A Brief Introduction to Optimization

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考博英语面试自我介绍考博英语面试自我介绍范文（精选12篇）参加外企的面试中，准备一段吸引人的自我介绍很有必要，那么你的`英文自我介绍准备好了吗？求职前的准备和英文自我介绍是非常重要的，那你会怎么介绍自己呢？下面是小编我为您准备的考博英语面试自我介绍范文，欢迎参考，希望能对您有所作用。

考博英语面试自我介绍篇1Good afternoon, profe ssors! It’s really a great pleasure for me to have this opportunity for the interview, and I hope I can make a good impression today and finally enroll in Huazhong University of Science and Technology as a PhD student. Now I will make a brief introduction about myself to you.My name is XXX. I was born in 1986 in Yichang City, a world renowned hydraulicxelectricity town where the Three Gorges Dam stands.Iam learning in Taiyuan University of Science and Technology, majoring in Chemical Process Machinery, and will get my master’s degree in June. Three years ago, I obtained a bachelor’s degree inChina Three Gorges University in the major of Mechanical and Electronic Engineering.In daily lives, I am quiet but not dull. I have many hobbies, such as listening music, reading and playing basketball with friends.These are good ways of relaxing myself in spare time. In learning, I am serious, steady and persistent. Sometimes I concentrate on some tough problems to get them well solved, though it takes much time.I stil l feel it’s worthy. In the past three years, Ihave studied hard and strived for excellence in my research work. I obtained the Scholarship for Postxgraduatesin TUST last year and published four papers as the first authorin some core journals.Mechanical engineering is an extensive and profound subject and I deeply feel that what I have learned is very limited. So I am longing for further study and looking forward to improving my selfxvalue in the next few years. No pains,no gains. Only with greater efforts can I get closer to success. I will make good use of my time and do my best to reach my goals if I am lucky to be a PhD student in HUST.That’s all. Thank you!考博英语面试自我介绍篇2Respected Professor：It is my great honor to introduce myself.My name is Jim ,I come from Zaozhuang ,Shandong Province.My major is mechanical design,and I received my Master’s degree from Dalian University of Technology in 2014.As you may know ,students from Shandong Province are always hardxworking, I am no exception.While obtaining m y Master’s degree,I devoted myself to mechanical design,especially in structure calculation and optimization fields. As a result,I have published several relevant theses and patents independently. These academic experiences have made me more openxminded,agile in thought and also very fond of scientific research.After graduation,I worked at XCMG,which is the biggest construction machinery manufacturer in China. We developed the most advanced scooptram in China,and I worked as one of its engineers. work experiences such as this have urged me develop an active and responsible work ethic.As time went on, I found that most companies utilise existing technologies exclusively,performing little new research. But I believe our society need us to develop moreinnovations .Furthermore,I really want to do some research work and study futher in my major.That is why I am eager to be a Doctoral student .Above all,I am sincerely looking forward to studying here, and I will do my very best. Thank you!考博英语面试自我介绍篇3Good morning, Dear Professors:it is my pleasure to introduce myself to you. My name is MSJ.I major in Pesticide Science and I will graduate from the Research and Development Center of Biorational Pesticide Northwest A&F University in July ,20XX. Hope a chance to work and develop myself in your department.I passed the CET band 6 test in20XX， after that， I tried my best to learn Medical English and mastered a lot of professional vocabulary. I can manipulate computer proficiently and master Microsoft Office software，also be familiar with SPSS and Photoshop.During the past three years， under the strict guidance of my tutor， professor MA.I have learned systematically the theory of profession and got the basic manipulative skills about Phytochemistry. With the help of my supervisor，I have successfully finished the subject “Agricultural Activity of Alkaloids from Cephalotaxus sinensis ” and grasped some experimental skill ， such as abstraction， separation.I am looking forward to working in your department. If I am admitted， I will be thankful and try my best to work for you.That’s all.SKS.考博英语面试自我介绍篇4Good morning, Dear Professors:It’s my honor to introduce myself. My name is XXX, I amfromXXCountyXXProvince, December XXXX I was born in a poor family, and my parents are peasants。

