce effective moves[39].In order to avoid manual tuning Cr,many parameter adaption tech-niques have been developed[48,30,33,80,4,34,79,61,31].These researches presented the effective methods to adaptively tune the Cr value.
On the other hand,from Table1,we can see that the studies on the new crossover scheme in DE are relatively few.In most of the DE variants,BinX is employed as the default.As mentioned above,the crossover operator has always been regarded as the primary search operator in GA,and the linkage identi?cation or recognizing BBs plays an important role in the GA opti-mization[8,65].However,in most of the crossover operators of DE,the linkage information is not effectively identi?ed and used to enhance the performance of DE.Based on these analyses,in this study,we develop HLX to utilize the problem-speci?c linkages to guide the crossover process of DE.
2.3.Linkage learning
In GA and EAs,the identi?cation and preservation of important interactions among variables have a desirable effect on the evolutionary process,which is generally called linkage learning.In biological systems,linkage refers to the level of asso-ciation in inheritance of two or more non-allelic genes on the same chromosome[28].These linked genes have a higher chance of being inherited from the same parent.In GA,linkage is used to describe and measure the interrelationships 246Y.Cai,J.Wang/Information Sciences320(2015)244–287
Y.Cai,J.Wang/Information Sciences320(2015)244–287247
Table1
Previous studies on crossover operator in DE.
Taxonomy Reference work Approaches
Tuning Cr Storn and Price[55]Cr could be set to0.1or0.9to obtain good performance
Mezura-Montes et al.[36]A low value of Cr?0:1was often the best chosen
Ron¨kkon¨en et al.[50]Cr60:2was more appropriate for the separable functions and Cr close to1.0
(e.g.,Cr>0:9)was the best for non-separable functions
Montgomery and Chen[39]DE behaved differently with low and high values of Cr and both extremes are
able to produce effective moves
Parameter adaption technique Qin et al.[48],Zhang et al.[83]Cr was gradually self-adapted by learning from their previous experiences in
generating promising solutions
Liu and Lampinen[33]Fuzzy logic controllers were used to adapt the Cr value
Zaharie[80]Adaptive control was based on the idea of controlling the population diversity
Brest et al.[4]Self-adaptive settings by extending individuals with the Cr value
Mallipenddi et al.[34]A pool of Cr values was taken in the range of0.1–0.9
Yu et al.[79]Two-level adaptive parameter control scheme based on the optimization states
and the individual’s?tness value
Tang et al.[61]Individual-dependent parameter setting with a rank-based scheme and a value-
based scheme
Crossover scheme Storn and Price[55]Two kinds of well-known crossover schemes,binomial and exponential
crossover
Zaharie[81]A systematic analysis of the in?uence of binomial and exponential crossover on
the behavior of DE
Zhao et al.[86]A linearly scalable exponential crossover operator based on a number of
consecutive dimensions to crossover
Weber and Neri[71]A contiguous binomial crossover with the exchange of contiguous block in a
fashion similar to the exponential crossover
Lin et al.[32]The choice of crossover method and parameters were related to the
mathematical features of the problems
Gou et al.[26]Eigenvector-based crossover operator by utilizing eigenvectors of covariance
matrix of individual solutions
Noman and Iba[43]A simplex crossover-based adaptive local search operator
Gong et al.[24],Wang et al.[69]An orthogonal crossover combined with the conventional crossover
existing between the genes.These highly interactive genes belong to a BB.When GA is applied to a given optimization prob-lem,Holland[29]suggested that the genes belonging to the same BB should be tightly linked together on the chromosome to improve performance.Otherwise,if these linked genes spread all over the chromosome,the BBs are very hard to create and are easy to be disrupted during crossover,for example,single-point crossover.This suggestion is also supported in some studies[8,21,62].Furthermore,for the continuous optimization,Chen et al.[7]suggested that the crossover with dynamic linkage technique is bene?cial to utilizing the obtained linkage information.Therefore,identifying or recognizing BBs plays an important role in crossover of GA and EAs.However,it is often dif?cult to know the linkage information of a speci?c prob-lem in the real world a priori.As a consequence,linkage learning has been studied in both the discrete and continuous GA and EAs[8,65,7,12,63].Table2provides a list of some previous studies on linkage learning for discrete and continuous opti-mization problems.
For the discrete optimization problems,there are many linkage learning techniques proposed to improve the performance of GA and EAs.From Table2,these linkage learning techniques can be classi?ed into three categories based on different aspects of GA and EAs:how to distinguish between the good and bad linkages,how to express or represent linkage informa-tion and how to store linkage information[8].More details of other linkage learning techniques in GA and EAs can be found in[8].
For the continuous optimization problems,linkage learning has been studied less.As shown in Table2,there are several linkage learning methods for continuous optimization,such as dynamic linkage discovery[7],estimation of dis-tribution algorithms(EDAs)[84],perturbation-based methods(PMs)[12,44]and data mining techniques[63].In dynamic linkage discovery,the linkage con?guration is adapted by assigning the linkage groups randomly[7]. Hence,dynamic linkage discovery does not rely on a systematic or smart procedure to discover the interactions among variables.It may happen that the problem-speci?c BBs are very hard to create and are destroyed easily during the crossover process.While identifying linkage in a statistical manner,EDAs generally tend to ignore BBs with a relatively low?tness contribution[9,63],and the computational cost of them is usually very high,for example,the Bayesian optimization algorithm(BOA)[45].Recently,in the context of PMs for continuous global optimization,differential grouping(DG)which is an automatic decomposition strategy,was superimposed on a cooperative co-evolutionary framework in[44].Based on the above analysis and the effectiveness of DG,a new linkage utilization technique based on DG is developed for the continuous optimization problems in this study.
3.Differential evolution with hybrid linkage crossover(HLXDE)
3.1.Motivation
As discussed above,the crossover operator plays an important role in the performance of DE[81,86,71,32,43,24,69]. The existing work[8,65,7,9,12]also demonstrates that the crossover with linkage learning can effectively prevent the linkages between pairs of variables from being destroyed and promote the cooperation of individuals of population. In most DE algorithms,BinX(see Eq.(4))is employed to generate a trial vector from a pair of target and mutant vectors. As we can?nd,each variable of the trial vector in BinX is randomly and independently inherited from either target vec-tor or mutant vector based on Cr.In this way,the linkage information between pairs of variables is ignored during the crossover process.That is,DE is linkage-blind,and thus the problem-speci?c linkages cannot be utilized to guide the evolutionary process.As discussed in[39,86,81,58],although DE can solve the non-separable functions with a high value of Cr,DE with a high Cr value will cause rapid and perhaps premature convergence unless the population size is large enough.In addition,DE with high values of Cr will take a longer time to solve these non-separable functions than that with low values of Cr[39].That is,DE has dif?culty on functions that are not linearly separable,and the linkage learning techniques might be used to further improve the performance of DE on these functions.Therefore,in order to alleviate this drawback and utilize the problem-speci?c linkages for enhancing the performance of DE,we propose HLX and then incorporate it into DE to present HLXDE in this study.The details of HLX and the complete framework of HLXDE are described as follows.
3.2.HLX
For many problems,the problem-speci?c knowledge does not exist in the individual variables but in the linkages between pairs of variables.In order to detect the underlying interaction structure of these variables and to guide the crossover process with the problem-speci?c linkage,HLX consists of three main operators:(1)constructing the linkage matrix to extract and store the linkage information;(2)adaptively grouping the problem variables to detect BBs;(3)applying group-wise cross-over to explicitly use BBs for guiding the crossover process.
