FERMION GREEN FUNCTIONS IN NON-ABELIAN GAUGE THEORIES IN FOUR DIMENSIONS

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油气田燃料天然气组分特征对实测碳排放因子的影响

油气田燃料天然气组分特征对实测碳排放因子的影响廉军豹付玥张鑫袁良庆刘宏彬李世熙谭小红（大庆油田设计院有限公司）摘要：通过实测碳排放因子计算公式理论分析及油气田典型燃料天然气实例分析，探索燃料天然气组分特征对实测碳排放因子的影响。

结果表明：各生产系统使用的油气田燃料天然气含碳原子数量较多的组分含量越多，实测含碳量碳排放因子及实测低位发热量碳排放因子越大，含碳原子数量较少的组分或H 2、O 2、N 2、He 不含碳的组分含量越多，实测含碳量碳排放因子及实测低位发热量碳排放因子越小；除实测方法系统性差异外，一定含量的CO 2，是导致油气田燃料天然气实测低位发热量碳排放因子与实测含碳量碳排放因子之间存在显著差异的重要原因；各类燃料天然气碳排放因子存在普遍性差异，干气的实测碳排放因子明显比湿气的小。

上述结论将为油气田燃料天然气碳排放核算提供技术支持。

关键词：油气田；燃料天然气；碳排放因子；组分特征；实测DOI :10.3969/j.issn.2095-1493.2023.11.016The influences of fuel natural gas composition characteristics on measured carbon emission factors in oil and gas fieldLIAN Junbao，FU Yue，ZHANG Xin，YUAN Liangqing，LIU Hongbin，LI Shixi，TAN Xiaohong Daqing Oilfield Design Institute Co ．，Ltd ．Abstract：The influences of fuel natural gas composition characteristics on measured carbon emission factors are explored through the theory analysis of measured carbon emission factors formula and the cas-es analysis of typical fuel natural gas in oil and gas field．The results show that the higher the content of components with more carbon atoms in the natural gas used as fuel of each production system in oil and gas fields，the greater the carbon emission factor from measured carbon content and that from measured low calorific value．The higher the content of components with less carbon atoms or components with-out carbon such as H 2，O 2，N 2，He in natural gas used as fuel in oil and gas fields，the smaller the car-bon emission factor from measured carbon content and that from measured low calorific value．What's more，in addition to systematic differences between measurement methods，a certain amount of CO 2is an important reason for the significant difference between the carbon emission factor from measured carbon content and that from measured low calorific value of natural gas used in oil and gas fields．In addition，there are universal differences in various carbon emission factors of fuel natural gases in oil and gas fields，and the measured carbon emission factors of dry gas are significantly smaller than those of wet gas．Most importantly，the above conclusions will be provided technical support for the carbon emis-sion accounting for fuel natural gas in oil and gas fields ．Keywords：oil and gas field；fuel natural gas；carbon emission factor；composition characteristics；measurement第一作者简介：廉军豹，高级工程师，硕士研究生，2010年毕业于中国地质大学（武汉）（应用化学专业），从事油气田碳资产研发技术研（碳控楼），163712。