Scheduling flow shops using differential evolution algorithm

Discrete OptimizationScheduling ﬂow shops using diﬀerential evolution algorithmGodfrey Onwubolu *,Donald DavendraDepartment of Engineering,The University of the South Paciﬁc,P.O.Box 1168,Suva,FijiReceived 17January 2002;accepted 5August 2004Available online 21November 2004AbstractThis paper describes a novel optimization method based on a diﬀerential evolution (exploration)algorithm and its applications to solving non-linear programming problems containing integer and discrete variables.The techniques for handling discrete variables are described as well as the techniques needed to handle boundary constraints.In particular,the application of diﬀerential evolution algorithm to minimization of makespan ,ﬂowtime and tardiness in a ﬂow shop manufacturing system is given in order to illustrate the capabilities and the practical use of the method.Experiments were carried out to compare results from the diﬀerential evolution algorithm and the genetic algorithm,which has a reputation for being very powerful.The results obtained have proven satisfactory in solution quality when compared with genetic algorithm.The novel method requires few control variables,is relatively easy to implement and use,eﬀec-tive,and eﬃcient,which makes it an attractive and widely applicable approach for solving practical engineering prob-lems.Future directions in terms of research and applications are given.Ó2004Elsevier B.V.All rights reserved.Keywords:Scheduling;Flow shops;Diﬀerential evolution algorithm;Optimization1.IntroductionIn general,when discussing non-linear programming,the variables of the object function are usually as-sumed to be continuous.However,in practical real-life engineering applications it is common to have the problem variables under consideration being discrete or integer values.Real-life,practical engineering opti-mization problems are commonly integer or discrete because the available values are limited to a set of commercially available standard sizes.For example,the number of automated guided vehicles,the number of unit loads,the number of storage units in a warehouse operation are integer variables,while the size of a pallet,the size of billet for machining operation,etc.,are often limited to a set of commercially available 0377-2217/$-see front matter Ó2004Elsevier B.V.All rights reserved.doi:10.1016/j.ejor.2004.08.043*Corresponding author.Tel.:+679212034;fax:+679302567.E-mail address:onwubolu_g@usp.ac.fj (G.Onwubolu).European Journal of Operational Research 171(2006)674–692/locate/ejorG.Onwubolu,D.Davendra/European Journal of Operational Research171(2006)674–692675 standard sizes.Another class of interesting optimization problem isﬁnding the best order or sequence in which jobs have to be machined.None of these engineering problems has a continuous objective function; rather each of these engineering problems has either an integer objective function or discrete objective func-tion.In this paper we deal with the scheduling of jobs in aﬂow shop manufacturing system.Theﬂow shop scheduling-problem is a production planning-problem in which n jobs have to be pro-cessed in the same sequence on m machines.The assumptions are that there are no machine breakdowns and that all jobs are pre-emptive.This is commonly the case in many manufacturing systems where jobs are transferred from machine to machine by some kind of automated material handling systems.For large problem instances,typical of practical manufacturing settings,most researchers have focused on developing heuristic procedures that yield near optimal-solutions within a reasonable computation time. Most of these heuristic procedures focus on the development of permutation schedules and use makespan as a performance measure.Some of the well-known scheduling heuristics,which have been reported in the literature,include Palmer(1965),Campbell et al.(1970),Gupta(1971),Dannenbring(1977),Hundal and Rajagopal(1988)and Ho and Chang(1991).Cheng and Gupta(1989)and Baker and Scudder(1990)pre-sented a comprehensive survey of research work done inﬂow shop scheduling.In recent years,a growing body of literature suggests the use of heuristic search procedures for combi-natorial optimization problems.Several search procedures that have been identiﬁed as having great poten-tial to address practical optimization problems include simulated annealing(Kirkpatrick et al.,1983), genetic algorithms(Goldberg,1989),tabu search(Glover,1989,1990),and ant colony optimization(Dor-igo,1992).Consequently,over the past few years,several researchers have demonstrated the applicability of these methods,to combinatorial optimization problems such as theﬂow shop scheduling(see for example, Widmer and Hertz,1989;Ogbu and Smith,1990;Taillard,1990;Chen et al.,1995;Onwubolu,2000).More recently,a novel optimization method based on diﬀerential evolution(exploration)algorithm(Storn and Price,1995)has been developed,which originally focused on solving non-linear programming problems containing continuous variables.Since Storn and Price(1995)invented the diﬀerential evolution(explora-tion)algorithm,the challenge has been to employ the algorithm to diﬀerent areas of problems other than those areas that the inventors originally focussed on.Although application of DE to combinatorial optimi-zation problems encountered in engineering is scarce,researchers have used DE to design complex digital ﬁlters(Storn,1999),and to design mechanical elements such as gear train,pressure vessels and springs (Lampinen and Zelinka,1999).This paper presents a new approach based on diﬀerential evolution algorithm for solving the problem of scheduling n jobs on m machines when all jobs are available for processing and the objective is to minimize the makespan.Other objective functions considered in the present work include meanﬂowtime and total tardiness.2.Problem formulationAﬂow shop scheduling is one in which all jobs must visit machines or work centers in the same sequence. Processing of a job must be completed on current machine before processing of the job is started on suc-ceeding machine.This means that initially all jobs are available and that each machine is restricted to pro-cessing only one job at any particular time.Since theﬁrst machine in the facility arrangement is theﬁrst to be visited by each job,the other machines are idle and other jobs are queued.Although queuing of jobs is prohibited in just-in-time(JIT)manufacturing environments,ﬂow shop manufacturing continues toﬁnd applications in electronics manufacturing,and space shuttle processing,and has attracted much research work(Onwubolu,2002).Theﬂow shop can be formatted generally by the sequencing of n jobs on m ma-chines under the precedence condition,with typical objective functions being the minimizing of average ﬂowtime,minimizing the time required to complete all jobs or makespan,minimizing maximum tardiness,and minimizing the number of tardy jobs.If the number of jobs is relatively small,then the problem can be solved without using any generic optimizing algorithm.Every possibility can be checked to obtain results and then sequentially compared to capture the optimum value.But,more often,the number of jobs to be processed is large,which leads to big-O order of n !Consequently,some kind of algorithm is essential in this type of problem to avoid combinatorial explosion.The standard three-ﬁeld notation (Lawler et al.,1995)used is that for representing a scheduling problem as a j b j F (C ),where a describes the machine environment,b describes the deviations from standard sched-uling assumptions,and F (C )describes the objective C being optimized.In the work reported in this paper,we are solving the n /m /F k F (C max )problem.Other problems solved include F ðC Þ¼F ðP C i Þand F ðC Þ¼F ðP T j Þ.Here a =n /m /F describes the multiple-machines ﬂow shop problem,b =null,and F ðC Þ¼F ðC max ;P C i ;and P T j Þfor makespan,mean ﬂowtime,and total tardiness,respectively.Stating these problem descriptions more elaborately,the minimization of completion time (makespan)for a ﬂow shop schedule is equivalent to minimizing the objective function I :I ¼X n j ¼1C m ;j ;ð1Þs :t :C i ;j ¼max C i À1;j ;C i ;j À1ÀÁþP i ;j ;ð2Þwhere C m ,j =the completion time of job j ,C 1,1=k (any given value),C i ;j ¼P j k ¼1C 1;k ;C j ;i ¼P i k ¼1C k ;1,i )machine number,j )job in sequence,P i ,j )processing time of job j on machine i .For a given sequence,the mean ﬂowtime,MFT =1P m i ¼1P n j ¼1c ij ,while the condition for tardiness is c m ,j >d j .The constraint of Eq.(2)applies to these two problem descriptions.3.Diﬀerential evolutionThe diﬀerential evolution (exploration)[DE]algorithm introduced by Storn and Price (1995)is a novel parallel direct search method,which utilizes NP parameter vectors as a population for each generation G .DE can be categorized into a class of ﬂoating-point encoded,evolutionary optimization algorithms .Currently,there are several variants of DE.The particular variant used throughout this investigation is the DE/rand/1/bin scheme.This scheme will be discussed here and more detailed descriptions are provided (Storn and Price,1995).Since the DE algorithm was originally designed to work with continuous variables,the opti-mization of continuous problems is discussed ﬁrst.Handling discrete variables is explained later.Generally,the function to be optimized,I ,is of the form I ðX Þ:R D !R .The optimization target is to minimize the value of this objective function I ðX Þ,min ðI ðX ÞÞ;ð3Þby optimizing the values of its parameters X ={x 1,x 2,...,x D },X 2R D ,where X denotes a vector composed of D objective function ually,the parameters of the objective function are also subject to lower and upper boundary constraints,x (L )and x (U ),respectively,x ðL Þj P x j P x ðU Þj8j 2½1;D :ð4Þ3.1.InitializationAs with all evolutionary optimization algorithms,DE works with a population of solutions,not with a sin-gle solution for the optimization problem.Population P of generation G contains NP solution vectors called individuals of the population and each vector represents potential solution for the optimization problem 676G.Onwubolu,D.Davendra /European Journal of Operational Research 171(2006)674–692P ðG Þ¼X ðG Þi ¼x ðG Þj ;i ;i ¼1;...;NP ;j ¼1;...;D ;G ¼1;...;G max :ð5ÞIn order to establish a starting point for optimum seeking,the population must be initialized.Often there is no more knowledge available about the location of a global optimum than the boundaries of the problem variables.In this case,a natural way to initialize the population P (0)(initial population)is to seed it with random values within the given boundary constraints:P ð0Þ¼x ð0Þj ;i ¼x ðL Þj þrand j ½0;1 Âx ðU Þj Àx ðL Þj 8i 2½1;NP ;8j 2½1;D ;ð6Þwhere rand j [0,1]represents a uniformly distributed random value that ranges from zero to one.3.2.MutationThe self-referential population recombination scheme of DE is diﬀerent from the other evolutionary algorithms.From the ﬁrst generation onward,the population of the subsequent generation P (G +1)is obtained on the basis of the current population P (G ).First a temporary or trial population of candidate vectors for the subsequent generation,P 0ðG þ1Þ¼V ðG þ1Þ¼v ðG þ1Þj ;i ,is generated as follows:v ðG þ1Þj ;i ¼x ðG Þj ;r 3þF Âx ðG Þj ;r 1Àx ðG Þj ;r 2 ;if rand j ½0;1 <CR _j ¼k ;x ðG Þi ;j ;otherwise ;8<:ð7Þwhere i 2[1,NP];j 2[1,D ],r 1,r 2,r 32[1,NP],randomly selected,except:r 15r 25r 35i ,k =(int(rand i [0,1]·D )+1),and CR 2[0,1],F 2(0,1].Three randomly chosen indexes,r 1,r 2,and r 3refer to three randomly chosen vectors of population.They are mutually diﬀerent from each other and also diﬀerent from the running index i .New random values for r 1,r 2,and r 3are assigned for each value of index i (for each vector).A new value for the random num-ber rand[0,1]is assigned for each value of index j (for each vector parameter).3.3.CrossoverThe index k refers to a randomly chosen vector parameter and it is used to ensure that at least one vector parameter of each individual trial vector V (G +1)diﬀers from its counterpart in the previous generation X (G ).A new random integer value is assigned to k for each value of the index i (prior to construction of each trial vector).F and CR are DE control parameters.Both values remain constant during the search process.Both values as well as the third control parameter,NP (population size),remain constant during the search pro-cess.F is a real-valued factor in range [0.0,1.0]that controls the ampliﬁcation of diﬀerential variations.CR is a real-valued crossover factor in the range [0.0,1.0]that controls the probability that a trial vector will be selected form the randomly chosen,mutated vector,V ðG þ1Þj ;i instead of from the current vector,x ðG Þj ;i .Gener-ally,both F and CR aﬀect the convergence rate and robustness of the search process.Their optimal values are dependent both on objective function characteristics and on the population size,ually,suitable values for F ,CR and NP can be found by experimentation after a few tests using diﬀerent values.Practical advice on how to select control parameters NP,F and CR can be found in Storn and Price (1995,1997).3.4.SelectionThe selection scheme of DE also diﬀers from the other evolutionary algorithms.On the basis of the cur-rent population P (G )and the temporary population P 0(G +1),the population of the next generation P (G +1)is created as follows:G.Onwubolu,D.Davendra /European Journal of Operational Research 171(2006)674–692677XðGþ1Þi ¼VðGþ1Þi;if I VðGþ1Þi6IðXðGÞiÞ;XðGÞi;otherwise:8<:ð8ÞThus,each individual of the temporary or trial population is compared with its counterpart in the current population.The one with the lower value of cost-function IðXÞto be minimized will propagate the pop-ulation of the next generation.As a result,all the individuals of the next generation are as good or better than their counterparts in the current generation.The interesting point concerning the DE selection scheme is that a trial vector is only compared to one individual vector,not to all the individual vectors in the cur-rent population.3.5.Boundary constraintsIt is important to notice that the recombination operation of DE is able to extend the search outside of the initialized range of the search space(Eqs.