Algorithm1.Linkage Matrix Construction(LMC)
1:Initialize a vector C0?ec0
1;...;c0
i
;...;c0
D
Tand set c0
i
as lbound i;i?1;...;D
2:Initialize D max?0
//calculate difference value of pair variables
3:For i?1to Dà1do
4:Set c0
i
as ubound i and name the new vector as C1
5:Calculate D1;x
i
?f eXT?feC1TàfeC0T
6:For j?it1to D do
7:Set c1
j
as midbound j and name the new vector as C2
8:Set c2
i
as lbound j and name the new vector as C3
9:Calculate D2;x
i
?f eXT?feC2TàfeC3T
10:Calculate D x
i ;x j
?f eXTusing Eq.(8)
11:If j D x
i ;x j
?f eXTj 12:Set D x i ;x j ?f eXT?0 13:End if 14:If j D x i ;x j ?f eXTj>D max Then 15:Set D max?D x i ;x j ?f eXT 16:End if 17:End for 18:End for //normalize difference values and store them in LM 19:For i?1to D do 20:For j?1to D do 21:calculate LM?i;j using Eq.(9) 22:End For 23:End For 248Y.Cai,J.Wang/Information Sciences320(2015)244–287 3.2.1.Linkage matrix construction (LMC) By detecting the ?tness changes from perturbing pairs of variables,the perturbation-based methods are employed to identify the interactive variables.Recently,differential grouping (DG)has been proposed to decompose the problem auto-matically,deriving from the de?nition of partial separability [44].Due to its theoretical basis and effectiveness,DG is adopted and improved in HLX to detect the underlying structure of a speci?c problem.With the linkage information obtained by the improved DG,a linkage matrix (LM )is constructed to explicitly represent the linkage information between pairs of variables. Given a function f ex T,two difference values with respect to variable x i are calculated as follows [44]: D d ;x i ?f eX Tj x i ?a ;x j ?b ?f e...;x i à1;a td ;x i t1;...;x j à1;b ;x j t1;...Tàf e...;x i à1;a ;x i t1;...;x j à1;b ;x j t1;...Te6TD d ;x i ?f eX Tj x i ?a ;x j ?c ?f e...;x i à1;a td ;x i t1;...;x j à1;c ;x j t1;...Tàf e...;x i à1;a ;x i t1;...;x j à1;c ;x j t1;...T e7T where a is an arbitrary value for x i ;d –0is a nonzero interval value,and b and c are two arbitrary different values for x j .In Eqs.(6)and (7),D d ;x i ?f eX Tj x i ?a ;x j ?b and D d ;x i ?f eX Tj x i ?a ;x j ?c refer to the forward difference of f ex Twith respect to x i with d .Then,the difference value between them is calculated as follows: D x i ;x j ?f eX T?D d ;x i ?f eX Tj x i ?a ;x j ?b àD d ;x i ?f eX Tj x i ?a ;x j ?c e8T After that,the difference value of each pair of variables is normalized and stored in LM ,as follows: LM ?i ;j ? D x i ;x j ?f eX Tmax e9T where D max is the maximum value in LM .If LM ?i ;j is zero,x i and x j are regarded to be independent of each other or separable.Otherwise,they will be considered to be interacting or non-separable. In this way,LM construction (LMC)operator extracts and stores the linkage information between pairs of variables in LM .Each element of LM stands for ‘‘linkage strength’’,which measures the likelihood of a pair of variables being tightly linked.The pseudo-code of LMC is described in Algorithm 1where lbound i ;ubound i and midbound i represent the lower,upper and center bound of x i respectively.Note that these values can be set randomly as long as they are not identical with each other Table 2 Previous studies on linkage learning in discrete and continuous optimization problems.Taxonomy Reference work Approaches Discrete optimization problems Salman et al.[51–53] The probabilistic inference framework was used for modeling crossover operators and proposed an adaptive linkage crossover Goldberg et al.[20,22],Bandyopadhyay et al.[3]Messy genetic algorithm (mGA)was proposed to solve problems by combining relatively short and well-tested building blocks to form longer and more complex substructures Emmendorfer and Pozo [14]A simple EDA based on low-order statistic and a clustering technique was combined to propose a new evolutionary algorithm,u -PBIL Yu et al.[75–78]A dependency structure matrix GA (DSMGA)was proposed by utilizing a dependency structure matrix (DSM)to analyze and explicitly decompose the problem and using the BBs information to accomplish crossover Fan et al.[17,16],Nikanjam et al.[42]Improved variants were proposed to enhance the performance of DSMGA Continuous optimization problems Chen et al.[7] Dynamic linkage discovery was proposed to adapt the linkage con?guration by employing the selection operator without extra judging criteria irrelevant to the objective function Zhange et al.[84] A regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA)for continuous multiobjective optimization problems with variable linkages Devicharan and Mohan [12] Problem speci?c linkages was learned by examining a randomly chosen collection of points in the search space to determine the correlations in ?tness changes resulting from perturbations in pairs of components of particle positions Omidvar et al.[44] Differential grouping was proposed to automatically decompose an optimization problem into a set of smaller problems for large scale optimization Ting et al.[63] Linkage was mined based on the analogy between building blocks and association rules Y.Cai,J.Wang /Information Sciences 320(2015)244–287 249 so as to obtain the nonzero difference value.Additionally,if the difference value between x i and x j is smaller than f eC 0T?10à3,they are regarded to be independent of each other in this study (see steps 11–13in Algorithm 1). In order to illustrate how LMC works,a simple example based on Noisy Quartic function at D ?8is shown here.The def-inition of Noisy Quartic function is as follows [74]: f eX T?X 8i ?1 ix 4 i trandom ?0;1T; à1:286x i 61:28 e10T Firstly,a vector is initialized as C 0?eà1:28;...;à1:28Tand the difference values for pairs of variables are calculated using Eq.(8)(Here,a ?b ?à1:28;d ?2?1:28?2:56;c ?0),as follows: D x 1;x 2?f eX T?ef e1:28;à1:28;...;à1:28Tàf eC 0TTàef e1:28;0;à1:28;...;à1:28Tàf eà1:28;0;à1:28;...;à1:28TTD x 1;x 3?f eX T?ef e1:28;à1:28;...;à1:28Tàf eC 0TTàef e1:28;à1:28;0;à1:28;...;à1:28T àf eà1:28;à1:28;0;à1:28;...;à1:28TT ááá D x 7;x 8?f eX T?ef eà1:28;...;à1:28;1:28;à1:28Tàf eC 0TTàef eà1:28;...;à1:28;1:28;0T àf eà1:28;...;à1:28;à1:28;0TT Secondly,a difference matrix (DM )is used to store all the difference values,as follows: 0:001:210:320:781:550:780:780:781:210:001:541:541:541:541:611:680:321:540:001:541:541:541:611:680:781:541:540:000:560:560:942:131:551:541:540:560:001:041:041:040:781:541:540:561:040:001:611:680:78 1:611:610:941:041:610:001:480:781:681:682:131:041:681:480:00 B B B B B B B B B B B B B @1 C C C C C C C C C C C C C A e11T Finally,all the difference values are normalized with D max ?2:13using Eq.(9),and LM is constructed as follows: 0:000:570:150:370:730:370:370:370:570:000:720:720:720:720:760:790:150:720:000:720:720:720:760:790:370:720:720:000:260:260:441:000:730:720:720:260:000:490:490:490:370:720:720:260:490:000:760:790:370:76 0:760:440:490:760:000:690:370:790:791:000:490:790:690:00 B B B B B B B B B B B B B @1 C C C C C C C C C C C C C A e12T 3.2.2.Adaptive grouping (AG) After LMC,BBs are identi?ed by AG to decompose the variables of a problem into different groups without overlap.Here,BB is a group of highly interactive variables.The pseudo-code of AG is described in Algorithm 2where a state vector (i.e.,Z )is used to examine whether the variable has been grouped.The algorithm starts by checking the linkage strength of the ?rst variable with other variables based on LM .If the state value of the j th variable (j ?2;3;...;D )is marked as not being grouped (i.e.,z j ?0)and LM ?1;j is greater than a threshold value ( ),the j th variable is placed into the same group with the ?rst vari-able and its state value is changed to 1(i.e.,z j ?1).This process is repeated until all the variables are grouped.In this study, is adaptively set as the mean value of all the elements in LM ,which is shown in step 2of Algorithm 2.Additionally,in order to