PACSnumbers1215Ff,1130Hv,1210Dm,1125Mj…

a r X i v :0803.2889v 2 [h e p -p h ] 14 J u l 2008Mapping Out SU (5)GUTs with Non-Abelian Discrete Flavor SymmetriesFlorian Plentinger ∗and Gerhart Seidl †Institut f¨u r Physik und Astrophysik,Universit¨a t W¨u rzburg,Am Hubland,D 97074W¨u rzburg,Germany(Dated:December 25,2013)We construct a class of supersymmetric SU (5)GUT models that produce nearly tribimaximal lepton mixing,the observed quark mixing matrix,and the quark and lepton masses,from discrete non-Abelian ﬂavor symmetries.The SU (5)GUTs are formulated on ﬁve-dimensional throats in the ﬂat limit and the neutrino masses become small due to the type-I seesaw mechanism.The discrete non-Abelian ﬂavor symmetries are given by semi-direct products of cyclic groups that are broken at the infrared branes at the tip of the throats.As a result,we obtain SU (5)GUTs that provide a combined description of non-Abelian ﬂavor symmetries and quark-lepton complementarity.PACS numbers:12.15.Ff,11.30.Hv,12.10.Dm,One possibility to explore the physics of grand uniﬁed theories (GUTs)[1,2]at low energies is to analyze the neutrino sector.This is due to the explanation of small neutrino masses via the seesaw mechanism [3,4],which is naturally incorporated in GUTs.In fact,from the perspective of quark-lepton uniﬁcation,it is interesting to study in GUTs the drastic diﬀerences between the masses and mixings of quarks and leptons as revealed by current neutrino oscillation data.In recent years,there have been many attempts to re-produce a tribimaximal mixing form [5]for the leptonic Pontecorvo-Maki-Nakagawa-Sakata (PMNS)[6]mixing matrix U PMNS using non-Abelian discrete ﬂavor symme-tries such as the tetrahedral [7]and double (or binary)tetrahedral [8]groupA 4≃Z 3⋉(Z 2×Z 2)and T ′≃Z 2⋉Q,(1)where Q is the quaternion group of order eight,or [9]∆(27)≃Z 3⋉(Z 3×Z 3),(2)which is a subgroup of SU (3)(for reviews see, e.g.,Ref.[10]).Existing models,however,have generally dif-ﬁculties to predict also the observed fermion mass hierar-chies as well as the Cabibbo-Kobayashi-Maskawa (CKM)quark mixing matrix V CKM [11],which applies especially to GUTs (for very recent examples,see Ref.[12]).An-other approach,on the other hand,is oﬀered by the idea of quark-lepton complementarity (QLC),where the so-lar neutrino angle is a combination of maximal mixing and the Cabibbo angle θC [13].Subsequently,this has,in an interpretation of QLC [14,15],led to a machine-aided survey of several thousand lepton ﬂavor models for nearly tribimaximal lepton mixing [16].Here,we investigate the embedding of the models found in Ref.[16]into ﬁve-dimensional (5D)supersym-metric (SUSY)SU (5)GUTs.The hierarchical pattern of quark and lepton masses,V CKM ,and nearly tribi-maximal lepton mixing,arise from the local breaking of non-Abelian discrete ﬂavor symmetries in the extra-dimensional geometry.This has the advantage that theFIG.1:SUSY SU (5)GUT on two 5D intervals or throats.The zero modes of the matter ﬁelds 10i ,5H,24H ,and the gauge supermul-tiplet,propagate freely in the two throats.scalar sector of these models is extremely simple without the need for a vacuum alignment mechanism,while of-fering an intuitive geometrical interpretation of the non-Abelian ﬂavor symmetries.As a consequence,we obtain,for the ﬁrst time,a realization of non-Abelian ﬂavor sym-metries and QLC in SU (5)GUTs.We will describe our models by considering a speciﬁc minimal realization as an example.The main features of this example model,however,should be viewed as generic and representative for a large class of possible realiza-tions.Our model is given by a SUSY SU (5)GUT in 5D ﬂat space,which is deﬁned on two 5D intervals that have been glued together at a common endpoint.The geom-etry and the location of the 5D hypermultiplets in the model is depicted in FIG.1.The two intervals consti-tute a simple example for a two-throat setup in the ﬂat limit (see,e.g.,Refs.[17,18]),where the two 5D inter-vals,or throats,have the lengths πR 1and πR 2,and the coordinates y 1∈[0,πR 1]and y 2∈[0,πR 2].The point at y 1=y 2=0is called ultraviolet (UV)brane,whereas the two endpoints at y 1=πR 1and y 2=πR 2will be referred to as infrared (IR)branes.The throats are supposed to be GUT-scale sized,i.e.1/R 1,2 M GUT ≃1016GeV,and the SU (5)gauge supermultiplet and the Higgs hy-permultiplets 5H and2neously broken to G SM by a 24H bulk Higgs hypermulti-plet propagating in the two throats that acquires a vac-uum expectation value pointing in the hypercharge direc-tion 24H ∝diag(−12,13,15i ,where i =1,2,3is the generation index.Toobtainsmall neutrino masses via the type-I seesaw mechanism [3],we introduce three right-handed SU (5)singlet neutrino superﬁelds 1i .The 5D Lagrangian for the Yukawa couplings of the zero mode fermions then readsL 5D =d 2θ δ(y 1−πR 1) ˜Y uij,R 110i 10j 5H +˜Y d ij,R 110i 5H +˜Y νij,R 15j5i 1j 5H +M R ˜Y R ij,R 21i 1j+h.c. ,(3)where ˜Y x ij,R 1and ˜Y x ij,R 2(x =u,d,ν,R )are Yukawa cou-pling matrices (with mass dimension −1/2)and M R ≃1014GeV is the B −L breaking scale.In the four-dimensional (4D)low energy eﬀective theory,L 5D gives rise to the 4D Yukawa couplingsL 4D =d 2θ Y u ij 10i 10j 5H +Y dij10i 5H +Y νij5i ∼(q i 1,q i 2,...,q i m ),(5)1i ∼(r i 1,r i 2,...,r im ),where the j th entry in each row vector denotes the Z n jcharge of the representation.In the 5D theory,we sup-pose that the group G A is spontaneously broken by singly charged ﬂavon ﬁelds located at the IR branes.The Yukawa coupling matrices of quarks and leptons are then generated by the Froggatt-Nielsen mechanism [21].Applying a straightforward generalization of the ﬂavor group space scan in Ref.[16]to the SU (5)×G A represen-tations in Eq.(5),we ﬁnd a large number of about 4×102ﬂavor models that produce the hierarchies of quark and lepton masses and yield the CKM and PMNS mixing angles in perfect agreement with current data.A distri-bution of these models as a function of the group G A for increasing group order is shown in FIG.2.The selection criteria for the ﬂavor models are as follows:First,all models have to be consistent with the quark and charged3 lepton mass ratiosm u:m c:m t=ǫ6:ǫ4:1,m d:m s:m b=ǫ4:ǫ2:1,(6)m e:mµ:mτ=ǫ4:ǫ2:1,and a normal hierarchical neutrino mass spectrumm1:m2:m3=ǫ2:ǫ:1,(7)whereǫ≃θC≃0.2is of the order of the Cabibbo angle.Second,each model has to reproduce the CKM anglesV us∼ǫ,V cb∼ǫ2,V ub∼ǫ3,(8)as well as nearly tribimaximal lepton mixing at3σCLwith an extremely small reactor angle 1◦.In perform-ing the group space scan,we have restricted ourselves togroups G A with orders roughly up to 102and FIG.2shows only groups admitting more than three valid mod-els.In FIG.2,we can observe the general trend thatwith increasing group order the number of valid modelsper group generally increases too.This rough observa-tion,however,is modiﬁed by a large“periodic”ﬂuctu-ation of the number of models,which possibly singlesout certain groups G A as particularly interesting.Thehighly populated groups would deserve further system-atic investigation,which is,however,beyond the scopeof this paper.From this large set of models,let us choose the groupG A=Z3×Z8×Z9and,in the notation of Eq.(5),thecharge assignment101∼(1,1,6),102∼(0,3,1),103∼(0,0,0),52∼(0,7,0),52↔4FIG.3:Eﬀect of the non-Abelian ﬂavor symmetry on θ23for a 10%variation of all Yukawa couplings.Shown is θ23as a function of ǫfor the ﬂavor group G A (left)and G A ⋉G B (right).The right plot illustrates the exact prediction of the zeroth order term π/4in the expansion θ23=π/4+ǫ/√2and the relation θ13≃ǫ2.The important point is that in the expression for θ23,the leading order term π/4is exactly predicted by thenon-Abelian ﬂavor symmetry G F =G A ⋉G B (see FIG.3),while θ13≃θ2C is extremely small due to a suppression by the square of the Cabibbo angle.We thus predict a devi-ation ∼ǫ/√2,which is the well-known QLC relation for the solar angle.There have been attempts in the literature to reproduce QLC in quark-lepton uniﬁed models [26],however,the model presented here is the ﬁrst realization of QLC in an SU (5)GUT.Although our analysis has been carried out for the CP conserving case,a simple numerical study shows that CP violating phases (cf.Ref.[27])relevant for neutri-noless double beta decay and leptogenesis can be easily included as well.Concerning proton decay,note that since SU (5)is bro-ken by a bulk Higgs ﬁeld,the broken gauge boson masses are ≃M GUT .Therefore,all fermion zero modes can be localized at the IR branes of the throats without intro-ducing rapid proton decay through d =6operators.To achieve doublet-triplet splitting and suppress d =5pro-ton decay,we may then,e.g.,resort to suitable extensions of the Higgs sector [28].Moreover,although the ﬂavor symmetry G F is global,quantum gravity eﬀects might require G F to be gauged [29].Anomalies can then be canceled by Chern-Simons terms in the 5D bulk.We emphasize that the above discussion is focussed on a speciﬁc minimal example realization of the model.Many SU (5)GUTs with non-Abelian ﬂavor symmetries,however,can be constructed along the same lines by varying the ﬂavor charge assignment,choosing diﬀerent groups G F ,or by modifying the throat geometry.A de-tailed analysis of these models and variations thereof will be presented in a future publication [30].To summarize,we have discussed the construction of 5D SUSY SU (5)GUTs that yield nearly tribimaximal lepton mixing,as well as the observed CKM mixing matrix,together with the hierarchy of quark and lepton masses.Small neutrino masses are generated only by the type-I seesaw mechanism.The fermion masses and mixings arise from the local breaking of non-Abelian ﬂavor symmetries at the IR branes of a ﬂat multi-throat geometry.For an example realization,we have shown that the non-Abelian ﬂavor symmetries can exactly predict the leading order term π/4in the sum rule for the atmospheric mixing angle,while strongly suppress-ing the reactor angle.This makes this class of models 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用密度函数理论和杜比宁方程研究活性炭纤维多段充填机理