(6)and(7)).It is also worthwhile to notice that sometimes this is a beneﬁcial property in problems with no boundary constraints because it is possible toﬁnd the optimum that is located outside of the initialized range.However,in boundary-constrained problems,it is essential to ensure that parameter values lie inside their allowed ranges after recombination.A simple way to guarantee this is to replace parameter values that violate boundary constraints with random values generated within the feasible range:uðGþ1Þj;i ¼xðLÞjþrand j½0;1 ÂðxðUÞjÀxðLÞjÞ;if uðGþ1Þj;i<xðLÞj_uðGþ1Þj;i>xðUÞj;uðGþ1Þi;j;otherwise;(ð9Þwhere i2[1,NP];j2[1,D].This is the method that was used for this work.Another simple but less eﬃcient method is to reproduce the boundary constraint violating values according to Eq.(7)as many times as is necessary to satisfy the boundary constraints.Yet another simple method that allows bounds to be approached asymptotically while minimizing the amount of disruption that results from resetting out of bound values(Price,1999) isuðGþ1Þj;i ¼ðxðGÞj;iþxðLÞjÞ=2;if uðGþ1Þj;i<xðLÞj;ðxðGÞj;iþxðUÞjÞ=2;if uðGþ1Þj;i>xðUÞj;uðGþ1Þj;i;otherwise:8>><>>:ð10Þ3.6.Conventional technique for integer and discrete optimization by DESeveral approaches have been used to deal with discrete variable optimization.Most of them round oﬀthe variable to the nearest available value before evaluating each trial vector.To keep the population robust,successful trial vectors must enter the population with all of the precision with which they were generated(Storn and Price,1997).In its canonical form,the diﬀerential evolution algorithm is only capable of handling continuous vari-ables.Extending it for optimization of integer variables,however,is rather mpinen and Zelinka (1999)discuss how to modify DE for mixed variable optimization.They suggest that only a couple of sim-ple modiﬁcations are required.First,integer values should be used to evaluate the objective function,even though DE itself may still works internally with continuousﬂoating-point values.Thus, Iðy iÞ;i2½1;D ;ð11Þ678G.Onwubolu,D.Davendra/European Journal of Operational Research171(2006)674–692wherey i ¼x i for continuous variables;INTðx iÞfor integer variables;&wherey i ¼x i;INTðx iÞ: &x i2X:INT()is a function for converting a real-value to an integer value by truncation.Truncation is performed here only for purposes of cost-function value evaluation.Truncated values are not elsewhere assigned. Thus,DE works with a population of continuous variables regardless of the corresponding object variable type.This is essential for maintaining the diversity of the population and the robustness of the algorithm. Second,in case of integer variable,instead of Eq.(6),the population should be initialized as follows: Pð0Þ¼xð0Þj;i¼xðLÞjþrand j½0;1 ÂðxðUÞjÀxðLÞjþ1Þ8i2½1;NP ;8j2½1;D :ð12ÞAdditionally,instead of Eq.(9),the boundary constraint handling integer variables should be performed as follows:uðGþ1Þj;i ¼xðLÞjþrand j½0;1 ÂðxðUÞjÀxðLÞjþ1Þ;if INTðuðGþ1Þj;iÞ<xðLÞj_INTðuðGþ1Þj;iÞ>xðUÞj;uðGþ1Þi;ji;otherwise;(ð13Þwhere i2[1,NP];j2[1,D].They also discuss how discrete values can also be handled in a straightforward manner.Suppose that the subset of discrete variables,X(d),contains l elements that can be assigned to var-iable x:XðdÞ¼xðdÞi;i2½1;l ;ð14Þwhere xðdÞi<xðdÞiþ1.Instead of the discrete value x i itself,we may assign its index,i,to x.Now the discrete variable can be handled as an integer variable that is boundary constrained to range1,...,l.To evaluate the objective func-tion,the discrete value,x i,is used instead of its index i.In other words,instead of optimizing the value of the discrete variable directly,we optimize the value of its index i.Only during evaluation is the indicated discrete value used.Once the discrete problem has been converted into an integer one,the previously de-scribed methods for handling integer variables can be applied(Eqs.(11)–(13)).3.7.Forward transformation and backward transformation techniqueThe problem formulation is already discussed in Section2.Solving theﬂow shop-scheduling problem and indeed most combinatorial optimization problems requires discrete variables and ordered sequence, rather than relative position indexing.To achieve this,we developed two strategies known as forward and backward transformation techniques respectively.In this paper,we present a forward transformation method for transforming integer variables into continuous variables for the internal representation of vec-tor values since in its canonical form,the DE algorithm is only capable of handling continuous variables.G.Onwubolu,D.Davendra/European Journal of Operational Research171(2006)674–692679We also present a backward transformation method for transforming a population of continuous variablesobtained after mutation back into integer variables for evaluating the objective function(Onwubolu,2001). Both forward and backward transformations are utilized in implementing the DE algorithm used in the present study for theﬂow shop-scheduling problem.Fig.1shows how to deal with this inherent represen-tational problem in DE.Level0deals with integer numbers(which are used in discrete problems).At this level,initialization andﬁnal solutions are catered for.In the problem domain areas of scheduling,TSP,etc., we are not only interested in computing the objective function cost,we are also interested in the proper order of jobs or cities respectively.Level1of Fig.1deals withﬂoating point numbers,which are suited for DE.At this level,the DE operators(mutation,crossover,and selection)take place.To transform the integer at level0intoﬂoating point numbers at level1for DEÕs operators,requires some speciﬁc kind of coding.This type of coding is highly used in mathematics and computing science.For the basics of trans-forming an integer number into its real number equivalence,interested readers may refer to Michalewicz (1994),and Onwubolu and Kumalo(2001)for its application to optimizing machining operations using genetic algorithms.3.7.1.Forward transformation(from integer to real number)In integer variable optimization a set of integer number is normally generated randomly as an initial solution.Let this set of integer number be represented asz0i2z0:ð15ÞLet the real number(ﬂoating point)equivalence of this integer number be z i.The length of the real number depends on the required precision,which in our case,we have chosen two places after the decimal point. The domain of the variable z i has length equal to5;the precision requirement implies that the range be [0...4].Although0is considered since it is not a feasible solution,the range[0.1,1,2,3,4]is chosen,which gives a range of5.We assign each feasible solution two decimal places and this gives us5·100=500.Accordingly,the equivalent continuous variable for z0iis given as100¼102<5Â1026103¼1000:ð16ÞThe mapping from an integer number to a real number z i for the given range is now straightforward,given asz i¼À1þz0iÂ510À1:ð17Þ680G.Onwubolu,D.Davendra/European Journal of Operational Research171(2006)674–692Eq.(17)results in most conversion values being negative;this does not create any accuracy problem any way.After some studies by Onwubolu(2001),the scaling factor f=100was found to be adequate for con-verting virtually all integer numbers into their equivalent positive real numbers.Applying this scaling factor of f=100givesz i¼À1þz0iÂfÂ510À1¼À1þz0iÂ50010À1:ð18ÞEq.(18)is used to transform any integer variable into an equivalent continuous variable,which is then used for the DE internal representation of the population of vectors.Without this transformation,it is not pos-sible to make useful moves towards the global optimum in the solution space using the mutation mecha-nism of DE,which works better on continuous variables.For example in aﬁve-job scheduling problem, suppose the sequence is given as{2,4,3,1,5}.This sequence is not directly used in DE internal representa-tion.Rather,applying Eq.(18),the sequence is transformed into a continuous form.Theﬂoating-pointequivalence of theﬁrst entry of the given sequence,z0i ¼2,is z i¼À1þ2Â500103À1¼0:001001.Other valuesare similarly obtained and the sequence is therefore represented internally in the DE scheme as {0.001001,1.002,0.501502,À0.499499,and1.5025}.3.7.2.Backward transformation(from real number to integer)Integer variables are used to evaluate the objective function.The DE self-referential population muta-tion scheme is quite unique.After the mutation of each vector,the trial vector is evaluated for its objective function in order to decide whether or not to retain it.This means that the objective function values of the current vectors in the population need to be also evaluated.These vector variables are continuous(from the forward transformation scheme)and have to be transformed into their integer number equivalence. The backward transformation technique is used for convertingﬂoating point numbers to their integer num-ber equivalence.The scheme is given as follows:z0 i ¼ð1þz iÞÂð103À1Þ500:ð19ÞIn this present form the backward transformation function is not able to properly discriminate between variables.To ensure that each number is discrete and unique,some modiﬁcations are required as follows: a¼intðz0iþ0:5Þ;ð20Þb¼aÀz0i;ð21ÞzÃi ¼ðaÀ1Þ;if b>0:5;a;if b<0:5:&ð22ÞEq.(22)gives zÃi ,which is the transformed value used for computing the objective function.It should bementioned that the conversion scheme of Eq.(19),which transforms real numbers after DE operations into integer numbers is not suﬃcient to avoid duplication;hence,the steps highlighted in Eqs.(20)–(22)are important.In our studies,these modiﬁcations ensure that after mutation,crossover and selection opera-tions,the convertedﬂoating numbers into their integer equivalence in the set of jobs for a new scheduling solution,or set of cities for a new TSP solution,etc.,are not duplicated.As an example,we consider a set of trial vector,z i={À0.33,0.67,À0.17,1.5,0.84}obtained after mutation.The integer values corresponding to the trial vector values are obtained using Eq.(22)as follows:G.Onwubolu,D.Davendra/European Journal of Operational Research171(2006)674–692681z0 1¼ð1À0:33ÞÂð103À1Þ=500¼1:33866;z02¼ð1þ0:67ÞÂð103À1Þ=500¼3:3367;z0 3¼ð1À0:17ÞÂð103À1Þ=500¼1:65834;z04¼ð1þ1:50ÞÂð103À1Þ=500¼4:9950;z05¼ð1þ0:84ÞÂð103À1Þ=500¼3:6763;a1¼intð1:333866þ0:5Þ¼2;b1¼2À1:33866¼0:66134>0:5;zÃ1¼2À1¼1;a2¼intð3:3367þ0:5Þ¼4;b2¼4À3:3367¼0:6633>0:5;zÃ2¼4À1¼3;a3¼intð1:65834þ0:5Þ¼2;b3¼2À1:65834¼0:34166<0:5;zÃ3¼2;a4¼intð4:995þ0:5Þ¼5;b4¼5À4:995¼0:005<0:5;zÃ4¼5;a5¼intð3:673þ0:5Þ¼4;b5¼4À3:673¼0:3237<0:5;zÃ5¼4:This can be represented schematically as shown in Fig.2.The set of integer values is given aszÃi ¼f1;3;2;5;4g.This set is used to obtain the objective function values.Like in GA,after mutation,crossover,and boundary checking operations,the trial vector obtained fromthe backward transformation is continuously checked until feasible solution is found.Hence,it is not nec-essary to bother about the ordered sequence,which is crucially important in the type of combinatorial opti-mization problems we are concerned with.Feasible solutions constitute about10–15%of the total trial vectors.3.8.DE strategiesPrice and Storn(2001)have suggested ten diﬀerent working strategies of DE and some guidelines in applying these strategies for any given problem.Diﬀerent strategies can be adopted in the DE algorithm depending upon the type of problem for which it is applied.Table1shows the ten diﬀerent working strat-egies proposed by Price and Storn(2001).The general convention used in Table1is as follows:DE/x/y/z.DE stands for diﬀerential evolution algorithm,x represents a string denoting the vector to be perturbed,y is the number of diﬀerence vectors considered for perturbation of x,and z is the type of crossover being used(exp:exponential;bin:binomial). Thus,the working algorithm outline by Storn and Price(1997)is the seventh strategy of DE,that is,DE/ rand/1/bin.Hence the perturbation can be either in the best vector of the previous generation or in any ran-domly chosen vector.Similarly for perturbation,either single or two vector diﬀerences can be used.For perturbation with a single vector diﬀerence,out of the three distinct randomly chosen vectors,the weighted vector diﬀerential of any two vectors is added to the third one.Similarly for perturbation with two vector682G.Onwubolu,D.Davendra/European Journal of Operational Research171(2006)674–692。