enhance the search ability of HLX,grouping is not carried out in sequential order but in a random order p .That is,let p ei Tbe a random permutation of i ?1;2;...;D and grouping is carried out following the order given by the permutation p ei T. Although employing a similar way of detecting the interaction between pairs of variables,AG has some differences from DG [44].First,as discussed in [44],without prior knowledge about the problem,the decomposition with a speci?ed thresh-old value is not effective for all the problems,and how to set the threshold value is still a dif?cult problem.In DG,the thresh-old value is pre-set,while the threshold value ( )in AG is set adaptively for different problems.The effectiveness of adaptive value will be studied in Section 4.7.Second,grouping in AG is carried out based on LM .In LM ,each element represents the linkage strength between a pair of variables.In addition,randomness is also introduced into AG to generate different 250Y.Cai,J.Wang /Information Sciences 320(2015)244–287 decompositions for the same problem.The bene?t of randomness will be studied in Section 4.8empirically.Third,AG is just as a linkage learning strategy for HLX,which is different from DG as a decomposition strategy for large scale optimization.In a sense,AG is an improved method of DG.Detailed discussions between HLXDE and the cooperative co-evolution with DG (CCDG)[44]will be given in Section 3.3.3.Algorithm 2.Adaptive Grouping (AG) 1:Initialize the state vector as Z ?e0;...;0;...0T 2:Set as the mean value of P D i ?1P D j ?1LM ?i ;j 3:Initialize the number of groups as num ?14:For i ?1to D do 5:If z p ei T?0Then 6:Set z p ei T?1;Group num ?f p ei Tg 7:For j ?1to D do 8:If z p ej T?0and LM ?p ei T;p ej T P Then 9:Set z p ej T?110:Group num Group num [f p ej Tg 11:End if 12:End for 13:End if 14:Set num ?num t115:End For 3.2.3.Group-wise crossover In order to explicitly use the identi?ed BBs,two group-wise crossover operators,named as group-wise binomial crossover (GbinX)and group-wise orthogonal crossover (GorthX),are introduced into HLX.Algorithm 3.Group-wise Binomial Crossover (GbinX)1:For i ?1to NumofGroup do 2:If rndreal e0;1T GbinX :Different from BinX in DE,GbinX exchanges the variables based on the identi?ed BBs.The pseudo-code of GbinX is described in Algorithm 3where Cr G is the crossover rate for groups.When GbinX is applied to a pair of X i and V i ,all variables belonging to the selected group in X i will be replaced with the corresponding variables of V i if a group is selected for exchange.In this way,GbinX can avoid the disruption of the problem-speci?c BBs during the crossover process.For simplic-ity,Cr G is set as Cr of DE. Algorithm 4.Group-wise Orthogonal Crossover (GorthX) 1:Generate an L M e2N TOA 2:Make up M tested solutions O i ei ?1;...;M Tby selecting the variables in the corresponding group from V i or X i according to the OA 3:Evaluate each tested solution O i ei ?1;...;M Tand record the best vector,denoted as O best 4:Calculate the effect of each level on each factor,and determine the best level for each factor using Eq.(10)5:Derive a predictive solution O pr with the identi?ed best level of each factor 6:Compare f eO best Twith f eO pr T,and output the better solution as U i Y.Cai,J.Wang /Information Sciences 320(2015)244–287251 GorthX :An ef?cient way to study the effect of several factors simultaneously is to use orthogonal experimental design (OED)with both orthogonal array (OA)and factor analysis (FA)[27,38].OED utilizes the properties of fractional factorial experiments to ef?ciently determine the best combination levels for different factors with a reasonably small number of experimental samples.Therefore,OED with OA and FA is regarded as a systematic reasoning experimental design method.For more details of OED,see [27,38].In order to make a systematic search in a region de?ned by a pair of parent vectors,GorthX is designed by using OED and BBs together to generate offspring.Here,OED is used to discover the best combination of a target vector and its mutant vector.Based on the identi?ed BBs,each group of variables is regarded as a factor of OED in GorthX.The pseudo-code of GorthX is described in Algorithm 4.In Algorithm 4,the two-level OA is ?rst generated as L M e2N Twhere L means OA,N means the number of identi?ed groups,and M ?2d log 2eN t1Te is the number of combinations of the test cases.The way of constructing OA can be found at [27,38,82]and a number of OAs can also be found in https://www.sodocs.net/doc/0f10426551.html,/$njas/oadir/.Then,the M combinations (i.e.,individuals)are constructed according to OA.After that,FA is used to discover the best combination of levels based on the experimental results of all the M combinations.The effect of each level on each factor is calculated as follows: S nq ? P M m ?1f m ?z mnq P m ?1z mnq e13T where S nq denotes the effect of the q th level in the n th factor and f m denotes the result of the m th combination.z mnq is 1if the m th combination is with the q th level of the n th factor,otherwise,z mnq is 0.When all the S nq values are calculated,the best level of each factor can be determined by selecting the level of each factor that provides the highest-quality S nq .After that,a predictive solution is derived with the identi?ed best level of each factor.Finally,the best combination among the M com-binations and the predictive solution is output as the trial vector.A simple example from chemical experiments for illustrat-ing how to use OED is shown in [82].Note that OED used in GorthX is different from that in [82].The variables belonging to the same group are regarded as a factor in GorthX,while each variable is regarded as a factor in [82].Algorithm 5.HLXDE with ‘‘DE/rand/1’’(HLXDE/rand/1) 1:Generate the initial population P and set G ?1;2:Evaluate the ?tness for each individual in P ;3:?Apply LMC (Algorithm 1) 4:While the terminated condition is not satis?ed do 5:?Select an index OX index from {1,...,NP }using the roulette wheel selection method based on the individuals’?tness 6:For each individual X i ;G do 7:Mutation : Randomly select r 1–r 2–r 3–i Generate V i ;G using Eq.(2)Crossover :?If X i ;G –X OX index ;G Then ?If rndreal e0;1T ?Generate U i ;G using BinX (Eq.(4))?Else ?Apply AG (Algorithm 2) ?Generate U i ;G using GbinX (Algorithm 3)?End if ?Else ?Apply AG (Algorithm 2) ?Generate U i ;G using GorthX (Algorithm 4)?End if 9: Selection : Select the vector in the next generation using Eq.(5)10:End For 11:Set G ?G t112:End while 3.3.HLXDE Combining HLX with DE,HLXDE is presented.The pseudo-code of HLXDE with ‘‘DE/rand/1’’(HLXDE/rand/1for short)is shown in Algorithm 5,where the differences with respect to the original DE/rand/1are highlighted with ‘‘?’’.From Algorithm 5,it is clear that HLXDE differs from the original DE algorithm only in the crossover operator. 252Y.Cai,J.Wang /Information Sciences 320(2015)244–287 Y.Cai,J.Wang/Information Sciences320(2015)244–287253 In Algorithm5,to save the computational cost and keep the implementation simple,GorthX is only applied to one indi-vidual which is selected by the roulette wheel selection method[2]based on the individual’s?tness.That is,the individual with a better?tness value has a higher probability of being selected for GorthX.In addition,BinX has more chances to be executed at the beginning of HLXDE,and GbinX is activated more and more frequently along with the evolutionary process of DE.In this way,HLXDE can effectively maintain the advantages of BinX and utilize the BBs of good or promising individ-uals through group-wise crossover. 