密度函数理论和杜比宁方程可以用来研究活性炭纤维在多段充填过程中的吸附行为。

密度函数理论是一种分子统计力学理论，它建立在分子统计学和热力学的基础上，用来研究一种系统中分子的分布。

杜比宁方程是一种描述分子吸附行为的方程，它可以用来计算吸附层的厚度、吸附速率和吸附能量等参数。

在研究活性炭纤维多段充填过程中，可以使用密度函数理论和杜比宁方程来研究纤维表面的分子结构和吸附行为。

通过分析密度函数和杜比宁方程的解，可以得出纤维表面的分子结构以及纤维吸附的分子的种类、数量和能量。

这些信息有助于更好地理解活性炭纤维的多段充填机理。

在研究活性炭纤维的多段充填机理时，还可以使用其他理论和方法来帮助我们更好地了解这一过程。

例如，可以使用扫描电子显微镜(SEM)和透射电子显微镜(TEM)等技术来观察纤维表面的形貌和结构。

可以使用X射线衍射(XRD)和傅里叶变换红外光谱(FTIR)等技术来确定纤维表面的化学成分和结构。

还可以使用氮气吸附(BET)和旋转氧吸附(BJH)等技术来测量纤维表面的比表面积和孔结构。

通过综合运用密度函数理论、杜比宁方程和其他理论和方法，可以更全面地了解活性炭纤维的多段充填机理，从而更好地控制和优化多段充填的过程。

在研究活性炭纤维多段充填机理时，还可以使用温度敏感性测试方法来研究充填过程中纤维表面的动力学性质。

例如，可以使用动态氧吸附(DAC)或旋转杆氧吸附(ROTA)等技术来测量温度对纤维表面吸附性能的影响。

通过对比不同温度下纤维表面的吸附性能，可以更好地了解充填过程中纤维表面的动力学性质。

此外，还可以使用分子动力学模拟方法来研究纤维表面的吸附行为。

例如，可以使用拉曼光谱或红外光谱等技术来测量纤维表面的分子吸附构型。

然后，使用分子动力学模拟方法来模拟不同分子吸附构型下的纤维表面的动力学性质，帮助我们更好地了解活性炭纤维的多段充填机理。

综述Representation learning a review and new perspectives

explanatory factors for the observed input. A good representation is also one that is useful as input to a supervised predictor. Among the various ways of learning representations, this paper focuses on deep learning methods: those that are formed by the composition of multiple non-linear transformations, with the goal of yielding more abstract – and ultimately more useful – representations. Here we survey this rapidly developing area with special emphasis on recent progress. We consider some of the fundamental questions that have been driving research in this area. Speciﬁcally, what makes one representation better than another? Given an example, how should we compute its representation, i.e. perform feature extraction? Also, what are appropriate objectives for learning good representations?

第七章 Green 函数法 - 数学物理方法

数学物理方法Mathematical Method in Physics西北师范大学物理与电子工程学院豆福全第七章Green函数法Green Function method引言前面几章我们系统的讨论了求解数学物理方法的几种典型方法：分离变量法，行波法以及积分变换法。

分离变量法主要适用于求解各种有界区域内的定解问题，行波法则主要适用于求解无界区域内的波动问题，而积分变换法也主要适用于求解无界区域内的定解问题，然而不受方程类型的限制。

同时，分离变量法，积分变换法这两种方法所给出的解,一般具有无穷级数与无穷积分的形式。

本章介绍求解数学物理方程的另一重要方法——Green函数法。

所不同的是，该法给出的是一种有限积分的解，便于人们进行理论分析与研究。

Green函数的特点是它仅与定解问题所定义的区域的形状及边界条件类型有关，而与定解条件及方程非齐次项所给出的具体形式无关。

特别是一些用分离变量法较难处理的非齐次方程的定解问题，Green函数法更能显示出其优越性。

从物理上看，一个数学物理方程在大多数情况下，往往表示一种特定的“场”和产生这种场的“源”之间的关系。

如热导方程表示的是温度场与点源之间的关系，泊松方程表示的是静电场和电荷分布之间的关系等。

这样，当源被分解成许多点源的叠加时，如果通过某一种方法知道各点源产生的场，然后再利用叠加原理，就可以求出同样边界条件下任意源的场，这种求解数理方程的方法被称为Green函数法，而点源产生的场就是Green函数。

本章首先复习Laplace方程边值问题的几种类型，然后由Green公式建立起Green函数的概念，并通过Green函数得到一般的泊松方程边值问题解的积分表达式，最后在几个特殊区域上讨论Green函数及Laplace方程的第一边值问题具体的求解过程。

7.1 Laplace 方程边值问题7.1.1 内问题Laplace 方程： 2222220u u ux y z∂∂∂++=∂∂∂0u ∆=描述物理中的平衡、稳定等现象，从而变化过程与时间无关，这时不提初始条件，边界条件常用到以下三种：1. 第一边值问题 Dirichlet 问题设曲面P 为空间某一区域Ω的边界，f 是定义在曲面P 上已知连续函数，求一函数(,,)u u x y z =满足Laplace 方程，满足光滑性条件：在区域Ω内有二阶连续偏导数，在Ω=Ω+Γ上连续，且有uf Γ=具有二阶连续偏导数且满足Laplace 方程的函数称为调和函数。

第七章 Green 函数法 - 数学物理方法

同时，分离变量法，积分变换法这两种方法所给出的解,一般具有无穷级数与无穷积分的形式。

本章介绍求解数学物理方程的另一重要方法——Green函数法。

所不同的是，该法给出的是一种有限积分的解，便于人们进行理论分析与研究。

Green函数的特点是它仅与定解问题所定义的区域的形状及边界条件类型有关，而与定解条件及方程非齐次项所给出的具体形式无关。

特别是一些用分离变量法较难处理的非齐次方程的定解问题，Green函数法更能显示出其优越性。

从物理上看，一个数学物理方程在大多数情况下，往往表示一种特定的“场”和产生这种场的“源”之间的关系。

如热导方程表示的是温度场与点源之间的关系，泊松方程表示的是静电场和电荷分布之间的关系等。

解释非阿伦尼乌斯和低温晶界迁移观测的经典方程

解释非阿伦尼乌斯和低温晶界迁移观测的经典方程解释非阿伦尼乌斯和低温晶界迁移观测的经典方程一、引言非阿伦尼乌斯（Non-Arrhenius）和低温晶界迁移（Low temperature grain boundary migration）是固体材料科学领域中的两个重要概念和现象。