高中同步测控优化设计英语必修一福建专版

高中同步测控优化设计英语必修一福建专版全文共10篇示例，供读者参考篇1Hello everyone! Today I want to talk about the topic of "high school synchronized measurement and control optimization design" in the special edition for Fujian province. It sounds like a mouthful, but don't worry, I'll break it down for you in simple terms!First of all, let's talk about what "synchronized measurement and control optimization design" means. Basically, it's all about making sure that everything in a system works together smoothly and efficiently. It's like when you're playing a game with your friends and you all need to work together to win. You have to communicate, make sure you're all on the same page, and adjust your strategies as needed. That's kind of what synchronized measurement and control optimization design is all about, but instead of a game, it's for things like electricity grids, traffic systems, and other complicated systems.In the Fujian special edition, they're teaching high school students how to apply these concepts to real-world situations.They learn about things like data collection, analysis, and using technology to make systems run better. It's pretty cool stuff, and it's also really important for the future. Our world is becoming more and more interconnected, and we need to make sure that everything runs smoothly so that we can all live better lives.So, that's a brief overview of "high school synchronized measurement and control optimization design" in the Fujian special edition. It may sound complicated, but it's really just about working together to make things better. And who knows, maybe one day you'll use these skills to help solve big problems in the world. Keep learning and growing, and you'll be unstoppable!篇2Hello everyone, today I want to talk to you about the topic of "High School Synchronous Measurement and Control Optimization Design". It sounds like a big and difficult topic, but don't worry, I will explain it in a simple way that everyone can understand.First of all, let's talk about what synchronous measurement and control mean. Synchronous measurement is a method that allows us to measure different variables at the same time, andcontrol is about adjusting and setting things to make sure they work properly. So when we put them together, it means we are measuring and controlling things at the same time to make them work better.In this subject, we will learn how to design systems that can measure and control things in a synchronous way. For example, we can design a system that measures temperature and humidity in a room, and then adjusts the air conditioning to make the room more comfortable. This is called optimization design, because we are trying to make things work in the best way possible.In the Fujian version of this subject, we will learn about the specific challenges and solutions related to measurement and control in the Fujian region. We will also learn about the latest technologies and tools that can help us design better systems.Overall, studying High School Synchronous Measurement and Control Optimization Design is not only interesting but also important for our future. So let's have fun learning and exploring this subject together!篇3Oh my gosh, guys! Today I'm gonna talk to you about this super cool book called "High School Synchronization Control and Optimization Design English One Fujian Edition". I know, I know, it sounds super boring, but trust me, it's actually pretty interesting.So basically, this book is all about how to control and optimize stuff in high school, like your studies and your time management. It teaches you all these cool techniques and tricks to help you do better in school and in life. And the best part is, it's made specifically for students in Fujian, so you know it's gonna be super helpful.One of my favorite parts of the book is when it talks about how to make a study schedule. It gives you tips on how to break down your day and prioritize your tasks so you can get everything done without feeling overwhelmed. It's been super helpful for me, especially during exam time.Another thing I love about this book is that it's full of fun illustrations and examples that make the concepts easy to understand. I used to struggle with some of the topics in English, but now I feel like a pro thanks to this book.Overall, I highly recommend "High School Synchronization Control and Optimization Design English One Fujian Edition" toall my fellow students. It's a game-changer and will help you succeed in high school and beyond. Trust me, you won't regret it!篇4Hello everyone! Today I want to talk to you about the advanced topic of "High School Synchronous Measurement and Control Optimization Design" in English. We will learn about the special edition for Fujian province!In this special edition, we will delve into the detailed study of measurement and control systems. We will explore how to design and optimize these systems to enhance their performance. It's really cool, right?Firstly, let's talk about synchronous measurement. Synchronous measurement is when multiple signals are measured at the same time. It helps us understand the relationships between different variables and make more accurate predictions. Isn't that interesting?Next, we will discuss control optimization design. This involves designing control systems that are efficient and effective. By optimizing the design, we can improve the overallperformance of the system. It's like solving a puzzle to make everything work perfectly!We will also learn about different tools and techniques used in measurement and control optimization. These include sensors, actuators, mathematical models, and software programs. It's like having a superhero toolkit to solve complex problems!In conclusion, this special edition of "High School Synchronous Measurement and Control Optimization Design" is a great opportunity to learn about some really cool stuff. So let's dive into the world of measurement and control and explore all the amazing possibilities it offers. Let's have fun while learning and growing together!That's all for today, thank you for listening and see you next time! Bye bye!篇5Oh my goodness, this high school synchronized control optimization design in English is so fun! It's like a super cool way to make sure everything is running smoothly and efficiently. Let's break it down in a super duper easy way!First off, let's talk about why we need synchronized control optimization. So basically, it's all about making sure things work together perfectly. Just like when we're doing a group project in class, everyone needs to work together and communicate well to get the best results. The same goes for synchronized control optimization - we want everything to work together smoothly and efficiently.Now, let's chat about some ways to optimize the design. One way is to use sensors to gather data and feedback. It's like having your own super smart detective that can tell you if something is going wrong. Another way is to use algorithms to analyze the data and make decisions. It's like having a super fast brain that can figure out the best way to do things.And you know what's super cool? This stuff is used in real life all the time! Like in traffic lights, where they use synchronized control to keep traffic flowing smoothly. Or in factories, where they use optimization design to make sure everything is working at its best.So next time you see a traffic light or a factory in action, remember that it's all thanks to synchronized control optimization design! Cool, right? It's like a super hero power that helps everything run like clockwork.篇6Hello guys! Today I want to talk to you about the subject of high school synchronous control optimization design in English. It's a super cool topic that involves a lot of interesting things like technology, engineering, and problem solving.In this subject, we learn about how to make things work together smoothly and efficiently. We also learn how to optimize our designs to make them even better. It's like solving a big puzzle, but instead of using pieces, we use advanced tools and knowledge.One of the things we learn in this subject is how to use different sensors and actuators to control systems. Sensors can help us detect things like temperature, pressure, or movement. Actuators, on the other hand, can help us make things move or change their state.We also learn about feedback control, which is really important in making sure that our systems work properly. It's like having a loop where we constantly check and adjust things to make sure everything is running smoothly.Overall, studying high school synchronous control optimization design is a fascinating journey that allows us toexplore the world of technology and engineering. It's a challenging subject, but it's also a lot of fun. So let's keep learning and exploring together!篇7Hello everyone, let's talk about the topic of "High School Synchronous Control and Optimization Design"! It sounds like a super long and boring topic, but don't worry, I'm going to explain it in a fun and easy way.So, what is "synchronous control and optimization design"? Basically, it means making sure things work together smoothly and making them work as well as possible. For example, when you're playing a video game, you want all the buttons on your controller to work properly and you want the game to run smoothly without any glitches. That's what synchronous control and optimization design is all about.In our English textbook, we have a special version for students in Fujian province. It's important for us to study this topic because it will help us understand how things are designed and how they can be improved. By learning about synchronous control and optimization design, we can become better problem solvers and make things work more efficiently.In conclusion, even though the topic of "High School Synchronous Control and Optimization Design" may sound complicated, it's actually really interesting and important. By studying this topic, we can learn how to make things work better and improve our problem-solving skills. Let's dive into this topic and have fun learning together!篇8Hello everyone! Today I’m going to talk about something super cool – the high school synchronous measurement and control optimization design in English for our Fujian province edition textbook.So first off, let’s talk about what synchronous measurement and control optimization design is all about. It’s basically a fancy way of saying that we use technology to make things work better and more efficiently. Like making sure our mobile phones have good signal, or that our air conditioners work just right.In our textbook, we will learn about all the different ways we can use technology to measure and control things in real time. We will also learn about how to optimize these systems to make them work even better. It’s like being a superhero and making sure everything in the city runs smoothly!One of the things we will learn in this textbook is about sensors and actuators. Sensors are like our ears and eyes – they can detect things like temperature, pressure, and light. Actuators are like our hands and feet – they can move things and make changes based on the information from the sensors. By using sensors and actuators together, we can create smart systems that can do all kinds of amazing things.I’m really excited to learn more about synchronous measurement and control optimization design in our English class. It’s going to be so much fun exploring all the ways we can use technology to make the world a better place. Let’s get ready to become tech wizards and make magic happen!篇9Title: Let's Learn about High School Synchronized Control Optimization Design!Hey guys, today I want to talk to you about something super cool - High School Synchronized Control Optimization Design! I know it sounds really fancy and complicated, but don't worry, I'm here to break it down for you in a fun and easy way.So, what is High School Synchronized Control Optimization Design? Well, it's basically a process of making things worktogether in the best possible way. It's like when you and your friends work together to build the best sandcastle on the beach - you want everything to be just right so it looks awesome!In high school, students learn how to use different technologies and tools to control and optimize systems. This could be anything from a computer program to a robot. By understanding how things work and using the right techniques, students can make the systems run more smoothly and efficiently.One cool thing about High School Synchronized Control Optimization Design is that it can be applied to so many different things. For example, it can be used to make a car run faster, to make a computer program more efficient, or even to control the temperature in a room. The possibilities are endless!By learning about High School Synchronized Control Optimization Design, students can develop important skills like problem-solving, critical thinking, and teamwork. These skills are not only useful in school, but also in the real world.So, the next time you hear about High School Synchronized Control Optimization Design, don't be scared or confused. Remember that it's all about making things work together in thebest possible way. Who knows, maybe one day you'll be the one designing the coolest system around!篇10Hey guys, today I want to talk to you about the exciting world of high school synchronous measurement and control optimization design in English textbooks! It may sound super fancy and complicated, but trust me, it's not as hard as it seems.So basically, this subject is all about using tools and technology to make things work better and more efficiently. Like, imagine your favorite video game - the designers had to use measurements and controls to make sure it runs smoothly and you have the best experience playing it.In our English textbook from Fujian province, we learn about different techniques and strategies to optimize designs and improve performance. We study things like feedback control systems, sensors, and actuators to make sure everything is working perfectly.One cool thing we learn about is how to use computer programs to simulate and test our designs before actually building them. It's like being a superhero and having superpowers to predict the future!Overall, studying high school synchronous measurement and control optimization design is super important because it helps us understand how to make things work better and more efficiently in the world around us. Who knows, maybe one day you'll come up with an amazing invention that changes the world!So there you have it, guys. High school synchronous measurement and control optimization design may seem a bit scary at first, but with some practice and hard work, you'll be a pro in no time. Keep exploring and learning, and who knows what amazing things you'll create in the future!。