3.3.1.Algorithmic functioning As pointed out in[41],reasons for the success of the DE variants are mainly due to the additional and alternative search moves integrating into the DE structure.Based on the discussions in[41],the algorithmic functioning of HLXDE is given as follows: The use of GorthX in HLXDE can be seen as an increase of the exploitation moves.Concretely,GorthX uses both OED and the identi?ed BBs to make a systematic search in the promising region de?ned by better parent vectors.In this way,GorthX can assist DE to promote the exploitation ability. GbinX and BinX are performed in a cooperative manner.Here,a question may arise?rstly:why GbinX does not com-pletely replace BinX in HLXDE.The reason lies in that the population at the beginning of the evolutionary process has poor quality;thus the linkage information learned from the population cannot effectively re?ect the underlying structure of a speci?c problem.By this way,BinX can maintain the exploration ability of DE by keeping population diversity at the begin-ning of the evolutionary process,while GbinX can utilize the identi?ed BBs of good or promising individuals to guide the choice of possible search moves.Therefore,combining them together in HLXDE can not only maintain the advantages of BinX,but also utilize the BBs by GbinX. In summary,by combining these three crossover operators,HLXDE can employ the linkage learning technique to enhance the search ability of DE.Therefore,it is expected that HLXDE can achieve a good balance between exploration and exploitation. https://www.sodocs.net/doc/0f10426551.html,plexity analysis The additional complexity of HLXDE depends on HLX,which consists of LMC,AG and group-wise crossover.For LMC,the complexity lies in the calculation and normalization of difference value for each pair of variables.The complexity of the for-mer is OeD?eDà1T=2T,and the complexity of the latter is OeD?eDt1T=2T.Thus,the total complexity of LMC is OeD?DT. One may?nd that LMC will lead to additional?tness evaluations(FEs),and the number is D?DtD.Note that the termi-nation criterion of the algorithm is set on the basis of number of FEs.Therefore,the additional FEs of LMC have been included in the total number of FEs.It will be con?rmed in the experimental study that the additional FEs of LMC are worthwhile for enhancing DE.For AG,the complexity is OeD?NGT,where NG is the number of groups.When AG is applied to the separable function,NG is D.This is the worst-case scenario for NG,and the complexity of AG in this case is OeD?DT.For the group-wise crossover,the complexity of GbinX and GorthX is OeDTand OeeMt1T?DTwhere M?2ed log2eNGt1TeT,respectively.Note that LMC is only carried out once at each run and GorthX is also only employed once at each generation.Since the complexity of the original DE algorithm is OeGmax?NP?DTwhere Gmax is the maximal number of generation,the total complexity of HLXDE is OeG max?NP?D?NGT. In order to analyze the computational overhead of DE and HLXDE empirically,a run-time based performance comparison is carried out here.The results are shown in Tables3and4.Note that these results are approximate.The measure of algo-rithm complexity used here is from[56].Table3shows that the complexities of HLXDE/rand/1is higher than DE/rand/1, especially for f6and f13.The reason is that HLX requires additional cost to extract the linkage information and execute the group-wise crossover.However,with the increase of dimension,the relative time required by HLX decreases with respect to the total run-time of HLXDE,especially for F11and F13.Table4also shows that HLXDE/rand/1can reach the prede?ned threshold value with less run-time in most cases,compared with DE/rand/1.These results indicate that the computational cost of HLX is worthwhile for enhancing the performance of DE. https://www.sodocs.net/doc/0f10426551.html,parison with cooperative co-evolution with DG(CCDG)[44] In CCDG[44],DG,as a decomposition strategy,is superimposed on CC to improve the performance for large scale opti-mization problems.As discussed in Section3.2.2,AG in HLXDE is similar to DG in CCDG.However,there are three major dif-ferences between HLXDE and CCDG.First,the difference values are represented and normalized as linkage strength in AG, which might make it easier to tune the value than CCDG.This will be con?rmed in Section4.7.In addition,by introducing randomness,the grouping structure will be changed dynamically.As stated in[7],the con?guration of BBs may dynamically change along with the search stages.In this sense,AG with randomness in HLX may be more reasonable and provide a ben-e?t to numerical optimization.The bene?t of randomness in AG will be studied in Section4.8.Second,in HLXDE,group-wise crossovers(GbinX and GorthX)are used to make a systematic search in the region de?ned by the pair of trial vector and parent vector,while DG with CC is used to decompose the large-scale problem into a set of smaller subproblems.That is, the functioning of AG in HLXDE is to enhance the exploitation ability of DE through group-wise crossovers,while DG is used for the divide-and-conquer strategy in CC.Third,although co-evolution with different subcomponents is similar to crossover in EAs,in HLXDE,three crossover operators(BinX,GbinX and GorthX)are employed and combined together to fully exploit the linkage information.In a word,HLXDE is proposed for explicitly utilizing the linkage information to guide the multiple crossover operators,which makes it distinctively different from CCDG.What’s more,HLXDE also provides some insights on how the idea of grouping variables can be extended beyond the CC framework. 3.3. https://www.sodocs.net/doc/0f10426551.html,parison with orthogonal crossover based DE (OXDE)[69] Recently,Wang et https://www.sodocs.net/doc/0f10426551.html,ed orthogonal crossover (OX)to enhance the search ability of DE and proposed OXDE.In OXDE,one vector is selected randomly for OX to generate its trial vector.Although employing a similar OX in DE,HLXDE differs from OXDE in the following aspects.First,the groups in HLXDE are constructed based on the linkage information between pairs of variables,while the groups in OXDE are randomly generated.That is,OXDE ignores the interaction between the vari-ables.Second,the number of groups is automatically decided in HLXDE,and the number of groups is speci?ed in OXDE to reduce the number of the orthogonal combinations.Third,HLXDE uses OED with both OA and FA,while OXDE only employs OX and is without FA.Due to these differences,HLXDE may be more effective than OXDE in enhance the performance of DE,which will be discussed in Section 4.5. https://www.sodocs.net/doc/0f10426551.html,parison with EDA-based DE Estimation of distribution algrotihm (EDA)is also incorporated into DE to enhance its performance,such as DE/EDA [57]and ED-DE [70].In DE/EDA,the global information extracted by EDA is combined with the differential information obtained by DE to generate the solutions [57].In ED-DE,EDA and DE are conducted in a serial cooperative way [70].However,both DE/EDA and ED-DE did not explicitly employ EDA to detect the interaction between pairs of variables.That is,EDAs in both of them are only used to sample the promising solutions but not employed to guide the crossover process with the linkage information,which is signi?cantly different from the motivations of HLXDE. Table 3 Comparison the computational complexity of DE/rand/1and HLXDE/rand/1when both the algorithms were run for a ?xed number of ?tness evaluations.Func. Dimension DE/rand/1HLXDE/rand/1T 0 T 1c T 2ec T 2àT 1T=T 0c T 2ec T 2àT 1T=T 0Step Function (f 6) 100.1870.2030.1280.519 2.656300.5160.5590.344 1.263 5.976500.9370.9440.056 1.8697.456Generalized Penalized Function (f 13) 100.5180.5590.3280.894 3.00830 1.64 1.6840.352 2.5787.504500.125 2.718 2.7470.232 3.98810.16Shifted Rotated Weierstrass Function (F 11) 1015.2515.431 1.44815.909 5.2723046.56247.135 4.58449.16920.8565079.20380.3058.81682.26624.504Shifted expanded Griewank’s +Rosenbrock’s function (F 13) 100.610.791 1.448 1.15 4.3230 2.719 3.238 4.152 