通过研究和观测这两个现象，我们可以深入了解材料的晶体结构、晶界特性以及在低温下材料的迁移动态。

本文将解释这两个概念，并基于已有的研究成果提供一个经典方程来描述非阿伦尼乌斯和低温晶界迁移的观测结果。

二、非阿伦尼乌斯的解释非阿伦尼乌斯，即不遵守阿伦尼乌斯（Arrhenius）方程的材料性质。

阿伦尼乌斯方程是用来描述温度对材料性质影响的经典方程，通常用于预测材料的热稳定性和反应动力学。

然而，在某些情况下，阿伦尼乌斯方程无法准确预测材料的性质变化。

非阿伦尼乌斯现象的观测结果往往表明材料的性质在低温下随着温度的变化而发生非线性的改变。

这种非线性关系可能是由于材料的微观结构和相互作用的复杂性引起的。

尽管非阿伦尼乌斯现象的解释依然存在争议，但许多研究者认为其中一个可能的因素是材料中存在的多种缺陷和杂质，它们在低温下的影响随着温度的降低而增大。

这些缺陷和杂质可能对材料的能量状态和粒子运动产生显著影响，从而导致非阿伦尼乌斯效应的观察。

三、低温晶界迁移的观测低温晶界迁移是指晶界在低温下的运动和改变。

晶界是固体材料中不同晶格结构之间的交界面，对材料的力学性能和导电性能等具有重要影响。

晶界迁移的研究关注晶界在低温下的可塑性、强度和稳定性等方面的变化。

实验观测发现，一些晶界在低温下表现出了非常明显的迁移现象。

与阿伦尼乌斯方程描述的晶界迁移不同，低温晶界迁移观测结果显示出低温下晶界迁移速率随温度的降低而减慢的现象。

这种低温效应可以通过一些经典方程来描述和解释。

其中一个经典方程是基于材料中各种缺陷和杂质的扩散理论，假设晶界迁移受到这些缺陷和杂质的限制。

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非一致椭圆型方程的广义green函数

非一致椭圆型方程的广义green函数广义Green函数是解偏微分方程的一种方法，它可以通过椭圆型方程的积分表示来表示非一致椭圆型方程的解。

本文将详细介绍广义Green函数的定义、性质和表示方法。

首先，我们来定义非一致椭圆型方程。

非一致椭圆型方程是指不满足Laplace方程的椭圆型方程。

它可以表示为：\[Lu=f(x)\]其中，\(L\)是一个椭圆型的偏微分算子，\(u\)是未知函数，\(f(x)\)是给定函数。

通常，非一致椭圆型方程的最常见形式是Poisson 方程：\[\Delta u = f(x)\]其中\(\Delta\)表示Laplace算子。

广义Green函数可以用于求解非一致椭圆型方程的边界值问题。

边界值问题是指在给定边界条件下求解方程的特解。

对于非一致椭圆型方程，广义Green函数的定义如下：\[L_x G(x,y) = \delta(x-y) - \frac{1}{，\Omega，}\]其中，\(L_x\)是关于\(x\)的椭圆型偏微分算子，\(G(x,y)\)是Green函数，\(\delta(x-y)\)是Dirac Delta函数，\(，\Omega，\)是定义域\(\Omega\)的体积。

广义Green函数的性质如下：1. 广义Green函数是关于\(x\)的椭圆型方程的唯一解。

2. 广义Green函数在定义域\(\Omega\)内满足边界条件。

3. 广义Green函数在边界\(\partial \Omega\)上满足约束方程。

接下来，我们介绍用积分方法来表示广义Green函数的方法。

\[u(y) = \int_\Omega G(x,y)f(x)dx\]其中，\(G(x,y)\)是广义Green函数。

这个积分表示了\(u(y)\)是在整个定义域\(\Omega\)上对\(f(x)\)与Green函数的积分。

根据广义Green函数的定义，可以将其表示为：\[G(x,y) = G_0(x,y) - \frac{1}{，\Omega，}\int_\OmegaG(x,z)dz\]其中，\(G_0(x,y)\)是关于\(x\)的椭圆型方程的Green函数。

IEEE参考文献格式

•Creating a reference list or bibliographyA numbered list of references must be provided at the end of thepaper. The list should be arranged in the order of citation in the text of the assignment or essay, not in alphabetical order. List only one reference per reference number. Footnotes or otherinformation that are not part of the referencing format should not be included in the reference list.The following examples demonstrate the format for a variety of types of references. Included are some examples of citing electronic documents. Such items come in many forms, so only some examples have been listed here.Print DocumentsBooksNote: Every (important) word in the title of a book or conference must be capitalised. Only the first word of a subtitle should be capitalised. Capitalise the "v" in Volume for a book title.Punctuation goes inside the quotation marks.Standard formatSingle author[1] W.-K. Chen, Linear Networks and Systems. Belmont, CA: Wadsworth,1993, pp. 123-135.[2] S. M. 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Canberra: Attorney- General's Department,2003.Manual[13] Bell Telephone Laboratories Technical Staff, TransmissionSystem for Communications, Bell Telephone Laboratories,1995.Catalogue[14] Catalog No. MWM-1, Microwave Components, M. W. Microwave Corp.,Brooklyn, NY.Application notes[15] Hewlett-Packard, Appl. Note 935, pp. 25-29.Note:Titles of unpublished works are not italicised or capitalised. Capitalise only the first word of a paper or thesis.Technical report[16] K. E. Elliott and C.M. Greene, "A local adaptive protocol,"Argonne National Laboratory, Argonne, France, Tech. Rep.916-1010-BB, 1997.Patent / Standard[17] K. Kimura and A. Lipeles, "Fuzzy controller component, " U.S. Patent 14,860,040, December 14, 1996.Papers presented at conferences (unpublished)[18] H. A. Nimr, "Defuzzification of the outputs of fuzzycontrollers," presented at 5th International Conference onFuzzy Systems, Cairo, Egypt, 1996.Thesis or dissertation[19] H. 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New York: McGraw-Hill, 1997, pp. 279-283.Study Guides and Unit ReadersNote: You should not cite from Unit Readers, Study Guides, or lecture notes, but where possible you should go to the original source of the information. If you do need to cite articles from the Unit Reader, treat the Reader articles as if they were book or journal articles. In the reference list or bibliography use the bibliographical details as quoted in the Reader and refer to the page numbers from the Reader, not the original page numbers (unless you have independently consulted the original).[6] L. Vertelney, M. Arent, and H. Lieberman, "Two disciplines insearch of an interface: Reflections on a design problem," in The Art of Human-Computer Interface Design, B. Laurel, Ed.Reading, MA: Addison-Wesley, 1990. Reprinted inHuman-Computer Interaction (ICT 235) Readings and Lecture Notes, Vol. 1. Murdoch: Murdoch University, 2005, pp. 32-37. 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Sridhar, "Analysis of software requirementsengineering exercises in a global virtual team setup,"Journal of Global Information Management, vol. 13, no. 2, p.21+, April-June 2005. [Online]. Available: Academic OneFile, . [Accessed May 31, 2005].[3] A. Holub, "Is software engineering an oxymoron?" SoftwareDevelopment Times, p. 28+, March 2005. [Online]. Available: ProQuest, . [Accessed May 23, 2005].Journal article in a scholarly journal (published free of charge on the internet)[4] A. Altun, "Understanding hypertext in the context of readingon the web: Language learners' experience," Current Issues in Education, vol. 6, no. 12, July 2003. [Online]. Available: /volume6/number12/. [Accessed Dec. 2, 2004].Journal article in electronic journal subscription[5] P. H. C. Eilers and J. J. Goeman, "Enhancing scatterplots withsmoothed densities," Bioinformatics, vol. 20, no. 5, pp.623-628, March 2004. [Online]. Available:. [Accessed Sept. 18, 2004].Newspaper article from online database[6] J. 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[Accessed: Sept. 12,2004].Internet document, no author given[4] 揂憀ayman抯?explanation of Ultra Narrow Band technology,?Oct.3, 2003. [Online]. Available:/Layman.pdf. [Accessed: Dec. 3, 2003].Non-Book FormatsPodcasts[1] W. Brown and K. Brodie, Presenters, and P. George, Producer, 揊rom Lake Baikal to the Halfway Mark, Yekaterinburg? Peking to Paris: Episode 3, Jun. 4, 2007. [Podcast television programme]. Sydney: ABC Television. Available:.au/tv/pekingtoparis/podcast/pekingtoparis.xm l. [Accessed Feb. 4, 2008].[2] S. Gary, Presenter, 揃lack Hole Death Ray? StarStuff, Dec. 23, 2007. [Podcast radio programme]. Sydney: ABC News Radio. Available: .au/newsradio/podcast/STARSTUFF.xml. [Accessed Feb. 4, 2008].Other FormatsMicroform[3] W. D. Scott & Co, Information Technology in Australia:Capacities and opportunities: A report to the Department ofScience and Technology. [Microform]. W. D. Scott & CompanyPty. Ltd. in association with Arthur D. Little Inc. Canberra:Department of Science and Technology, 1984.Computer game[4] The Hobbit: The prelude to the Lord of the Rings. [CD-ROM].United Kingdom: Vivendi Universal Games, 2003.Software[5] Thomson ISI, EndNote 7. [CD-ROM]. Berkeley, Ca.: ISIResearchSoft, 2003.Video recording[6] C. Rogers, Writer and Director, Grrls in IT. [Videorecording].Bendigo, Vic. : Video Education Australasia, 1999.A reference list: what should it look like?The reference list should appear at the end of your paper. Begin the list on a new page. The title References should be either left justified or centered on the page. The entries should appear as one numerical sequence in the order that the material is cited in the text of your assignment.Note: The hanging indent for each reference makes the numerical sequence more obvious.[1] A. Rezi and M. Allam, "Techniques in array processing by meansof transformations, " in Control and Dynamic Systems, Vol.69, Multidemsional Systems, C. T. Leondes, Ed. 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基于离散蛙跳算法的零空闲流水线调度问题求解