Introduction to Optimization

Course Overview
5/29
Convex Optimization Example: Minimum Cost Flow
Given a directed network G = (V, E ) with cost ce ∈ R+ per unit of trafﬁc on edge e, and capacity de , ﬁnd the minimum cost routing of r divisible units of trafﬁw
11/29
Who Should Take this Class
Anyone planning to do research in the design and analysis of algorithms
Course Overview
2/29
Convex Optimization Problem
A continuous optimization problem where f is a convex function on X , and X is a convex set. Convex function: f (αx + (1 − α)y ) ≤ αf (x) + (1 − α)f (y ) for all x, y ∈ X and α ∈ [0, 1] Convex set: αx + (1 − α)y ∈ X , for all x, y ∈ X and α ∈ [0, 1] Convexity of X implied by convexity of gi ’s For maximization problems, f should be concave Typically solvable efﬁciently (i.e. in polynomial time) Encodes optimization problems from a variety of application areas

优化方案英文

优化方案英文Optimization PlanIntroduction:In this article, we will discuss an optimization plan aimed at improving the efficiency and effectiveness of a certain process. The plan consists of several strategies and techniques that can be implemented to enhance the overall performance. By following this plan, organizations can maximize their productivity and achieve better results.1. Definition of Optimization:Optimization, in the context of this plan, refers to the process of refining and improving a system, process, or method to achieve the best possible outcome. It involves identifying and eliminating bottlenecks, streamlining operations, and enhancing overall efficiency.2. Analyzing Current Performance:Before implementing any optimization strategies, it is crucial to thoroughly analyze the current performance of the process or system. This can be done by collecting data, identifying key performance indicators (KPIs), and evaluating the strengths and weaknesses.3. Identifying Areas for Improvement:Based on the analysis, it is important to identify specific areas that require improvement. This could include reducing costs, enhancing workflow, improving communication, or eliminating redundant tasks. Byfocusing on these areas, organizations can prioritize their efforts and resources effectively.4. Implementing Technology Solutions:One effective way to optimize processes is by implementing appropriate technology solutions. This can involve using software applications, automation tools, or advanced equipment to streamline operations and eliminate manual tasks. For example, integrating a Customer Relationship Management (CRM) system can enhance customer interactions and improve overall sales efficiency.5. Streamlining Workflow:Workflow optimization plays a vital role in enhancing overall productivity. It involves evaluating the sequence of tasks, identifying unnecessary steps, and finding ways to simplify the process. Organizations can adopt Lean Six Sigma methodologies to eliminate waste, standardize processes, and improve overall workflow efficiency.6. Training and Development:Investing in employee training and development is crucial for optimization. By providing relevant training programs, organizations can equip their workforce with the necessary skills and knowledge to perform their tasks efficiently. Training should focus on both technical expertise and soft skills such as communication, problem-solving, and teamwork.7. Continuous Improvement:Optimization is an ongoing process and should be approached with a mindset of continuous improvement. Regular monitoring, feedback collection, and analysis of performance metrics help identify areas that still have room for enhancement. By fostering a culture of continuous improvement, organizations can ensure long-term success and stay ahead of their competitors.Conclusion:In conclusion, this optimization plan provides a comprehensive framework for improving the efficiency and effectiveness of a process or system. By implementing the strategies and techniques outlined in this plan, organizations can achieve better results, reduce costs, and increase overall productivity. Optimization should be seen as an ongoing effort, and organizations should continuously evaluate their performance and make necessary adjustments to stay competitive in today's dynamic business environment.。

关于粒子群优化的英文摘要范文

关于粒子群优化的英文摘要范文Particle Swarm Optimization (PSO) is a fascinating approach to optimization problems. It's inspired by the social behavior of birds flocking and fish schooling. In PSO, we have a group of particles, each representing a potential solution to the problem. These particles move around in the search space, adjusting their positions and velocities based on their own best-found solution and the best-found solution among the entire group.One cool thing about PSO is how it mimics natural behaviors. Particles communicate with each other indirectly, sharing information through the global best position. This collaboration helps them converge towards optimal solutions faster than traditional methods. Plus, PSO is pretty easyto implement and doesn't require a lot of parameter tuning.The diversity of solutions explored by the particles is crucial in PSO. By having a group of particles searching independently but also influenced by the group's bestperformance, we can explore a wider range of potential solutions. This diversity can be further enhanced by techniques like introducing mutation or randomness into the particle's movement.The flexibility of PSO is another advantage. It can be applied to a wide variety of problems, from simple function optimization to complex optimization problems in machine learning and engineering. And because it's a stochastic method, it's often able to find good solutions even for problems that are difficult to solve using deterministic methods.In summary, Particle Swarm Optimization is a fun and effective optimization technique. It combines the power of swarm intelligence with.。