4.18111.69650 6.266 7.1 6.672 8.65 19.072 The meaning of T 0;T 1and c T 2can be referred to [56]. Table 4 Comparison of absolute run-times of DE/rand/1and HLXDE/rand/1when both the algorithms were run until they attain a pre-de?ned objective function value.Func. Dimension Threshold objective function value to reach Mean computing time DE/rand/1 HLXDE/rand/1Step Function (f 6) 100.0190.02530 1.00E à08 0.1840.169500.4880.431Generalized Penalized Function (f 13) 100.0940.11230 1.00E à080.9120.79150 2.393 1.925Shifted Rotated Weierstrass Function (F 11) 10 1.00E à0313.88314.46930 4.10E+0133.43223.647507.50E+017.391 2.657Shifted Expanded Griewank’s +Rosenbrock’s Function (F 13) 10 1.00E+00 1.177 1.58030 5.00E+0018.51914.92250 1.00E+01 63.228 47.422 254Y.Cai,J.Wang /Information Sciences 320(2015)244–287 4.Experimental study In this section,comprehensive experiments are carried out to evaluate the effectiveness of HLXDE.Thirty-eight bench-mark functions are selected as the test suite,including the classic functions [74]and the functions from the CEC 2005special session on real-parameter optimization [56].Here,the benchmark functions are presented ?rst.Secondly,the experimental setup is shown.Finally,the comparisons between HLXDE and the corresponding DE algorithms are made.4.1.Benchmark functions Thirty-eight benchmark functions are used in this study.These functions are widely used in evaluating global numerical optimization algorithms.The ?rst 13functions (denoted as f 1àf 13)are selected from the classical benchmark function suite in [74],which includes 6unimodal functions and 7multimodal functions.The next 25functions (denoted as F 1àF 25)are selected from the special session on real-parameter optimization of CEC 2005[56].These functions span a diverse set of problem characteristics,such as multimodality,ill conditioning,interdependence,and rotation.They can be categorized into four groups:unimodal functions (F 1àF 5),basic multimodal functions (F 6àF 12),expanded multimodal functions (F 13and F 14),and hybrid composition functions (F 15àF 25).The short descriptions of these 38functions are shown in Tables 5and 6,and more details of them can be found in [74,56],respectively.4.2.Experimental setup To make a fair comparison,the same initial random population is used to evaluate different algorithms,and the param-eters for all the DE algorithms are set as follows unless a change is mentioned. Dimension of the function (D ):30and 50. Population size (NP ):100[4,43]. Scaling Factor (F ):0.5[55,33,4]. Crossover Probability (Cr ;Cr G ):0.9[55,4]. Maximal number of ?tness function evaluations (MNFES ):If D =30,150,000for f 1;f 6;f 10;f 12and f 13;500,000for f 3àf 5;200,000for f 2and f 11;300,000for other functions.If D ?50;D ?10000for all the functions [56]. Number of runs:30. In the experiments,comparisons between six original DE algorithms (i.e.,DE/rand/1,DE/rand/2,DE/best/1,DE/best/2,DE/current-to-best/1and DE/rand-to-best/1)and their corresponding HLXDE algorithms are made ?rst.Then,the perfor-mance of several advanced DE variants with the corresponding HLXDE variants are compared,including the opposition Table 5 Classical Benchmark functions [74].Name Characteristics Test functions S Sphere Separable,scalable f 1?P D i ?1x 2 i ?à100;100 D Schwefel 2.22Separable,scalable f 2?P D i ?1j x i j tQ D i ?1j x i j ?à10;10 D Schwefel 1.2Nonseparable,scalable f 3?P D i ?1P i j ?1x j 2 ?à100;100 D Schwefel 2.21Nonseparable,scalable f 4?max i fj x i j ;16i 6D g ?à100;100 D Rosenbrock Nonseparable,scalable,narrow valley f 5?P D à1i ?1?100ex i t1àx 2i T2 tex i à1T2 ?à30;30 D from local to global optimum Step Separable,scalable f 6?P D i ?1eb x i t0:5cT2 ?à100;100 D Quartic Separable,scalable f 7?P D i ?1ix 4 i trandom ?0;1T?à1:28;1:28 D Schwefel 2.26Separable,scalable,numerous local optima f 8?P D i ?1eàx i sin e???????j x i j p TT?à500;500 D Rastrigin Separable,scalable,numerous local optima f 9?P D i ?1?x 2 i à10cos e2p x i Tt 10 ?à5:12;5:12 D Ackley Separable,scalable,numerous local optima f 10 ?à20exp à0:2???????????????????1D P D i ?1x 2i q àexp e1 D P D i ?1cos 2p x i Tt20te ?à32;32 D Griewank Separable,scalable,numerous local optima f 11?1 4000 P D i ?1x 2 i à Q D i ?1cos ex i ?i p T t1 ?à600;600 D Penalized 1Separable,scalable,numerous local optima f 12?p D f 10sin 2ep y 1Tt P D à1 i ?1ey i à1T2 ?1t10sin 2ep y i t1T ?à50;50 D tey D à1T2g tP D i ?1u ex i ;10;100;4T Penalized 2 Separable,scalable,numerous local optima f 13?0:1f sin 2e3p x 1TtP D à1i ?1ex i à1T2 ?1tsin 2e3p x i t1T ?à50;50 D tex D à1T2?1tsin 2e2p x D T g tP D i ?1u ex i ;5;100;4Twhere u ex i ;a ;k ;m T?k ex i àa T m x i >a 0àa 6x i 6a k eàx i àa Tm x i <àa 8<: y i ?1t0:25ex i t1T Y.Cai,J.Wang /Information Sciences 320(2015)244–287 255 based DE (ODE)[49],DE with strategy adaptation (SaDE)[48],the composite DE (CoDE)[68],the modi?ed DE with p -best crossover (MDE_p BX)[30]and the modi?ed DE (MoDE)[35].All the parameters of these DE variants are set as their original papers.The simulations are carried out on an Intel Core 2duo PC with 3.20GHz CPU and 3GB RAM.Due to space limitation,only mean and standard deviation of the best error values obtained by algorithms are shown in this paper.The best and worst values obtained by algorithms are presented in the supplemental ?le of this paper.1 Furthermore,in order to show the signi?cant differences between HLXDE and the corresponding competitors,several nonparametric statistical tests [18]are also carried out by the KEEL software [1].The results of the single-problem Wilcoxon signed-rank test [18]at a ?0:05are summarized in the last row of the tables as ‘‘w/t/l ’’,which means that HLXDE wins,ties and loses on w ;t and l functions,compared with its competitors. https://www.sodocs.net/doc/0f10426551.html,parison with original DE algorithms In this section,HLXDE is compared with the original DE algorithms to test the effectiveness of HLX for the original DE mutation strategies.The results for the functions at 30D are shown in Table 7and the convergence graphs for some test Table 6 Benchmark functions from the special session on real-parameter optimization of CEC2005[56].Name Characteristics Test Functions S F 1:Shifted Sphere Function Shifted,separable,scalable ?à100;100 D F 2:Shifted Schwefel’s Problem 1.2 Shifted,nonseparable,scalable ?à100;100 D F 3:Shifted Rotated High Conditioned Elliptic Function Shifted,rotated,nonseparable,scalable ?à100;100 D F 4:Shifted Schwefel’s Problem 1.2with Noise in Fitness Shifted,nonseparable,scalable,noise in ?tness ?à100;100 D F 5:Schwefel’s Problem 2.6with Global Optimum on Bounds Nonseparable,scalable ?à100;100 D F 6:Shifted Rosenbrock’s Function Shifted,nonseparable,scalable,narrow valley from local to global optimum ?à100;100 D F 7:Shifted Rotated Griewank’s Function without Bounds Rotated,shifted,nonseparable,scalable ?0;600 D F 8:Shifted Rotated Ackley’s Function with Global Optimum on Bounds Rotated,shifted,nonseparable,scalable ?à32;32 D F 9:Shifted Rastrigin’s Function Shifted,separable,scalable,numerous local optima ?à5;5 D F 10:Shifted Rotated Rastrigin’s Function Shifted,rotated,noseparable,scalable,numerous local optima ?à5;5 D F 11:Shifted Rotated Weierstrass Function Shifted,rotated,noseparable,scalable ?à0:5;0:5 D F 12:Schwefels Problem 2.13 Shifted,nonseparable,scalable ?àp ;p D F 13:Shifted Expanded Griewanks +Rosenbrocks Function Shifted,nonseparable,scalable Given in [56]}?à3;1 D F 14:Shifted Rotated Expanded Scaffers F6Shifted,nonseparable,scalable ?à100;100 D F 15:Hybrid Composition Function Scalable,numerous local optima ?à5;5 D F 16:Rotated Hybrid Composition Function Rotated,nonseparable,scalable,numerous local optima ?à5;5 D F 17:Rotated Hybrid Composition Function with Noise in Fitness Scalable,rotated,nonseparable,numerous local optima ?