第36卷第1期2010年1月北京工业大学学报J OURN AL OF BE IJI NG UNI VERS I TY OF TEC HNOLOG YVo.l 36No .1Jan .2010基于离散蛙跳算法的零空闲流水线调度问题求解王亚敏1,2,冀俊忠1,潘全科2(11北京工业大学多媒体与智能软件技术北京市重点实验室,北京 100124;21聊城大学计算机学院,山东聊城 252059)摘要:针对零空闲流水线调度问题,提出了一种新的离散化蛙跳求解算法.该算法借助蛙跳算法优化机理,采用基于工件序列的编码方式和新的个体产生方法扩展了传统蛙跳算法的求解模型,并结合简化邻域搜索算法给出了3种改进策略.仿真实验表明了所提算法及策略的有效性.关键词:零空闲流水线调度;离散蛙跳算法;邻域搜索中图分类号:TP 18文献标志码:A文章编号:0254-0037(2010)01-0124-07收稿日期:2008205226.基金项目:北京市自然科学基金资助项目(4083034),北京市教育委员会科技发展资助项目(KM 200610005020).作者简介:王亚敏(1979)),女,山东菏泽人,讲师.车间调度问题的求解及其优化技术是制造业实现生产过程合理化、自动化、集成化的基础和关键.其中,零空闲流水线调度(no -idle fl o w shop ,记为N I FS)是一类组合优化问题[1];Baptiste 等[2]提出了解决N I FS 问题的分枝限界法;K alcz ynski 等[3]提出了解决N I FS 问题的构造式启发方法;Bzraz 等[4]提出了有效的改进贪心算法;一些基于离散粒子群优化算法[5]、差分进化算法[6]等相继被提出;Eusu f f 等[7]首次提出了蛙跳算法(shu f fled frog leap i n g algorith m,记为SFL A ),并应用于水管网络扩充中管道尺寸最小化问题的求解.由于蛙跳算法能结合生物种群的遗传行为和群落间信息交流的社会行为,是解决组合优化问题的有效工具[8].本文提出了基于离散蛙跳算法的N I FS 问题的求解方法.采用基于工件序列的编码方式和新的个体产生方法扩展了传统蛙跳算法的求解模型,提出了解决N I FS 问题的蛙跳算法,并给出了3种提高性能的改进策略.1 N IFS 问题描述及邻域搜索算法111 N IFS 问题描述n 个工件在m 台机器上流水加工,每个工件在机器上的加工顺序相同,同时,约定每个工件在每台机器上只加工1次,而在同一机器上加工的相邻工件之间没有等待时间,且机器之间存在无限缓冲区.在已知各工件在各台机器上所需加工时间的前提下,问题的求解目标是得到满足上述约束条件的可行调度,使得最大完工时间最短.文献[5]提出了通过完工时间差或开工时间差来计算最大完工时间的方法.给定单个工件的排序P ={P 1,P 2,,,P n },而P e (i)={P 1,P 2,,,P i }和P j(i)={P i ,P i +1,,,P n }表示其中的2个部分排序.令F (P e(i),j ,j +1)表示排序P e(i)中机器j 和j +1的完工时间差,E (P f(i),j ,j +1)表示排序P f(i)中机器j 和j +1的开工时间差,而p(P i ,j)表示工件P i 在机器j 上的加工时间.如图1(a )所示,当从前往后依次增加工件时最大完工时间F (P e(1),j ,j +1)=p(P 1,j +1),j =1,2,,,m -1(1)第1期王亚敏,等:基于离散蛙跳算法的零空闲流水线调度问题求解F (P e(i),j ,j +1)=max {F (P e(i -1),j ,j +1)-p (P i ,j),0}+p (P i ,j +1) i =2,3,,,n,j =1,2,,,m -1(2)从前往后计算方式排列P 的最大完工时间为C m ax (P )=Em-1j=1F (P ,j ,j +1)+Eni=1p (P i ,1)(3)如图1(b )所示,当从后往前依次增加工件时最大完工时间E (P f(n),j ,j +1)=p(P n ,j), j =1,2,,,m -1(4)E (P f(i),j ,j +1)=max {E (P f(i +1),j ,j +1)-p (P i ,j +1),0}+p(P i ,j) i =n -1,n -2,,,1,j =1,2,,,m -1(5)图1 最大完工时间计算方法示意F ig .1 Sketch m ap of co mputi ng the m ax i m u m co mp l etio n ti m e for bot h cases从后往前计算方式排列P 的最大完工时间C m ax (P )=Em-1j=1E (P ,j ,j +1)+Eni=1p (P i ,m )(6)求最大完工时间的复杂度为O (mn).如图1(b )所示,在一个排列之前增加工件时完工时间差F (P f(n),j ,j +1)=p(P n ,j +1),j =1,2,,,m -1(7)F (P f(i),j ,j +1)=max {p(P i ,j +1)-E (P f(i +1),j ,j +1),0}+F (P f(i +1),j ,j +1)i =n -1,n -2,,,1,j =1,2,,,m -1(8)112 邻域搜索算法在排列P 中,随机选择不同的2个位置k 、j ,将j 处的零件移动到k 处,称为插入移动v(j ,k),其中j ,k I {1,2,,,n }.由移动可以得到原排列的一个邻居.所有这样的邻居构成插入邻域,则该邻域的规模为n (n -1),评价该邻域的时间复杂度为O (mn 3).如果将排列P 看作是2个排列P 1和P 2合并在一起得到的排列,其中P 2在P 1之后,如图2所示.则图2 2个排列合并在一起的最大完工时间计算方法示意F ig .2 Sketch m ap of co mputi ng the m axi m u m co m pletio n ti m e for co m bi natio n t w o per muta ti onsF (P ,j ,j +1)=max {F (P 1,j ,j +1)-E (P 2,j ,j +1),0}+F (P 2,j ,j +1) j =1,2,,,m -1(9)125北京工业大学学报2010年若记排列P进行插入移动v(j,k)之后的新排列为P c,对比P c和P可得到邻域搜索算法.第1步,按照式(1)和(2)从前往后依次求出每个P e(i)的完工时间差,按照式(4)、(5)和(7)、(8)从后往前依次求出每个P f(i)的完工时间差和开工时间差,进而得到排列P的C m ax(P).第2步,取出P中的第j个工件,将其依次插入P的k处,其中k=1,2,,,n,且k X j.得到新P c,则此时P c可以看作由k之前的P e(k-1)、k之后的P f(k+1)和k处的工件j3部分组成.第3步,在P e(k-1)后面增加工件j得到P c的P c e(k),由式(2)可以求出P c e(k)的完工时间差;P c的另一部分P c j(k+1)与P f(k+1)相同.由式(9)可求出P c的完工时间差F(P c,j,j+1),由式(3)得P c的C max(P c).第4步,重复第2和第3步,直到将排列P的插入邻域搜索一遍.上述算法中,第2步和第3步的时间复杂度为O(mn).所以整个算法的时间复杂度为O(mn2).2蛙跳算法SFLA蛙跳算法是一种新的元启发式的搜索算法[6],通过模拟青蛙群体在觅食过程中所体现出的协同行为来完成对问题的求解.这种算法按照族群分类进行信息传递,并将全局信息的交换与局部进化搜索相结合.在蛙跳算法中,种群由很多青蛙组成,每只青蛙代表1个解.种群被分成了多个子群,每个子群包括一定数量的青蛙,称为1个me meplex.在每个子群内分别执行局部搜索.每只青蛙都受自己和其他青蛙想法的影响,并通过m e m etic进化来调整位置.经过一定数量的进化后,不同子群间的青蛙通过跳跃过程来传递信息.这种局部进化和跳跃过程相间进行,直到满足收敛的条件为止.首先,由随机初始化一组解组成青蛙的初始种群,然后,将所有青蛙按照它们的适配值降序排列,并分别放入各个me mep lex中,用P b和P w分别表示该子群中位置(适应值)最好和最坏的青蛙.另外,用P g表示整个种群中最好的青蛙.在每一轮的进化中,通过与PS O算法近似的方法改善最坏青蛙P w的位置.青蛙移动的距离D i=rand()*(P b-P w)(10)新的位置P w=P w(当前位置)+D i,(D m ax\D i\-D m ax)(11)式中,rand()为0到1之间的随机数;D max为允许青蛙移动的最大距离.如果这个过程能产生一个较好解,那么就用新位置的青蛙取代原来的青蛙P w;否则,用P g代替P b,重复上述过程.如果上述方法仍不能生成更好的青蛙,那么就随机生成一个新解取代原来最坏的青蛙P w.按照这种方法执行一定次数的进化.最后,将所有的青蛙重新排序、子群划分,继续进化、跳跃,重复上述过程直到收敛为止.3N IFS问题的离散蛙跳求解算法DSFLA311个体矢量编码建立个体矢量与调度方案之间的映射关系.对于零空闲流水线编码方案就的个体矢量的每一维表示1个工件.这样,个体本身就表示所有工件的一个排列.表1为个体矢量与调度方案之间的对应关系.