Technical Writing

Improving your technical writing skillsVersion 4.125 September 2003Norman FentonComputer Science DepartmentQueen Mary (University of London)London E1 4NSnorman@/~norman/Tel: 020 7882 7860AbstractThis document describes the basic principles of good writing. It is primarily targeted at students and researchers writing technical and business reports, but the principles are relevant to any form of writing, including letters and memos. Therefore, the document contains valuable lessons for anybody wishing to improve their writing skills. The ideas described here are, apart from fairly minor exceptions, not original. They are drawn from a range of excellent books and have also been influenced by various outstanding authors I have worked with. Thus, the approach represents a kind of modern consensus. This approach is very different to the style that was promoted by the traditional English schools’ system, which encouraged students to write in an unnecessarily complex and formal way. The approach described here emphasises simplicity (‘plain English’) and informality. For example, it encourages shorter sentences and use of the simplest words and phrases possible. It explains how you can achieve simplicity by using the active rather than the passive style, personal rather than impersonal style, and by avoiding noun constructs in favour of verbs. Crucially, this approach leads to better reports because they are much easier to read and understand.Document change historyVersion 1.0, 11 September 2000: Derived from Norman Fenton’s ‘Good Writing’ web pages. Version 2.0, 21 September 2001. Minor changes including addition of student project guidelines.Version 2.1, 20 September 2002. Minor corrections made.Version 3.0, 14 September 2003. Major revision.Version 4.0, 23 September 2003. Restructuring and editing.Version 4.1, 25 September 2003. Various typos fixed and polemic removed.Table of contents1.INTRODUCTION (4)2.BEFORE YOU START WRITING (5)ING PLAIN ENGLISH: STYLE (6)3.1S ENTENCE AND PARAGRAPH LENGTH (6)3.2B ULLET POINTS AND ENUMERATED LISTS (7)3.3U SING THE SIMPLEST WORDS AND EXPRESSIONS POSSIBLE (8)3.3.1Replace difficult words and phrases with simpler alternatives (9)3.3.2Avoid stock phrases (9)3.3.3Avoid legal words and pomposity (10)3.3.4Avoid jargon (10)3.4A VOIDING UNNECESSARY WORDS AND REPETITION (10)3.5U SING VERBS INSTEAD OF NOUNS (12)3.6U SING ACTIVE RATHER THAN PASSIVE STYLE (13)3.7U SING PERSONAL RATHER THAN IMPERSONAL STYLE (13)3.8E XPLAIN NEW IDEAS CLEARLY (15)3.9U SE CONSISTENT NAMING OF THE SAME ‘THINGS’ (15)3.10P AINLESS POLITICAL CORRECTNESS (16)3.11S UMMARY (17)ING PLAIN ENGLISH: THE MECHANICS (18)4.1A VOIDING COMMON VOCABULARY AND SPELLING ERRORS (18)4.2A BBREVIATIONS (19)4.3P UNCTUATION (19)4.3.1Capital letters (20)4.3.2Apostrophes (20)4.3.3Commas (21)4.3.4Exclamation marks (21)4.4S UMMARY (22)5.BASIC STRUCTURE FOR REPORTS (23)5.1W HAT EVERY REPORT SHOULD CONTAIN (23)5.2G ENERAL LAYOUT (24)5.3S ECTIONS AND SECTION NUMBERING (24)5.4T HE CRUCIAL ROLE OF ‘INTRODUCTIONS’ AND SUMMARIES (25)5.5F IGURES AND TABLES (26)5.6 A STRUCTURE FOR STUDENT PROJECT REPORTS (27)5.7S UMMARY AND CHECKLIST FOR WHEN YOU FINISH WRITING (28)6.ABSTRACTS AND EXECUTIVE SUMMARIES (29)7.WRITING THAT INCLUDES MATHEMATICS (31)8.SUMMARY AND CONCLUSIONS (32)9.REFERENCES (33)1. IntroductionCompare the following two sentences that provide instructions to a set of employees (this Example is given in [Roy 2000]):1. It is of considerable importance to ensure that under no circumstances shouldanyone fail to deactivate the overhead luminescent function at its local activationpoint on their departure to their place of residence, most notably immediatelypreceding the two day period at the termination of the standard working week.2. Always turn the lights out when you go home, especially on a Friday.The meaning of both sentences is, of course, equivalent. Which one was easier to read and understand? The objective of this document is to show people how to write as in the second sentence rather than the first. If you actually prefer the first, then there is little point in you reading the rest of this document. But please do not expect to win too many friends (or marks) from any writing that you produce.Unfortunately, the great shame for anybody having to read lots of reports in their everyday life is that the schools’ system continues to produce students who feel they ought to write more like in the first sentence than the second. Hence, the unnecessarily complex and formal style is still common. This document shows you that there is a better way to write, using simple, plain English.One of the good things about technical writing is that you really can learn to improve. You should not believe people who say that being a good writer is a natural ability that you either have or do not have. We are talking here about presenting technical or business reports and not about writing novels. I speak from some experience in this respect, because in the last ten years I have learned these ideas and applied them to become a better writer. When I was writing my first book in 1989 an outstanding technical editor highlighted the many problems with my writing. I was guilty of many of the examples of bad practice that I will highlight throughout this document. You too can improve your writing significantly if you are aware of what these bad practices are and how to avoid them.The document contains the following main sections:• Before you start writing (Section 2): This is a simple checklist that stresses the importance of knowing your objective and audience.• Using plain English: style (Section 3). This is the heart of the document because it explains how to write in the simplest and most effective way.• Using plain English: the mechanics (Section 4). This covers vocabulary, spelling, and punctuation.• Basic structure for reports (Section 5). This section explains how to organise your report into sections and how to lay it out.• Abstracts and executive summaries (Section 6). This explains the difference between informative and descriptive abstracts. It tells you why you should always use informative abstracts and how to write them.• Writing that includes mathematics (Section 7). This contains some simple rules you should follow if your writing includes mathematical symbols or formulas.2. Before you start writingBefore you start producing your word-processed report you must make sure you do the following:• Decide what the objective of the report is. This is critical. If you fail to do this you will almost certainly produce something that is unsatisfactory. Every report should have a single clear objective. Make the objective as specific as possible.• Write down the objective. Ideally, this should be in one sentence. For example, the objective of this document is “to help students write well structured, easy-to-understand technical reports”. The objective should then be stated at the beginning of the report. If you cannot write down the objective in one sentence, then you are not yet ready to start any writing.• Always have in mind a specific reader. You should assume that the reader is intelligent but uninformed. It may be useful to state up front what the reader profile is. For example, the target readers for this document are primarily students and researchers with a good working knowledge of English. The document is not suitable for children under 13, or people who have yet to write documents in English. It is ideal for people who have written technical or business documents and wish to improve their writing skills.• Decide what information you need to include. You should use the objective as your reference and list the areas you need to cover. Once you have collected the information make a note of each main point and then sort them into logical groups. Ultimately you have to make sure that every sentence makes a contribution to the objective. If material you write does not make a contribution to the objective remove it – if it is good you may even be able to reuse it in a different report with a different objective.• Have access to a good dictionary. Before using a word that ‘sounds good’, but whose meaning you are not sure of, check it in the dictionary. Do the same for any word you are not sure how to spell.• Identify someone who can provide feedback. Make sure you identify a friend, relative or colleague who can read at least one draft of your report before you submit it formally. Do not worry if the person does not understand the technical area – they can at least check the structure and style and it may even force you to write in the plain English style advocated here.The following checklist should be applied before you give even an early draft of your document out for review:• Check that the structure conforms to all the rules described in this document.• Run the document through a spelling checker.• Read it through carefully, trying to put yourself in the shoes of your potential readers.3. Using plain English: styleWhen you are producing a technical or business report you want it to ‘get results’. If you are a student this can mean literally getting a good grade. More generally we mean that you want to convince the reader that what you have to say is sensible so that they act accordingly. If the report is a proposal then you want the reader to accept your recommendations. If the report describes a piece of research then you want the reader to understand what you did and why it was important and valid. Trying to be ‘clever’ and ‘cryptic’ in the way you write will confuse and annoy your readers and have the opposite effect to what you wanted. In all cases you are more likely to get results if you present your ideas and information in the simplest possible way. This section describes how to do this.The section is structured as follows:• Sections 3.1 and 3.2 describe structural techniques for making your writing easier to understand. Specifically:o Sentence and paragraph length: keeping them short is the simplest first step to improved writing.o Bullet points and lists: using these makes things clearer and less cluttered.• Sections 3.3 and 3.4 describe techniques for using fewer words. Specifically: o Using the simplest words and expressions available: this section also describes words and expressions to avoid.o Avoiding unnecessary words: this is about removing redundancy.• Sections 3.5 to 3.7 describe techniques for avoiding common causes of poorly structured sentences. Specifically:o Using verbs instead of nounso Using active rather than passive styleo Using personal rather than impersonal style• Section 3.8 describes how to explain new ideas clearly.• Section 3.9 explains the importance of naming things consistently.• Section 3.10 gives some rules on how to achieve political correctness in your writing without adding complexity.3.1 Sentence and paragraph lengthContrary to what you may have learnt in school, there is nothing clever about writing long, complex sentences. For technical writing it is simply wrong. You must get used to the idea of writing sentences that are reasonably short and simple. In many cases shorter sentences can be achieved by sticking to the following principles:1. A sentence should contain a single unit of information. Therefore, avoid compoundsentences wherever possible. In particular, be on the lookout for words like and, or and while which are often used unnecessarily to build a compound sentence.2. Check your sentences for faulty construction. Incorrect use of commas (see Section4.3 for how to use commas correctly) is a common cause of poorly constructed andexcessively long sentences.Example (this example fixes some other problems also that are dealt with below) Bad: “Time division multiplexed systems are basically much simpler, thecombination and separation of channels being affected by timing circuitsrather than by filters and inter-channel interference is less dependent onsystem non-linearities, due to the fact that only one channel is using thecommon communication medium at any instant.”Good: “Systems multiplexed by time division are basically much simpler.The channels are combined and separated by timing circuits, not byfilters. Interference between channels depends less on non-linear featuresof the system, because only one channel is using the commoncommunication medium at any time.”3. Use parentheses sparingly. Most uses are due to laziness and can be avoided bybreaking up the sentence. Never use nested parentheses if you want to retain your reader.Learning about some of the principles described below, especially using active rather than passive constructs, will go a long way toward helping you shorten your sentences.Just as it is bad to write long sentences it is also bad to write long paragraphs. A paragraph should contain a single coherent idea. You should always keep paragraphs to less than half a page. On the other hand, successive paragraphs that are very short may also be difficult to read. Such an approach is often the result of poorly structured thinking. If you need to write a sequence of sentences that each express a different idea then it is usually best to use bullet points or enumerated lists to do so. We consider these next.3.2 Bullet points and enumerated listsIf the sentences in a paragraph need to be written in sequence then this suggests that there is something that relates them and that they form some kind of a list. The idea that relates them should be used to introduce the list. For example, the following paragraph is a mess because the writer is trying to make what is clearly a list into one paragraph:Getting to university on time for a 9.00am lecture involves following a number of steps. First of all you have to set your alarm – you will need to do this before you go to bed the previous night. When the alarm goes off you will need to get out of bed.You should next take a shower and then get yourself dressed. After getting dressed you should have some breakfast. After breakfast you have to walk to the tube station, and then buy a ticket when you get there. Once you have your ticket you can catch the next train to Stepney Green. When the train arrives at Stepney Green you should get off and then finally walk to the University.The following is much simpler and clearer:To get to university on time for a 9.00am lecture:1. Set alarm before going to bed the previous night2. Get out of bed when the alarm goes off3. Take a shower4. Get dressed5. Have some breakfast6. Walk to the tube station7. Buy ticket8. Catch next train to Stepney Green9. Get out at Stepney Green10. Walk to the UniversityThe simple rule of thumb is: if what you are describing is a list then you should always display it as a list.The above is an example of an enumerated list. The items need to be shown in numbered order. If there is no specific ordering of the items in the list then you should use bullet points instead. For example consider the following paragraph:Good software engineering is based on a number of key principles. One such principle is getting a good understanding of the customer requirements (possibly by prototyping). It is also important to deliver in regular increments, involving the customer/user as much as possible. Another principle it that it is necessary to do testing throughout, with unit testing being especially crucial. In addition to the previous principles, you need to be able to maintain good communication within the project team (and also with the customer).The paragraph is much better when rewritten using bullet points:Good software engineering is based on the following key principles:• Get a good understanding of the customer requirements (possibly byprototyping).