à5;5 D F 18:Rotated Hybrid Composition Function Rotated,nonseparable,scalable,numerous local optima ?à5;5 D F 19:Rotated Hybrid Composition Function with a Narrow Basin for the Global Optimum Nonseparable,scalable,numerous local optima ?à5;5 D F 20:Rotated Hybrid Composition Function with the Global Optimum on the Bounds Nonseparable,scalable,numerous local optima ?à5;5 D F 21:Rotated Hybrid Composition Function Rotated,nonseparable,scalable,numerous local optima ?à5;5 D F 22:Rotated Hybrid Composition Function with High Condition Number Matrix Nonseparable,scalable,numerous local optima ?à5;5 D F 23:Non-Continuous Rotated Hybrid Composition Function Nonseparable,scalable,numerous local optima,non-continuous ?à5;5 D F 24:Rotated Hybrid Composition Function Rotated,nonseparable,scalable,numerous local optima ?à5;5 D F 25:Rotated Hybrid Composition Function without Bounds Nonseparable,scalable,numerous local optima ?2;5 D } The detail de?nitions of these 25CEC’05test functions can be found in [56],and the program codes for all of them can be available from https://www.sodocs.net/doc/0f10426551.html,.sg/home/EPNSugan/. 1 The supplemental ?le can be obtained from the ?rst author. 256Y.Cai,J.Wang /Information Sciences 320(2015)244–287 functions are plotted in Fig.1.The better values in terms of mean solution error compared between HLXDE and its corre-sponding DE algorithm are highlighted in boldface in the following tables of this paper. From Table 7,we can ?nd that HLXDE signi?cantly outperforms the corresponding DE algorithm with respect to the over-all performance.Speci?cally,according to the Wilcoxon’s test,HLXDE/rand/1signi?cantly improves the performance of DE/rand/1on 19out of 38functions and loses on only two functions.For DE/rand/2,HLXDE is signi?cantly better on 35func-tions and is worse on only one function.For DE with the exploitative strategies,HLXDE is signi?cantly better than DE/best/1and DE/best/2on 18and 20functions,respectively.The signi?cant improvements are also yielded for DE/current-to-best/1and DE/rand-to-best/1.HLXDE is signi?cantly better than DE/current-to-best/1and DE/rand-to-best/1on 16and 18func-tions,respectively. For further investigating HLXDE on the functions at higher dimension,the comparisons are made on these functions at 50D .The results shown in Table 8indicate that HLXDE is consistently superior to the corresponding DE algorithm.Speci?cally,for DE/rand/1and DE/rand/2,HLXDE signi?cantly outperforms them on 13and 33functions,respectively.HLXDE/best/1is signi?cantly better than DE/best/1on 19functions,while HLXDE/best/2is signi?cantly better than DE/best/2on 22functions.The signi?cant improvements for DE/current-to-best/1and DE/rand-to-best/1are also obtained on 19and 18functions,respectively. In terms of the best and worst values for the functions at 30D and 50D (presented in the supplemental ?le ),HLXDE is consistently superior to the corresponding DE algorithm in most cases.Furthermore,the convergence graphs in Fig.1show that HLXDE is better than the corresponding DE algorithm in terms of the convergence rate for most of the selected functions. To show the signi?cant differences between HLXDE and its corresponding DE algorithm,the multi-problem Wilcoxon signed-rank tests [18]between pairs of algorithms on all the functions are also carried out.The results are shown in Y.Cai,J.Wang /Information Sciences 320(2015)244–287259 262Y.Cai,J.Wang/Information Sciences320(2015)244–287 Table9.It is clear that HLXDE obtains higher Rtvalues than Ràvalues in all the cases.Furthermore,the p values of all the cases are less than0.05,which indicates that HLXDE is signi?cantly better than its corresponding DE algorithm overall. In summary,the overall results of Tables7–9and Fig.1clearly show that HLX can effectively improve the performance of most of the original DE algorithms studied. With respect to the characteristics of the benchmark functions,a close inspection of Tables7–9suggests some interesting observations. For most of the separable functions(i.e.,f1àf2;f6àf13;F1and F9),HLXDE consistently obtains signi?cantly better results than the corresponding DE algorithm.Speci?cally,in127out of144cases,HLXDE signi?cantly outperforms the corresponding DE algorithm,and in the remaining17cases,there are no signi?cant differences between pairs of competi-tors.In order to clearly explain this observation,the average number of groups decomposed by HLXDE for all the38func-tions is shown in Table10.From Table10,we can?nd that HLXDE correctly identi?es the real number of groups for most of the separable functions.When solving these functions,GbinX is similar to BinX,and thus HLXDE differs from the orig-inal DE algorithm only in GorthX.Therefore,the signi?cant improvements for these functions mainly contribute to GorthX. For the nonseparable functions,HLXDE signi?cantly outperforms the corresponding DE algorithm in121out of312cases, while it is outperformed in only16cases.The reasons may be twofold.On the one hand,for these functions,the inter-action between the pair of variables is not clear and rarely discussed.Although the grouping by HLX may be not accurate, HLX with group-wise crossovers is veri?ed to be bene?cial for solving these nonseparable functions from the results in Tables7–9.On the other hand,the research by Chen et al.[7]has shown that the dynamically changed con?guration of BBs provides a bene?t to the optimizer and the decompositions may be changed with different search stages.In general, the results have demonstrated the advantages of utilizing linkage information for the nonseparable functions. https://www.sodocs.net/doc/0f10426551.html,parison with advanced DE variants In order to further evaluate the effectiveness of the proposed algorithm,HLX is incorporated into several advanced DE variants,namely,ODE[49],SaDE[48],CoDE[68],MDE_p BX[30]and MoDE[35].The comparisons between HLXDE and Table9 Results of the multi-problem Wilcoxon’s test for HLXDE vs.the corresponding DE algorithm for all the functions at30D and50D. Algorithm at30D RtRàp-Value a?0:05 HLXDE/rand/1vs.DE/rand/1531.5171.5 5.76Eà03Yes HLXDE/rand/2vs.DE/rand/273110 3.13Eà10Yes HLXDE/best/1vs.DE/best/168655 4.12Eà07Yes HLXDE/best/2vs.DE/best/2528.5212.5 2.11Eà02Yes HLXDE/current-to-best/1vs.DE/curren-to-best/1542.5198.5 1.17Eà02Yes HLXDE/rand-to-best/1vs.DE/rand-to-best/173657.27Eà11Yes Algorithm at50D RtRàp-Value a?0:05 HLXDE/rand/1vs.DE/rand/1495.5207.5 2.92Eà02Yes HLXDE/rand/2vs.DE/rand/2736.5 4.5 6.19Eà11Yes HLXDE/best/1vs.DE/best/168358 5.80Eà07Yes HLXDE/best/2vs.DE/best/2565.5175.5 3.94Eà03Yes HLXDE/current-to-best/1vs.DE/curren-to-best/1583.5119.5 2.60Eà04Yes HLXDE/rand-to-best/1vs.DE/rand-to-best/1700417.24Eà08Yes Table10 Results of the average number of groups obtained by HLXDE for all the functions at30D and50D. Func.30D50D Func.30D50D Func.30D50D f13050F13050F1414.49.3 f23050F21117.6F157.815 f31117F37.88.4F167.9 6.8 f43050F4 5.6 6.6F17 6.1 6.7 f53050F58.615.4F18 6.98.1 f63050F613.724F197.57.9 f7 5.1 5.4F7 5.9 6.7F207.38.7 f83050F8 6.77.1F219.812.0 f93050F93050F2211.219.7 f103050F10 5.8 6.9F2310.012.4 f113050F11 5.67F2410.98.2 f123050F127.150F25 6.17.4 f133050F1311.420.4 以太网端口有 3种链路类型:access、trunk、hybrid Access类型端口只能属于1个VLAN用于连接计算机端口； Trunk类型端口可以允许多个VLAN通过可以接收和发送多个VLAN报文般用于交换机的间连接端口； Hybrid类型端口可以允许多个VLAN通过可以接收和发送多个VLAN报文可以用于交换机的间连接也可以用于连接用户计算机 Hybrid端口和Trunk端口在接收数据时处理思路方法是样唯区别的处在于发送数据 时:Hybrid端口可以允许多个VLAN报文发送时不打标签而Trunk端口只允许缺省VLAN报文发送时不打标签 缺省VLAN: Access端口只属于1个VLAN所以它缺省VLAN就是它所在VLAN不用设置；Hybrid端口和Trunk端口属于多个VLAN所以需要设置缺省VLAN ID.