表1个体矢量及对应的工件排列Tab le1Ind ivi dua l vector and cor r espond i ng job perm u ta tions个体矢量维数个体矢量工件序列133211个体矢量维数个体矢量工件序列322444个体矢量维数个体矢量工件序列566655126第1期王亚敏,等:基于离散蛙跳算法的零空闲流水线调度问题求解127 312个体矢量的更新青蛙所代表的解向量在连续解空间跟踪其局部极值或全局极值的向量运算.换句话说,式(10)、(11)表示P w向P b学习逼近的过程,其中rand()表示学习的程度,将式(10)、(11)合并可知P w=P w(当前位置)+rand()*(P b-P w(当前位置))(12)式中,rand()代表青蛙P w从局部极值P b的信息继承度,反映了对P b信息的置信指标.当rand()=1时,P w=P b,当rand()=0时,P w=P w(当前位置).定义f(P w,P b)为P w向P b的学习过程,该过程可以通过交叉操作实现.1)在P b中随机选择1个交叉区域,其中rand()决定着交叉区域的大小.2)将P b的交叉区域加到P w的前面或后面,并删除P w中已在P b的交叉区中出现过的数字.采用这种更新策略,子串能继承父串的有效模式,实现了从局部极值P b获得更新信息的目的.313工序编码的DSLFA调度算法Step0初始化.选择M和N,M表示me meplex的数量,即子群的数量,N表示每个m e m eplex中青蛙的个数.那么,整个种群的数量F=M@N.Step1生成初始种群.在可行解空间8<R n,生成F个青蛙U(1),U(2),,,U(F),其中n为工件数量.每个青蛙(Fr og)原本代表青蛙的当前位置,对于N I FS问题则表示解空间的1个候选解.第i个青蛙可以表示为U(i)=(U1i,U2i,,,U n i).计算出工件序列U(i)的最大完工时间makespan,用f(i)表示.则f(i)的值越小,表示该解的适应度越高.Step2对青蛙划分等级.将F只青蛙按照适应度的降序排列,生成数组X={U(i),f(i),i=1,2, ,,F},这样的话,i=1表示这只青蛙的位置(适应度)最好,记录下种群中位置最好青蛙P g=U(1).Step3将青蛙分组,放入不同的me mep lex.将数组X分成M个me m eplex:Y1,Y2,,,Y M.每个me meplex中包含N只青蛙,即:Y k={U(j)k,f(j)k|U(j)k=U(k+M(j-1)),f(j)k=f(k+M(j-1)),j=1, ,,N},其中k=1,2,,,M;比如M=3,那么第1只青蛙属于子群me m eplex1,第2只青蛙属于子群me meplex2,第3只青蛙属于子群me mep lex3,第4只青蛙属于子群me mep lex1,等等.Step4在每个me mep l e x中执行me metic进化.在每个me meplex中,每只青蛙受到其他青蛙想法的影响,通过me metic进化,使得各个青蛙朝目标位置逼近.Step4-0设i M=0,i M表示对me mep lex的计数,在0到M之间变化,与m e m eplex的数量M比较.设i N=0,i N表示进化次数,与每个m e m eplex中允许的最大进化次数N max比较.用P b和P w分别表示每个me meplex中位置(适应度)最好的和最坏的青蛙,用P g表示整个种群中最好的青蛙.在每轮的进化中,改善最坏青蛙P w的位置,注意,并非对所有的青蛙都优化.Step4-1i M=i M+1.Step4-2i N=i N+1.Step4-3采用式(12)调整最坏青蛙的位置.Step4-4如果Step4-3能使得青蛙有一个更好的位置,即能产生一个更好的解,那么就用新位置的青蛙取代原来的青蛙,执行step4-6;否则,用P g代替P b,利用式(12)计算f(P w,P g),如果能产生一个更好的解,取代原来的青蛙,执行step4-6.Step4-5随机生成一个新解取代原来最坏的青蛙P w.Step4-6如果i N<N max,那么执行4-2.Step4-7如果i M<M,那么执行4-1,否则执行Step5.Step5青蛙在me mep l e x之间跳跃移动.在每个me m eplex中执行了一定次数的m e m etic进化之后,将各个子群Y1,Y2,,,Y M合并到X,即X={Y k,k=1,2,,,M}.将X重新按降序排列,并更新种群中最好的青蛙P g.Step6检查终止条件.如果迭代终止条件满足,则停止.否则,重新执行step3.一般情况下,当执北京工业大学学报2010年行了一定次数的循环进化,代表最好解的青蛙不再改变的时候,算法停止.有时也定义最大进化次数作为停止标准.314 蛙跳算法的改进31411 引入邻域搜索算法的改进策略蛙跳算法中青蛙从局部极值或全局极值中获得更新信息,其信息共享机制中信息的流动是单向的,信息流动的目的性更强,效率更高.同时,搜索过程受局部极值P b 以及全局极值P g 的影响较大.加强P b 和P g 的局部探测能力可提高算法性能.改进SFL A 的方法是在每组me mep lex 进化过程中,对P b 执行简化插入邻域搜索算法,如果搜索之后发现更好的解,则用该解代替原来的P b ,如果新得到的P b 优于P g ,更新P g .并且在整个种群的每次迭代中,对P g 也执行简化邻域搜索算法.通过对P b 和P g 的细搜索,使得整个种群能更快的向最优解移动,有利于增加算法的收敛速度,记为DSFL A1.31412 增加随机扰动的改进策略DSFL A 1虽然增强了局部搜索能力,但细搜索范围仅限于P b 和P g 的最近邻居,范围较小,有可能使P b 和P g 长时间/徘徊0在若干旧状态上,容易陷入局部最优.为了增强算法跳出局部最优的能力,可以在1次邻域搜索之后,对P b 和P g 执行1次随机插入移动,对所得结果再执行邻域搜索算法,如此将随机插入和邻域搜索过程重复几次,即通过增加扰动来扩大细搜索的范围.虽然细搜索的时间有所增加,有利于优化过程中状态的局部小范围趋化性移动,从而增强了算法在解空间的探索能力和效率.记为DS FL A2.31413 结合模拟退火机理的改进策略正是因为种群进化受P b 和P g 影响,一旦为局部最优,青蛙将难以摆脱局部极值,其信息将覆盖整个邻域种群,导致该种群以较大概率陷入局部收敛.由此,还可以借鉴模拟退火中的概率接收[9]准则优化P b 和P g ,即在DSFL A2的基础上,在对P b 和P g 进行多次邻域搜索后,如果找到更好的解,那么就接受这个解,如果找不到更好的解,就以一定概率接受次优解.这种在DSFL A2中S A 的嵌入,赋予优化过程在各状态具有可控的概率突跳特性,尤其在高温时使得算法具有较大的突跳性,是避免P b 和P g 陷入局部极小和算法/早熟收敛0的有力手段,记为DSFL A 3.4 仿真试验采用包含120个流水线调度的Ta ill a rd Benchmar k 问题作为实例,每个实例计算5次,求算法所得解的平均相对偏差(PRD)和平均方差(SD).设种群规模为20,因算法受初始解情况的影响,如果初始解先通过某种智能优化算法优化生成,算法的收敛性及其他性能会有所提高.但是,为了检验该算法的鲁棒性,初始解采用随机生成的方法.对局部极值P b 和全局极值P g 执行3次随机插入移动和邻域搜索,模拟退火接受标准的温度系数t =0105E ni=1Emj=1P ij /(mn ).并与基于离散粒子群优化DPS O 算法进行了比较.实验的运行环境为:操作系统W i n dows XP ,CP U 为P Ô115G H z ,内存为256MB ,算法用C++语言编程.各算法采用相同的终止条件,即最大运行时间为10ms .结果如表2所示.DSFL A 算法所得的平均相对偏差和平均方差近似于DPSO 算法,由此表明具有信息共享、协同进化机制的DSFL A 能在较短时间内较快得向最优解逼近,是一种有效的解决N I FS 问题的方法.由DSFL A 和DSFL A 1、DSFL A2和DSFL A3各个算法的对比分析可以看出,通过简化邻域搜索算法提高局部极值和全局极值之后,平均偏差减少,解的质量有所提高,尤其是加入随机扰动对算法性能提高有很大作用.并可以看出,DSFL A2和DSFL A3的平均方差明显减少,表明这2种改进策略使得算法的稳定性有所提高.原因在于P b 和P g 对种群的进化搜索过程起着引导作用,其性能对算法结果影响很大,所以DS FL A 和DS FL A1算法性能对P b 和P g 的依赖性较大,而对于改进策略DS FL A2和DSFL A3,由于在对P b 和P g 邻域搜索时增加了扰动,扩大了搜索范围,从而使得算法在每一代进化过程中对P b 和P g 的初始性能的依赖性降低,进而使得算法的稳定性提高.128第1期王亚敏,等:基于离散蛙跳算法的零空闲流水线调度问题求解表2 不同算法的比较Tab le 2 C o m pa r ison of d iffer ent a lgor ithm sInstance DPSODSFL A DSFL A1DSFL A2DSFLA3n @m PRD SD PRD SD PRD S D PRD SD PRD SD 20@59171151915611919166212514111215136114820@102319221712316421962313521441513811615168117120@2048149211749132183491163133371352157381411950@561941169713211445199113331701953153111650@1022182212423185211920195212917104210916161119650@20551243134551931245012131534117231614016312100@54115110141751112301881195018911810174100@102010521292110121111612611451317116413121166100@204616921634818521640107310335152197341452187200@10151131111161031129111311146101091121101241122200@2038116115540132118301312176291831195281572112500@202612511092719111252312111323169113723131113分别选取一个50@20的中等规模和大规模的N I FS 问题进行分析,各算法的进化过程如图3所示.