• Deliver in regular increments (involve the customer/user as much aspossible).• Do testing throughout, (unit testing is especially crucial).• Maintain good communication within the project team (and also with the customer).There are numerous examples throughout this report of bullet points and enumerated lists. You should never be sparing in your use of such lists. Also, note the following rule for punctuation in lists:If all the list items are very short, by which we normally mean less than one line long, then there is no need for any punctuation. Otherwise use a full stop at the end of each list item.3.3 Using the simplest words and expressions possibleOn a recent trip to Brussels by Eurostar the train manager made the following announcement: “Do not hesitate to contact us in the event that you are in need if assistance at this time”. What she meant was: “Please contact us if you need help now”,but she clearly did not use the simplest words and expressions possible. While this maybe acceptable verbally, it is not acceptable in writing.The golden rules on words and expressions to avoid are:• Replace difficult words and phrases with simpler alternatives;• Avoid stock phrases;• Avoid legal words and pomposity;• Avoid jargon.We will deal with each of these in turn.3.3.1 Replace difficult words and phrases with simpler alternativesTable 1 lists a number of words and expressions that should generally be avoided in favour of the simple alternative.Table 1 Words and expressions to avoidWord/expression to avoid SimplealternativeWord/expressiontoavoidSimplealternativeutilise use endeavourtry facilitate help terminate end,stop at this time now transmit sendin respect of about demonstrate showcommence start initiate begin terminate end, stop assist, assistance helpascertain findout necessitate needin the event of if in excess of more thanin consequence so dwelling houseenquire askAlso, unless you are talking about building maintenance or computer graphics, never use theverb ‘render’ as in:The testing strategy rendered it impossible to find all the faults.The ‘correct’ version of the above sentence is:The testing strategy made it impossible to find all the faults.In other words, if you mean ‘make’ then just write ‘make’ not ‘render’.3.3.2 Avoid stock phrasesStock phrase like those shown in Table 2 should be avoided in favour of the simpler alternative. Such phrases are cumbersome and pompous.Table 2 Stock phrases to avoidBAD GOODThere is a reasonable expectation that ... Probably …Owing to the situation that … Because, since …Should a situation arise where … If …Taking into consideration such factors as … Considering …Prior to the occasion when … Before …At this precise moment in time … Now …Do not hesitate to … Please …I am in receipt of … I have …3.3.3 Avoid legal words and pomposityLawyers seem to have a language of their own. This is primarily to ensure that their documents are so difficult to understand that only other lawyers can read them. This ensures more work and money for lawyers because it forces ordinary people to pay lawyers for work they could do themselves. For some strange reason ordinary people often think they are being very clever by using legal words and expressions in their own writing. Do not fall into this trap. Avoid legal words like the following:forthwith hereof Of the (4th) inst. thereofhenceforth hereto thereat whereat hereat herewith therein whereonAlso avoid nonsensical legal references like the following:“The said software compiler…”which should be changed to“The software compiler…”and:“The aforementioned people have agreed …”which should be changed to“A and B have agreed…”3.3.4 Avoid jargonExpressions like MS/DOS, Poisson distribution, and distributor cap are examples of jargon.In general, jargon refers to descriptions of specific things within a specialised field. The descriptions are often shorthand or abbreviations. If you are certain that every reader of your report understands the specialist field then it can be acceptable to use jargon. For example, if your only potential readers are computer specialists then it is probably OK to refer toMS/DOS without the need to explain what MS/DOS is or stands for. The same applies to Poisson distribution if your readers are all statisticians or distributor cap if your readers are car mechanics. In all other cases (which is almost always) jargon should be avoided. If you cannot avoid it by using alternative expressions then you should define the term the first time you use it and/or provide a glossary where it is defined.3.4 Avoiding unnecessary words and repetitionMany sentences contain unnecessary words that repeat an idea already expressed in another word. This wastes space and blunts the message. In many cases unnecessary words are causedby ‘abstract’ words like nature, position, character, condition and situation as the following examples show:BADGOOD The product is not of a satisfactory natureThe product is unsatisfactory The product is not of a satisfactory characterThe product is unsatisfactory After specification we are in a position tobegin detailed designAfter specification we can begin detailed design We are now in the situation of being able tobegin detailed designWe can now begin detailed designIn general, you should therefore use such abstract words sparingly, if at all.Often writers use several words for ideas that can be expressed in one. This leads to unnecessarily complex sentences and genuine redundancy as the following examples show:WITH REDUNDANCYWITHOUT REDUNDANCY The printer is located adjacent to the computerThe printer is adjacent to the computer The printer is located in the immediate vicinity of the computerThe printer is near the computer The user can visibly see the image movingThe user can see the image moving He wore a shirt that was blue in colour He wore a blue shirt The input is suitably processed The input is processed This is done by means of inserting an artificial faultThis is done by inserting an artificial fault The reason for the increase in number of faults found was due to an increase in testingThe increase in number of faults found was due to an increase in testing It is likely that problems will arise with regards to the completion of thespecification phaseYou will probably have problemscompleting the specification phase Within a comparatively short period we will be able to finish the designSoon we will be able to finish the designAnother common cause of redundant words is when people use so-called modifying words. For example, the word suitable in the sentence “John left the building in suitable haste” is a modifying word. It is redundant because the sentence “John left the building in haste” has exactly the same meaning. Similarly, the other form of a modifying word – the one ending in ‘y’ as in suitably – is also usually redundant. For example, “John was suitably impressed” says nothing more than “John was impressed”. Other examples are:BADGOOD absolute nonsense nonsense absolutely critical critical considerable difficulty difficulty considerably difficult difficultModifying words can be fine when used with a concrete reference, as in the example “Jane set John a suitable task” but in many cases they are not and so are best avoided: Here are the most common modifying words to avoid:appreciable excessive sufficientapproximate fair suitablecomparative negligible unduedefinite reasonableutter evident relativeFinally, one of the simplest ways to shorten and simplify your reports is to remove repetition. Poorly structured reports are often characterised by the same idea being described in different places. The only ‘allowable’ repetition is in introductions and summaries, as we shall see in Section 5.4. You can avoid repetition by checking through your report and jotting down a list of the key ideas as they appear. Where the same idea appears more than once, you have to decide once and for all the place where it should best go and then delete and/or merge the text accordingly.3.5 Using verbs instead of nounsLook at the following sentence:“Half the team were involved in the development of system Y”.This sentence contains a classic example of a common cause of poor writing style. The sentence is using an abstract noun ‘development’ instead of the verb ‘develop’ from which it is derived. The simpler and more natural version of the sentence is:“Half the team were involved in developing system Y”.Turning verbs into abstract nouns always results in longer sentences than necessary, so you should avoid doing it. The following examples show the improvements you can achieve by getting rid of nouns in favour of verbs:BAD GOODHe used to help in the specification of newsoftwareHe used to help specify new softwareAcid rain accounts for the destruction of ancientstone-workAcid rain destroys ancient stone-work When you take into consideration … When you consider …Clicking the icon causes the execution of the program The program executes when the icon is clickedMeasurement of static software properties was performed by the tool The tool measured static software propertiesThe analysis of the software was performed byFredFred analysed the software The testing of the software was carried out by Jane Jane tested the softwareIt was reported by Jones that method x facilitated the utilisation of inspection techniques by the testing team Jones reported that method x helped the testing team use inspection techniquesThe last example is a particular favourite of mine (the bad version appeared in a published paper) since it manages to breach just about every principle of good writing style. It uses a noun construct instead of a verb and it includes two of the forbidden words (facilitated, utilisation). However, one of the worst features of this sentence is that it says “It was reported by Jones” instead of simply “Jones reported”. This is a classic example of use of passive rather active constructs. We deal with this in the next section.3.6 Using active rather than passive styleConsider the following two sentences:1. Joe tested the software2. The software was tested by JoeBoth sentences provide identical information. The first is said to be in the active style and the second is said to be passive style. In certain situations it can make sense to use the less natural passive style. For example, if you really want to stress that a thing was acted on, then it is reasonable to use the passive style as in “the city was destroyed by constant bombing”. However, many writers routinely use the passive style simply because they believe it is more ‘formal’ and ‘acceptable’. It is not. Using the passive style is the most common reason for poorly structured sentences and it always leads to longer sentences than are necessary. Unless you have a very good reason for the change in emphasis, you should always write in the active style.The following examples show the improvements of switching from passive to active: BAD GOODThe report was written by Bloggs, and was found to be excellent Bloggs wrote the report, and it was excellentThe values were measured automatically by the control system The control system measured the values automaticallyIt was reported by the manager that the project was in trouble The manager reported that the project was in troubleThe precise mechanism responsible for this antagonism cannot be elucidated We do not know what causes this antagonismThe stability of the process is enhanced by co-operation Co-operation improves the stability of the process3.7 Using personal rather than impersonal styleSaying“My results have shown…”is an example of a sentence using the personal (also called first person) style. This contrasts with:“The author’s results have shown…”which is an example of the impersonal (also called third person) style.。