缺省情况下Hybrid端口和Trunk端口缺省VLAN为VLAN 1； 如果设置了端口缺省VLAN ID当端口接收到不带VLAN Tag报文后则将报文转发到属于缺省VLAN端口；当端口发送带有VLAN Tag报文时如果该报文VLAN ID和端口缺省VLAN ID相同则系统将去掉报文VLAN Tag然后再发送该报文 注:对于华为交换机缺省VLAN被称为“Pvid Vlan”对于思科交换机缺省VLAN被称为“Native Vlan” 交换机接口出入数据处理过程: Acess端口收报文:收到个报文判断是否有VLAN信息:如果没有则打上端口PVID并进行交换转发如果有则直接丢弃(缺省) Acess端口发报文: 将报文VLAN信息剥离直接发送出去 trunk端口收报文: 收到个报文判断是否有VLAN信息:如果没有则打上端口PVID并进行交换转发如果有判断该trunk端口是否允许该VLAN数据进入:如果可以则转发否则丢弃 trunk端口发报文: 比较端口PVID和将要发送报文VLAN信息如果两者相等则剥离VLAN信息再发送如果不相 南车四方机车车辆股份有限公司 青岛喜盈门集团公司 青岛广源发集团有限公司 青岛美高集团有限公司 济南山水集团有限公司青岛水泥分公司青岛正进集团有限公司 青岛大农服装有限公司 山东黄岛发电厂 青岛金晶股份有限公司 青岛恒源热电有限公司 青岛浮法玻璃有限公司 青岛压花玻璃有限公司 青岛市圣戈班韩洛玻玻璃有限公司 青岛高合有限公司 青岛浦项不锈钢有限公司 青岛北海船舶重工有限责任公司 青岛经济技术开发区热电燃气总公司 青岛赛轮子午线轮胎信息化生产示范基地 1 即墨市热电厂 青岛即发集团控股有限公司 青岛新源热电有限公司 青岛三湖制鞋有限公司 青岛正大有限公司 青岛高丽钢线有限公司 青岛北汇玻璃有限公司 即墨市双春水泥有限公司 青岛红领服饰股份有限公司 青岛恒光热电有限公司 青岛恒源化工有限公司 青岛天元化工股份有限公司 青岛海王纸业股份有限公司 青岛琅琊台酒业（集团）股份有限公司青岛胶南明月海藻工业有限责任公司 胶南易通热电有限责任公司 青岛泰发集团股份有限公司 青岛东亚轮胎有限公司 青岛康大外贸集团有限公司 胶南供电公司 胶南市水泥厂 2 胶南市海龙福利板纸有限公司 青岛振华工业集团有限公司 青岛德固萨化学有限公司 青岛龙发热电有限公司 青岛恒祥化肥有限公司 青岛世原鞋业有限公司 青岛华威建材有限公司 青岛广源发玻璃有限公司 青岛大明皮革有限公司 青岛昌新鞋业有限公司 青岛衣东纺织有限公司 青岛海尔金塑制品有限公司 山东金湖水泥有限公司青岛分公司 青岛福生食品有限公司 青岛信五皮革有限公司 青岛多福康食品有限公司 胶州天成玻璃工艺品厂 胶州市新纪元帘子布有限公司 青岛昌华集团股份有限公司 青岛热电集团金莱热电有限公司 青岛金浪热电有限公司 3 青岛泰光制鞋有限公司 青岛现代人热力发展有限公司 青岛金浪化工集团有限公司 青岛凤凰东翔印染有限公司 青岛九联集团股份有限公司 青岛海升果业有限责任公司 青岛交河技工塑料有限公司 青岛东方化工股份有限公司 海尔集团公司 青岛崂山玻璃有限公司 青岛啤酒第五有限公司 1 配置本地端口镜像 2 1.2.1 配置任务简介 本地端口镜像的配置需要在同一台设备上进行。 首先创建一个本地镜像组，然后为该镜像组配置源端口和目的端口。 表1-1 本地端口镜像配置任务简介 ●一个端口只能加入到一个镜像组。 ●源端口不能再被用作本镜像组或其它镜像组的出端口或目的端口。 3 1.2.2 创建本地镜像组 表1-2 创建本地镜像组 配置源端口目的端口后，本地镜像组才能生效。 4 1.2.3 配置源端口 可以在系统视图下为指定镜像组配置一个或多个源端口，也可以在端口视图下将当前端口配置为指定镜像组的源端口，二者的配置效果相同。 1. 在系统视图下配置源端口 表1-3 在系统视图下配置源端口 2. 在端口视图下配置源端口 表1-4 在端口视图下配置源端口 一个镜像组内可以配置多个源端口。 5 1.2.4 配置源CPU 表1-5 配置源CPU 一个镜像组内可以配置多个源CPU。 6 1.2.5 配置目的端口 可以在系统视图下为指定镜像组配置目的端口，也可以在端口视图下将当前端口配置为指定镜像组的目的端口，二者的配置效果相同。 1. 在系统视图下配置目的端口 表1-6 在系统视图下配置目的端口 2. 在端口视图下配置目的端口 表1-7 在端口视图下配置目的端口 ●一个镜像组内只能配置一个目的端口。 ●请不要在目的端口上使能STP、MSTP和RSTP，否则会影响镜像功能的正常使 用。 ●目的端口收到的报文包括复制自源端口的报文和来自其它端口的正常转发报文。 为了保证数据监测设备只对源端口的报文进行分析，请将目的端口只用于端口镜 像，不作其它用途。 ●镜像组的目的端口不能配置为已经接入RRPP环的端口。 7 1.3 配置二层远程端口镜像 8 1.3.1 配置任务简介 二层远程端口镜像的配置需要分别在源设备和目的设备上进行。 ●一个端口只能加入到一个镜像组。 ●源端口不能再被用作本镜像组或其它镜像组的出端口或目的端口。 ●如果用户在设备上启用了GVRP（GARP VLAN Registration Protocol，GARP VLAN注册协议）功能，GVRP可能将远程镜像VLAN注册到不希望的端口上， 此时在目的端口就会收到很多不必要的报文。有关GVRP的详细介绍，请参见“配 置指导/03-接入/GVRP配置”。 以太网端口聚合+RSTP配置 拓扑图 功能要求： 通过在网络中配置RSTP功能，实现消除网络环路的目的， 当RSTP的根桥DOWN掉后，可以通过非根桥正常通信，达到根桥和备用根桥的切换，某个链路DOWN后，可以通过将某个阻塞端口恢复为根端口或转发端口，以实现正常的数据通信， 当聚合链路中的某个链路DOWN掉后，不会影响正常的通信 配置过程： S5700-LSW1 [Huawei]DIS CU # sysname Huawei # vlan batch 10 20 # stp mode rstp # cluster enable ntdp enable ndp enable # drop illegal-mac alarm # diffserv domain default # drop-profile default # aaa authentication-scheme default authorization-scheme default accounting-scheme default domain default domain default_admin local-user admin password simple admin local-user admin service-type http # interface Vlanif1 # interface MEth0/0/1 # interface GigabitEthernet0/0/1 port link-type trunk port trunk allow-pass vlan 10 20 # interface GigabitEthernet0/0/2 port link-type trunk port trunk allow-pass vlan 10 20 # interface GigabitEthernet0/0/3 port link-type access port default vlan 10 stp disable # interface GigabitEthernet0/0/4 port link-type access port default vlan 20 stp disable # interface GigabitEthernet0/0/5 # interface GigabitEthernet0/0/6 # interface GigabitEthernet0/0/7 # interface GigabitEthernet0/0/8 # interface GigabitEthernet0/0/9 聚 氨 酯 丙 烯 酸 酯 的 合 成 及 应 用 姓名：樊荣 学号：2009296015 专业：化学 化学化工学院 聚氨酯丙烯酸酯的合成及应用 樊荣 2009296014 化学 （山西大学化学化工学院山西太原030006） 摘要：聚氨酯丙烯酸酯（PUA）体系综合了聚氨酯树脂和丙烯酸酯树脂各自的优点，使得该体系具有耐溶剂性，耐低温性，耐磨性，耐热冲击性，柔韧性和良好的粘结性，成为目前研究比较活跃的体系。本文就对近年来聚氨酯丙烯酸酯的一些合成方法、性能研究及在各个领域中的应用景做一个简单的综述。 关键字：聚氨酯丙烯酸酯合成性能应用前景 Synthesis of polyurethane acrylate and its application Fan rong 2009296014 chemical (Chemistry and Chemical Engineering of Shanxi University, Taiyuan, Shanxi 030006) Abstract: polyurethane acrylate (PUA) system integrated polyurethane resin and acrylic resin and their respective advantages, so that the system is solvent resistance, low temperature resistance, wear resistance, thermal shock resistance, flexibility and good adhesion, becomes the present study comparing active system. The article in recent years polyurethane acrylate some synthetic methods, properties and applications in various fields of king to do a simple review. Keywords: acrylate polyurethane ，synthesis ，properties ， potential applications 前言 聚氨酯丙烯酸酯（PUA）的分子中含有丙烯酸官能团和氨基甲酸酯键，固化后的胶黏剂具有聚氨酯的高耐磨性、粘附力、柔韧性、高剥离强度和优良的耐低温性能以及聚丙烯酸酯卓越的光学性能和耐候性，是一种综合性能优良的辐射固化材料。该体系涂料已经广泛应用于金属、木材、塑料涂层，油墨印刷，织物印花，光纤涂层等方面.目前，PUA已成为防水涂料领域应用非常重要的一大类低聚物，鉴于PUA固化速度较慢、价格相对较高，在常规涂料配方中较少以PUA为主体低聚物，往往作为辅助性功能树脂使用，大多数情况下，配方中使用PUA主要是为了增加涂层的柔韧性、降低应力收缩、改善附着力。但是由于PUA树脂优异的性能，对PUA的研究也日益增多，聚氨酯丙烯酸酯也逐步向跟其他类型的树脂共聚形成杂化体系，向水性体系发展，特别是水性体系因直接采用水稀释降低粘度，使制成的涂料更加环保和健康，减少了活性单体的使用，在很大程度上弥补了PUA树脂价格贵的不足，可以扩大PUA树脂的应用范围，同时减少甚至不使用单体，有效地降低了防水涂料的收缩，减少固化时的内应力，增加涂料的附着力和提高涂膜的柔韧。 目录 第1章以太网端口配置 ............................................................................................................ 1-1 1.1 以太网端口简介.................................................................................................................. 1-1 1.2以太网端口配置步骤.......................................................................................................... 1-1 1.2.1 配置以太网端口描述................................................................................................ 1-1 1.2.2 配置以太网接口状态变化上报抑制时间................................................................... 1-1 1.2.3 以太网端口专有参数配置......................................................................................... 1-2 1.3 以太网端口显示和调试....................................................................................................... 1-4 1.4 以太网端口配置示例 .......................................................................................................... 1-6 1.5 以太网端口排错.................................................................................................................. 1-7第2章以太网端口聚合配置..................................................................................................... 2-1 2.1 以太网端口聚合简介 .......................................................................................................... 2-1 2.2以太网端口聚合配置步骤 .................................................................................................. 2-1 2.3 以太网端口聚合显示和调试................................................................................................ 2-2 2.4 以太网端口聚合配置示例 ................................................................................................... 2-2 2.5 以太网端口聚合排错 .......................................................................................................... 2-3第3章以太网端口镜像配置..................................................................................................... 3-1 3.1 以太网端口镜像简介 .......................................................................................................... 3-1 3.2 以太网端口镜像配置步骤 ................................................................................................... 3-1 3.3 以太网端口镜像显示和调试................................................................................................ 3-2 3.4 以太网端口镜像配置示例 ................................................................................................... 3-2 3.5以太网端口镜像排错.......................................................................................................... 3-4 1功能需求及组网说明 交换机Hybrid端口隔离配置图1 『配置环境参数』 1. PC1、PC2和PC3分别连接到二层交换机SwitchA的端口E0/1 、E0/2和 E0/3，端口分属于VLAN10、20和30，服务器连接到端口G2/1，属于VLAN100。 2. PC1的IP地址为10.1.1.1/24，PC2的IP地址为10.1.1.2/24，PC3的IP地址为10.1.1.3/24，服务器的IP地址为10.1.1.254/24。 『组网需求』 1. PC1和PC2之间可以互访； 2. PC1和PC3之间可以互访； 3. PC1、PC2和PC3都可以访问服务器； 4. 其余的PC间访问均禁止。 交换机Hybrid端口隔离配置图2 『配置环境参数』 1. PC1、PC2和PC3分别连接到二层交换机SwitchA的端口E0/1 、E0/2和 E0/3，端口分属于VLAN10、20和30；PC4和PC5分别连接到二层交换机SwitchB 的端口E0/1和E0/2，端口分属于VLAN10和20； 2. SwitchA通过端口G2/1，连接到SwitchB的端口G1/1；SwitchA的端口G2/1和SwitchB的端口G1/1均不是Trunk端口； 3. PC1的IP地址为10.1.1.1/24，PC2的IP地址为10.1.1.2/24，PC3的IP地址为10.1.1.3/24，PC4的IP地址为10.1.1.4/24，PC5的IP地址为10.1.1.5/24。 『组网需求』 1. PC1和PC3之间可以互访； 2. PC2和PC3之间可以互访； 3. PC1和PC4之间可以互访； 4. PC2和PC5之间可以互访； 5. 其余PC之间均禁止互相访问。 