图3(a )为50@20的中等规模N I FS 问题Ta051的各算法进化曲线.对于中等规模的问题,DSFL A 具有较好的计算性能和较强的全局搜索能力.与DSFL A 相比较,DSFL A1明显加快了简化邻域搜索的收敛速度,由于P b 和P g 搜索范围不大,易陷入局部最优,进而整个种群也更易陷入局部极值.加入随机扰动后的DSFL A2和DSFL A3,扩大了P b 和P g 的搜索范围,不仅收敛速度更快,而且易于跳出局部极值,并且融合了模拟退火机理的改进策略对于跳出局部最优也有一定作用.由此可以看出,DS FL A2和DSFL A3在搜索广度和深度上能达到较好的均衡,是解决N I FS 这类组合优化问题的有效工具.图3(b )为500@20的大规模N I FS 问题Ta111的各算法进化曲线.对于大规模问题,虽然DSFL A 收敛速度比DPSO 稍慢一些,但是从试验中看出相对不易陷入局部极值,依然是一种解决N I FS 问题的有效工具.这是由于DSFL A 中对于较差解可能有变异操作,这对保持种群多样性可以起到一定的作用,能在一定程度上减少陷入局部极值的可能.而对于3种改进策略,尽管较大规模问题的邻域搜索算法本身需要占用较多的时间,对整体的收敛进度依然起到了极大的促进作用,使得收敛速度有较大提高.图3 各算法进化曲线比较F i g .3 Evol utio n curves of different algorith m s129130北京工业大学学报2010年5结论蛙跳算法结合了粒子群优化算法的社会特性和m e m etic算法的遗传特性,具有连续性和较强的全局搜索能力.本文基于该算法的优化机理,提出了适合于解决零空闲流水线调度问题的离散蛙跳算法,并研究了几种改进策略,仿真试验表明,离散蛙跳算法是解决零空闲流水线调度问题的有效方法,几种改进策略都有助于改善解的质量和提高算法的收敛速度.参考文献:idle/cmax proble m[J].[1]S AADA N I N E I,GUI NET A,MOAL A M.A trave li ng sa les m an approach to sol ve the f/no-European Journa l of Ope ratio n R esearch,2005,161:11220.[2]S AADA N I N E H,BAPTIS ETE P,MOALL A M.The si m p le F2M C m ax w ith forb i ddden tasks i n first or last positi on:Aproble m more co mp l ex t han i t see m s[J].Eur J Oper R es,2005,161:21231.[3]KALCZ YNS K I P J,KA MBURO WSKI J.A heuristic f or m i n i m i zing the m akespan i n no2idle pe r muta tion flo w s hop[J].Co mput Ind Eng,2005,49:1462154.[4]BZ RAZ D,MOS HEIO V G.A note on a greedy heuristi c for t he fl o w2shop makespan m i n i m izati on with no m achi ne idle2ti m e[J].Eur J Ope r R es,2008,184(2):8102813.[5]PA N Quan2ke,WANG L i ng.No2i dle per muta ti on fl o w shop schedu li ng based on a hybr i d d i scre te particle s war m o pti m izati ona l gor it hm[J].The Inte rnati onal Journa l of Advanced M anu fact ur i ng Technol ogy,2008,39(728):7962807.[6]PA N Quan2ke,WAN G L i ng.A novel diff e renti a l evol utio n a l gor it hm for no2i dle per m utatio n flo w2shop scheduli ng prob l em s[J].European J.of Industrial Engi nee ri ng,2008,2(3):2792297.[7]EUS UFF M M,LA NSEY K E.Opti m i zati on ofwate r distributi on net work desig n usi ng t he shu ffl ed fro g leap i ng algor i th m[J].W ater R esour P lan M anage,2003,129(3):2102225.[8]EL BELT AG I E,HEGAZ Y T,GR IER S ON D.Co m parison among fi ve evol utio nary2based opti m izati on algorith m[J].AdvancedEngineer i ng In f or m atics,2005,19(1):43253.[9]王凌.智能优化算法及其应用[M].北京:清华大学出版社,2001,10.An Algor ithm Based on Discrete Shuffled Frog L eap i ng forNo-Id le Per m uta ti on F lo w Shop Sc hedu li ng Proble mWANG Y a2m in1,2,JI Jun2zhong1,P AN Quan2ke2(11Be iji ng Munic i pal Key Laboratory ofM ulti m edia and Intelli gent Soft w are Technol ogy,Be iji ng Un i versity of Technol ogy,B eiji ng100124;21College of Co mpu ter Sc i ence,L i aocheng Un i versity,Liaocheng,252059,Ch i na)Abstr act:A D iscrete Shuffled Frog Leap i n g A l g orit h m(DS FL A)is proposed to solve the No-Idle per m utati o n F l o w Shop schedu ling proble ms(N I FS).I n the li g ht of the opti m ization m echan is m of genera l SFL A,the algorithm adopts an encoding sche me based on job per m utation and a ne w method of indivi d ual producti o n to extend the trad itionalmodel of SFL A,and e mp l o ys the si m ple neighbor hood search to present t h ree i m pr ove ment strategi e s.The experi m en tal resu lts sho w that the proposed algorithm and its stra tegies are eff ective and e f ficient i n d iff erent scale bench m ar ks ofN I FS.K ey w ord s:no-idle flo w shop;discrete shu f fled frog leapi n g a l g orit h m;neighbor hood search(责任编辑张士瑛)。