2数据配置步骤 『交换机Hybrid端口配置流程』 华为交换机端口镜像配置举例 配置实例 文章出处：https://www.sodocs.net/doc/0f10426551.html, 端口镜像是将指定端口的报文复制到镜像目的端口，镜像目的端口会接入数据监测设备，用户利用这些设备分析目的端口接收到的报文，进行网络监控和故障排除。本文介绍一个在华为交换机上通过配置端口镜像实现对数据监测的应用案例，详细的组网结构及配置步骤请查看以下内容。 某公司内部通过交换机实现各部门之间的互连，网络环境描述如下： 1）研发部通过端口Ethernet 1/0/1接入Switch C；λ 2）市场部通过端口Ethernet 1/0/2接入Switch C；λ 3）数据监测设备连接在Switch C的Ethernet 1/0/3端口上。λ 网络管理员希望通过数据监测设备对研发部和市场部收发的报文进行监控。 使用本地端口镜像功能实现该需求，在Switch C上进行如下配置： 1）端口Ethernet 1/0/1和Ethernet 1/0/2为镜像源端口；λ 2）连接数据监测设备的端口Ethernet 1/0/3为镜像目的端口。λ 配置步骤 配置Switch C： # 创建本地镜像组。 配置以太网单板的内部端口 当网元通过以太网板内部端口（即VCTRUNK）将以太网业务传输到SDH侧时，需配置VCTRUNK端口的各种属性，以便配合对端网元的以太网单板，实现以太网业务在SDH网络中的传输。 前提条件 用户具有“网元操作员”及以上的网管用户权限。 已创建以太网单板。 注意事项 注意：错误的配置绑定通道，可能会导致业务中断。 操作步骤 1.在网元管理器中选择以太网单板，在功能树中选择“配置 > 以太网接口管理 > 以太 网接口”。 2.选择“内部端口”。 3.配置内部端口的TAG属性。 a.选择“TAG属性”选项卡。 b.配置内部端口的TAG属性。 c.单击“应用”。 4.配置内部端口的网络属性。 a.选择“网络属性”选项卡。 b.配置内部端口的网络属性。 图1支持QinQ功能的以太网单板的内部端口属性 图2支持MPLS功能的以太网单板的内部端口属性 c.单击“应用”。 5.配置内部端口使用的封装映射协议。 a.选择“封装/映射”选项卡。 b.配置内部端口使用的封装协议及各参数。 说明：传输线路两端的以太网单板的VCTURNK的“映射协议”和协议参数应保 持一致。 c.单击“应用”。 6.配置内部端口的LCAS功能。 a.选择“LCAS”选项卡。 b.设置“LCAS使能”以及LCAS其他参数。 说明：传输线路两端的以太网单板的VCTURNK的“LCAS使能”和LCAS协议参 数应保持一致。 c.单击“应用”。 7.设置端口的绑定通道。 a.选择“绑定通道”选项卡，单击“配置”，出现“绑定通道配置”对话框。 b.在“可配置端口”中选择VCTRUNK端口作为配置端口，在“可选绑定通道”中 选择承载层时隙。单击。 c.单击“确定”，单击“是”。出现“操作结果”对话框，提示操作成功。 华为交换机端口的hybrid属性配置 先说一下以太网中端口类型： 以太网端口有三种链路类型：Access、Hybrid和Trunk。 Access类型的端口只能属于1个VLAN,一般用于连接计算机的端口; Trunk类型的端口可以允许多个VLAN通过,可以接收和发送多个VLAN的报文,一般用于交换机之间连接的端口; Hybrid类型的端口可以允许多个VLAN通过,可以接收和发送多个VLAN的报文,可以用于交换机之间连接,也可以用于连接用户的计算机。 Hybrid端口和Trunk端口在接收数据时,处理方法是一样的,唯一不同之处在于发送数据时：Hybrid端口可以允许多个VLAN的报文发送时不打标签 ,而Trunk端口只允许缺省VLAN的报文发送时不打标签。 交换机上如果已经设置了某个端口为trunk端口，则不可以再把另外的端口设置为hybrid端口。 端口hybrid属性配置 『配置环境参数』 1.交换机SwitchA的端口E0/1.E0/2和E0/3和E0/4.E0/5分属于VLAN10、20和30，服务器Server1连接到端口E0/23，Server2连接到端口E0/24,分 别属vlan40，vlan50. 2.所有设备的ip地址均在同一网段。 『组网需求』 1.只有Vlan10.20及VLAN30中的4端口可访问Sever2； 2.Vlan10中的2端口pc可访问Vlan30； 3.三个Vlan的PC都可以访问服务器Server1； 4.Vlan20可访问Vlan30的5端口。 『交换机Hybrid端口配置流程』 利用Hybrid端口的特性――一个端口可以属于多个不同的VLAN，来完成分属不同VLAN内的同网段PC机的访问需求。 『配置过程』 【SwitchA相关配置】 1.首先创建业务需要的vlan 一以太网端口配置命令 1.1．1 display interface 【命令】 display interface[ interface_type | interface_type interface_num | interface_name ] 【视图】 所有视图 【参数】 interface_type：端口类型。 interface_num：端口号。 interface_name：端口名，表示方法为interface_name=interface_type interface_num。 参数的具体说明请参见interface命令中的参数说明。 【描述】 display interface命令用来显示端口的配置信息。 在显示端口信息时，如果不指定端口类型和端口号，则显示交换机上所 有的端口信息；如果仅指定端口类型，则显示该类型端口的所有端口信 息；如果同时指定端口类型和端口号，则显示指定的端口信息。 【举例】 # 显示以太网端口Ethernet0/1的配置信息。 端口镜像典型配置举例 1.5.1 本地端口镜像配置举例 1. 组网需求 某公司内部通过交换机实现各部门之间的互连，网络环境描述如下： ●研发部通过端口GigabitEthernet 1/0/1接入Switch C； ●市场部通过端口GigabitEthernet 1/0/2接入Switch C； ●数据监测设备连接在Switch C的GigabitEthernet 1/0/3端口上。 网络管理员希望通过数据监测设备对研发部和市场部收发的报文进行监控。 使用本地端口镜像功能实现该需求，在Switch C上进行如下配置： ●端口GigabitEthernet 1/0/1和GigabitEthernet 1/0/2为镜像源端口； ●连接数据监测设备的端口GigabitEthernet 1/0/3为镜像目的端口。 2. 组网图 图1-3 配置本地端口镜像组网图 3. 配置步骤 配置Switch C： # 创建本地镜像组。 注意：以下内容请进一步总结！ 青岛恒源热电有限公司 目标公司主要从事蒸汽、热水的生产及供应、蒸汽余热发电业务，同时提供供热管道及设施维修、安装业务。据介绍，目标公司开发了循环水供热工程项目，该项目是青岛市获批的第一个清洁发展机制(CDM)项目；前处该项目处于施工建设阶段，预计将于2009年上半年内正式投产。据介绍，目标公司主要负责临港工业区辖区内的蒸汽供应及热网管理，发电业务，对居民的用热服务。 公司成立于2001年，主要从事蒸汽、热水的生产及供应、蒸汽余热发电业务。 青岛恒源热电有限公司位于开发区B区供热范围，拥有12MW的抽凝式汽轮发电机组1台及12MW的背压机组1台，75t/h循环流化床锅炉3台和150t/h锅炉1台，最大供热能力是355t/h，担负着B区的生产、民用供热负荷，主要满足热电厂东部居民小区供热和山东科技大学供热。 青岛恒源热电有限公司位于青岛经济技术开发区临港工业区的中北部，海尔大道与渭河路交界处东北角，渭河路777号。厂区所在地东侧隔宽约100m绿化地为鑫龙物流公司，该公司东侧、距离本项目最近300m处为澳柯玛人才公寓；厂区南侧隔渭河路、绿化带100m处为东小庄村（原村庄平房已搬迁，现建有多座两层复式楼房），该村庄南侧、距离本项目约420m处为山孚日水食品有限公司；项目隔渭河路东南方向约200m处为澳柯玛工业园；西及西南方向隔海尔大道、渭河路均为浦项制铁有限公司；北侧与开发区消防大队以及正友砼业相邻。 企业所在地厂址东南距市中心约8km，东面距前湾港区约4.5km。 现有工程内容：青岛恒源热电有限公司主要服务于黄岛供热分区B 区（齐长城路以北、疏港高速以南、镰湾河以西、柳花泊和珠山以东片区（包括柳花泊），总占地面积约60平方公里）。企业现有锅炉规模为3×75t/h+1×130t/h 循环流化床蒸汽锅炉，总计约355t/h锅炉容量；发电机组规模为1×12MW C12-34.9/0.98（抽凝）+1×12MW B12-4.9/0.98（背压），总计发电装机容量24 MW。 近几年，恒源热电强化能源管理，合理调整运行方式，加强节能技术改造，企业能源管理工作上了一个新台阶，先后通过了“企业能源审计”、“热电联产机组认定”等审核认证工作，被评为“青岛市清洁生产企业”，2007年度“山东省节能先进企业”。 为进一步加强企业能源管理，完善优化企业节能减排工作，公司在本年度开始推行循环经济试点工作。目前，作为试点工作重点项目之一的企业冷渣机改造项目已基本完成，初步具备投运条件，预计本年度六月份正式投入运行。该项目是将循环流化床锅炉的人工排渣（温度一般在900℃），通过加装冷渣机把炉渣余热加热除盐水，将锅炉效率提高1-3%，同时解决人工放渣存在安全隐患、能源浪费以及不环保等问题，项目投资为85万元，年可节标煤700吨。 1 配置基于Access端口的VLAN 配置基于Access端口的VLAN有两种方法：一种是在VLAN视图下进行配置，另一种是在接口视图/端口组视图/二层聚合接口视图或二层虚拟以太网接口视图下进行配置。 表1-4 配置基于Access端口的VLAN（在VLAN视图下） 表1-5 配置基于Access端口的VLAN（在接口视图/端口组视图下/二层聚合接口视图/二层虚拟以太网接口视图） ●在将Access端口加入到指定VLAN之前，要加入的VLAN必须已经存在。 ●在VLAN视图下向VLAN中添加端口时，只能添加二层以太网端口。● 2 1.4. 3 配置基于Trunk端口的VLAN Trunk端口可以允许多个VLAN通过，只能在接口视图/端口组视图/二层聚合接口视图或二层虚拟以太网接口视图下进行配置。 表1-6 配置基于Trunk端口的VLAN ●Trunk端口和Hybrid端口之间不能直接切换，只能先设为Access端口，再设 置为其它类型端口。例如：Trunk端口不能直接被设置为Hybrid端口，只能先 设为Access端口，再设置为Hybrid端口。 ●配置缺省VLAN后，必须使用port trunk permit vlan命令配置允许缺省VLAN 的报文通过，出接口才能转发缺省VLAN的报文。 3 1.4. 4 配置基于Hybrid端口的VLAN Hybrid端口可以允许多个VLAN通过，只能在接口视图/端口组视图/二层聚合接口视图或二层虚拟以太网接口视图下进行配置。 表1-7 配置基于Hybrid端口的VLAN ●Trunk端口和Hybrid端口之间不能直接切换，只能先设为Access端口，再设 置为其它类型端口。例如：Trunk端口不能直接被设置为Hybrid端口，只能先 设为Access端口，再设置为Hybrid端口。 ●在设置允许指定的VLAN通过Hybrid端口之前，允许通过的VLAN必须已经存 在。 ●配置缺省VLAN后，必须使用port hybrid vlan命令配置允许缺省VLAN的报 文通过，出接口才能转发缺省VLAN的报文。 4 1.4. 5 基于端口的VLAN典型配置举例 1. 组网需求 ●Host A和Host C属于部门A，但是通过不同的设备接入公司网络；Host B和 Host D属于部门B，也通过不同的设备接入公司网络。 ●为了通信的安全性，也为了避免广播报文泛滥，公司网络中使用VLAN技术来 隔离部门间的二层流量。其中部门A使用VLAN 100，部门B使用VLAN 200。 ●现要求不管是否使用相同的设备接入公司网络，同一VLAN内的主机能够互 通。即Host A和Host C能够互通，Host B和Host D能够互通。 2. 组网图 图1-6 基于端口的VLAN组网图 3. 配置步骤 (1)配置Device A # 创建VLAN 100，并将Ethernet1/1加入VLAN 100。 端口Access、Hybrid和Trunk三种模式的理解 2010-06-15 23:27:00| 分类：网络工程师学习日| 标签：|字号大中小订阅 Access、Hybrid和Trunk三种模式的理解 以太网端口的三种链路类型：Access、Hybrid和Trunk： Access 类型的端口只能属于1个VLAN，一般用于连接计算机的端口,也可以连接交换机和交换机。 Trunk 类型的端口可以允许多个VLAN通过，可以接收和发送多个VLAN的报文，trunk口一般用于连接两台交换机，这样可以只用一条trunk连接实现多个vlan的扩展（因为trunk允许多个vlan的数据通过，如果用access口，那么一个vlan就要一条连接，多个vlan 要多个连接，而交换机的接口是有限的）。对于trunk口发送出去的报文，只有默认vlan的报文不带vlan ID，其它vlan的报文都要带vlan ID（要不然，对端的交换机不知道该报文属于哪个vlan，无法处理，也就不能实现vlan跨交换机扩展了）。简而言之，trunk端口的设计目的就是通过一条连接实现多个vlan的跨交换机扩展。Hybrid 类型的端口可以允许多个VLAN通过，可以接收和发送多个VLAN的报文，可以用于交换机之间连接，也可以用于连接用户的计算机。trunk端口是hybrid端口的特例，就是说hybrid端口可以实现 比trunk端口更多的功能。hybrid端口可以加入多个vlan，并可以设置该vlan的报文通过该端口发送是是否带vlan ID（trunk端口不能设置，只有默认vlan的报文不带vlan ID进行发送）。通过下面的两个例子（转载的），大家应该可以看出hybrid端口的设计目的。 例一：『配置环境参数』 1. PC1、PC2和PC3分别连接到二层交换机SwitchA的端口E0/1 、E0/2和E0/3，端口分属于VLAN10、20和30，服务器连接到端口G2/1，属于VLAN100。 2. PC1的IP地址为10.1.1.1/24，PC2的IP地址为10.1.1.2/24，PC3的IP地址为10.1.1.3/24，服务器的IP地址为10.1.1.254/24。『组网需求』 1. PC1和PC2之间可以互访； 2. PC1和PC3之间可以互访； 3. PC1、PC2和PC3都可以访问服务器； 4. 其余的PC间访问均禁止。 【SwitchA相关配置】 1. 创建（进入）VLAN10，将E0/1加入到VLAN10 [SwitchA]vlan 10 [SwitchA-vlan10]port Ethernet 0/1 2. 创建（进入）VLAN20，将E0/2加入到VLAN20 的需要，也迫切需要 例如，模块1中端口1和端口2同属VLAN1，端口3在VLAN2，端口4和5在VLAN2，端口2监听端口1和3、4、5， set span 1/1，1/3-5 1/2 2950/3550/3750 格式如下： #monitor session number source interface mod_number/port_number both #monitor session number destination interface mod_mnumber/port_number //rx-->指明是进端口得流量，tx-->出端口得流量 both 进出得流量 for example: 第一条镜像，将第一模块中的源端口为1-10的镜像到端口12上面； #monitor session 1 source interface 1/1-10 both #monitor session 1 destination interface 1/12 第二条镜像，将第二模块中的源端口为13-20的镜像到端口24上面； #monitor session 2 source interface 2/13-20 both #monitor session 2 destination interface 2/24 当有多条镜像、多个模块时改变其中的参数即可。 Catalyst 2950 3550不支持port monitor C2950#configure terminal C2950(config)# C2950(config)#monitor session 1 source interface fastEthernet 0/2 !--- Interface fa 0/2 is configured as source port. C2950(config)#monitor session 1 destination interface fastEthernet 0/3 !--- Interface fa0/3 is configured as destination port. 4配置命令 1. 指定分析口 feature rovingAnalysis add，或缩写 f r a， 例如： Select menu option: feature rovingAn alysis add Select analysis slot: 1?& nbsp; Select analysis port: 2 2. 指定监听口并启动端口监听 feature rovingAnalysis start，或缩写 f r sta， 例如： Select menu option: feature rovingAn alysis start Select slot to monitor ?(1-12): 1 Select port to monitor&nb sp;?(1-8): 3浅析hybrid端口的收发报文模式
青岛市重点用能企业名单
h3c端口镜像配置及实例
以太网端口聚合+RSTP配置案例
聚氨酯丙烯酸酯的合成及应用
以太网端口
hybrid端口配置
华为交换机端口镜像配置举例
配置以太网单板的内部端口
华为交换机端口的hybrid属性配置
以太网端口配置命令
端口镜像典型配置举例
青岛恒源热电
配置基于端口的vlan及实例
端口Access、Hybrid和Trunk三种模式的区别及配置实例
端口镜像配置