科学思维

1998年诺贝尔生理学或医学奖（NO是体内重要的信号分子）科学思维
穆拉德发现硝化甘油等一些化学物质能激活GC(可溶性鸟氨酸环化酶），把这些物质加入到气管、肠等组织中，发现还能使这些组织的平滑肌松弛。

而这些物质都能通过反应生成NO。

由此他推测是NO使平滑肌细胞松弛。

弗奇戈特研究乙酰胆碱对血管扩张作用时，发现乙酰胆碱仅能使内皮细胞扩张，不能使平滑肌细胞扩张。

由此他做了一系列实验，发现内皮细胞产生了一种信使分子EDRF, 作用于平滑肌细胞而使平滑肌细胞扩张。

伊格纳罗通过比较NO和EDRF的生物化学性质，发现他们的很多性质都非常相似。

再通过灌流——生物鉴定法等，从不同侧面证明了EDRF就是NO。

以上三位科学家的发现综合说明了是NO使平滑肌细胞舒张，从而在扩张血管中起到重要信号分子的作用。

非均匀圆环形薄膜的径向格林函数计算

非均匀圆环形薄膜的径向格林函数计算何敏;王其申【摘要】The Green′s function in the qualitative research of linear vibration has important applications .Based on the radial Green′s function of circular membrane with axial symmetry mass distribution, the radial Green's function of annular membrane is calculated when the mass surface density is the single valued function of radius .%格林函数在线性振动的定性研究中有重要应用，在质量轴对称分布的圆膜的格林函数基础上，计算了质量面密度是半径的单值函数时的圆环形薄膜的径向格林函数。

【期刊名称】《安庆师范学院学报（自然科学版）》【年(卷),期】2016(022)003【总页数】3页(P55-56,105)【关键词】轴对称;圆环形薄膜;径向格林函数【作者】何敏;王其申【作者单位】安庆师范大学物理与电气工程学院，安徽安庆 246133;安庆师范大学物理与电气工程学院，安徽安庆 246133【正文语种】中文【中图分类】O32格林函数是偏微分方程的一个基本工具，广泛应用于现代数学和现代物理学中。

关于弹性体线性振动的定性性质问题[1]，文[2]研究了杆和梁等各类段状连续体的连续系统的格林函数，在此基础上，本文计算一种新的二维弹性体——类非均匀圆环形薄膜，即质量轴对称分布的圆环形薄膜的径向格林函数。

对于一般的二维弹性薄膜，其质量面密度为ρ(x,y)，张力T视为常数，占有二维域Ω，并以∂Ω为边界，它作横向微振动时的模态方程为[3]T(uxx+uyy)+λρ(x,y)u(x,y)=0，(x,y)∈Ω式中n是区域外法向单位矢量，h代表边界处支承弹簧的刚度。

一种广义非线性互补问题的新的光滑牛顿算法

一种广义非线性互补问题的新的光滑牛顿算法
徐引玲
【期刊名称】《南通大学学报（自然科学版）》
【年(卷),期】2015(014)002
【摘要】提出了一种新的光滑牛顿法,即在算法中嵌入非单调的线搜索技术,并将该算法从非线性互补问题(NCP)推广到广义非线性互补问题(GNCP).通过证明,该算法对GNCP问题是适定的,并在GNCP解集非空有界的假设条件下,证明了该算法的全局收敛性和局部二次收敛性.
【总页数】6页(P85-90)
【作者】徐引玲
【作者单位】西安财经学院应用数学系,陕西西安710061
【正文语种】中文
【中图分类】O224
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2.一种基于新NCP函数的非线性互补问题的光滑牛顿法 [J], 朱琳;芮绍平;
3.一类新的光滑函数及求解非线性互补问题的光滑牛顿算法 [J], 李杰;李梅霞;刘丽娟
4.广义非线性互补问题的非光滑牛顿算法 [J], 李梅霞;田治平
5.一种新的解箱约束变分不等式的光滑牛顿算法 [J], 江莉
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