六西格玛指导手册说明书

@RISK and Six-Sigma GuideThis short guide is designed to give you a very brief introduction to Six Sigma, and an overview of the features that @RISK provides to aid your Six Sigma analyses.In today’s competitive business environment, quality is more important than ever. @RISK is the perfect companion for any Six Sigma or quality professional.ContentsWhat is Six Sigma? (2)The Importance of Variation (2)Six Sigma Methodologies (3)Six Sigma / DMAIC (3)Design for Six Sigma (DFSS) (4)Lean or Lean Six Sigma (4)@RISK and Six Sigma (5)@RISK and DMAIC (5)@RISK and Design for Six Sigma (DFSS) (6)@RISK and Lean Six Sigma (6)Using @RISK for Six Sigma (7)RiskSixSigma Property Function (7)Six Sigma Statistics Functions (9)Six Sigma and the Results Summary Window (10)Six Sigma Markers on Graphs (11)Six Sigma Example Models (13)Version 1 - Last Updated 4/17/2020@RISK | Six Sigma Guide What is Six Sigma?Six Sigma is a set of practices to systematically improve processes by reducing process variation and thereby eliminating defects. A defect is defined as nonconformity of a product or service to its specifications. While the particulars of the methodology were originally formulated by Motorola in the mid-1980s, Six Sigma was heavily inspired by six preceding decades of quality improvement methodologies such as quality control, TQM, and Zero Defects. Like its predecessors, Six Sigma asserts the following:•Continuous efforts to reduce variation in process outputs is key to business success•Manufacturing and business processes can be measured, analyzed, improved and controlled •Succeeding at achieving sustained quality improvement requires commitment from the entire organization, particularly from top-level managementSix Sigma is driven by data, and frequently refers to “X” and “Y” variables. X variables are independent input variables that affect the dependent output variables, Y. Six Sigma focuses on identifying and controlling variation in X variables to maximize quality and minimize variation in Y variables.The term Six Sigma (or in symbols, 6σ) is very descriptive.The Greek letter sigma (σ) signifies standard deviation, an important measure of variation. The variation of a process refers to how tightly all outcomes are clustered around the mean. The probability of creating a defect can be estimated and translated into a “Sigma level.” The higher the Sigma level, the better the performance. Six Sigma refers to having six standard deviations between the average of the process center and the closest specification limit or service level. That translates to fewer than 3.4 defects per one million opportunities (DPMO).The cost savings and quality improvements that have resulted from Six Sigma corporate implementations are significant. Motorola has reported billions in savings since implementation in the mid-1980s. Lockheed Martin, GE, Honeywell, and many others have also experienced tremendous benefits from Six Sigma.The Importance of VariationM any Six Sigma practitioners rely on static models that don’t account for inherent uncertainty and variability in their processes or designs. In the quest to maximize quality, it’s vital to consider as many scenarios as possible.That’s where @RISK comes in. @RISK uses Monte Carlo simulation to analyze thousands of different possible outcomes, showing you the likelihood of each occurring. Uncertain factors are defined with probability distribution functions that describe the possible range of values your inputs couldtake. @RISK allows you to define Upper and Lower Specification Limits and Target values for each output, and it includes a wide range of Six Sigma statistics and capability metrics on the outputs.@RISK | Six Sigma Guide@RISK Industrial edition also includes RISKOptimizer, which combines the power of Monte Carlo simulation with genetic algorithm-based optimization. This gives you the ability to tackle optimization problems that have inherent uncertainty, such as:•Resource allocation to minimize cost•Project selection to maximize profit•Optimize process settings to maximize yield or minimize cost•Optimize tolerance allocation to maximize quality•Optimize staffing schedules to maximize serviceSix Sigma Methodologies@RISK can be used in a variety of Six Sigma and related analyses. The three principal areas of analysis are:•Six Sigma / DMAIC•Design for Six Sigma (DFSS)•Lean or Lean Six SigmaEach of these is described in a little more detail below.Six Sigma / DMAICWhen most people refer to Six Sigma, they are in fact referring to the DMAIC methodology. The DMAIC methodology should be used when a product or process is in existence but is not meeting customer specification or is not performing adequately.DMAIC focuses on evolutionary and continuous improvement in manufacturing and services processes, and is almost universally defined as being comprised of five phases - Define, Measure, Analyze, Improve and Control:1. Define the project goals and customer (internal and external Voice of Customer or VOC)requirements2. Measure the process to determine current performance3. Analyze and determine the root cause(s) of the defects4. Improve the process by eliminating defect root causes5. Control future process performance@RISK | Six Sigma Guide Design for Six Sigma (DFSS)DFSS is used to design or re-design a product or service from the ground up. The expected process Sigma level for a DFSS product or service is at least 4.5 (no more than approximately 1 defect per thousand opportunities), but can be 6 Sigma or higher depending on the product. Producing such a low defect level from a product or service launch means that customer expectations and needs (Critical-To-Qualities or CTQs) must be completely understood before a design can be completed and implemented. Successful DFSS programs can reduce unnecessary waste at the planning stage and bring products to market more quickly.Unlike the DMAIC methodology, the steps of DFSS are not universally recognized or defined; almost every company or training organization will define DFSS differently. One popular Design for Six Sigma methodology is called DMADV, and retains the same number of letters, number of phases, and general feel as the DMAIC acronym. The five phases of DMADV are defined as: Define, Measure, Analyze, Design and Verify:1. Define the project goals and customer (internal and external VOC) requirements2. Measure and determine customer needs and specifications; benchmark competitors andindustry3. Analyze the process options to meet the customer needs4. Design (detailed) the process to meet the customer needs5. Verify the design performance and ability to meet customer needsLean or Lean Six Sigma“Lean Six Sigma” is the combination of Lean manufacturing (originally developed by Toyota) and Six Sigma statistical methodologies in a synergistic tool. Lean deals with improving the speed of a process by reducing waste and eliminating non-value added steps. Lean focuses on a customer “pull” strategy, producing only those products demanded with “just in time” delivery. Six Sigma improves performance by focusing on those aspects of a process that are critical to quality from the customer perspective and eliminating variation in that process. Many service organizations, for example, have already begun to blend the higher quality of Six Sigma with the efficiency of Lean into Lean Six Sigma.Lean utilizes “Kaizen events” -- intensive, typically week-long improvement sessions -- to quickly identify improvement opportunities and goes one step further than a traditional process map in its use of value stream mapping. Six Sigma uses the formal DMAIC methodology to bring measurable and repeatable results.Both Lean and Six Sigma are built around the view that businesses are composed of processes that start with customer needs and should end with satisfied customers using your product or service.@RISK | Six Sigma Guide@RISK and Six SigmaWhether it’s in DMIAC, DFSS, or Lean Six Sigma, uncertainty and variability lie at the core of any Six Sigma analysis. @RISK uses Monte Carlo simulation to identify, measure, and root out the causes of variability in your production and service processes. Each of the Six Sigma methodologies can benefit from @RISK throughout the stages of analysis.@RISK and DMAIC@RISK is useful at each stage of the DMAIC process to account for variation and hone in on problem areas in existing products.1. Define. Define your process improvement goals, incorporating customer demand and business strategy. Value-stream mapping, cost estimation, and identification of CTQs (Critical-To-Qualities) are ************************************************************************@RISKzoomsin on CTQs that affect your bottom-line profitability.2. Measure. Measure current performance levels and their variations. Distribution fitting and over 35 probability distributions make defining performance variation accurate. Statistics from @RISK simulations can provide data for comparison against requirements in the Analyze phase.3. Analyze. Analyze to verify relationship and cause of defects, and attempt to ensure that all factors have been considered. Through @RISK simulation, you can be sure all input factors have been considered and all outcomes presented. You can pinpoint the causes of variability and risk with sensitivity and scenario analysis, and analyze tolerance. Use @RISK’s Six Sigma statistics functions to calculate capability metrics which identify gaps between measurements and requirements. Here we see how often products or processes fail and get a sense of reliability.4. Improve. Improve or optimize the process based upon the analysis using techniques like Design of Experiments. Design of Experiments includes the design of all information-gathering exercises where variation is present, whether under the full control of the experimenter or not. Using @RISK simulation, you can test different alternative designs and process changes. @RISK is also used for reliability analysis and – using RISKOptimizer - resource optimization at this stage.5. Control. Control to ensure that any variances are corrected before they result in defects. In the Control stage, you can set up pilot runs to establish process capability, transition to production and thereafter continuously measure the process and institute control mechanisms. @RISK automatically calculates process capability and validates models to make sure that quality standards and customer demands are met.@RISK | Six Sigma Guide @RISK and Design for Six Sigma (DFSS)One of @RISK’s main us es in Six Sigma is with DFSS at the planning stage of a new project. Testing different processes on physical manufacturing or service models or prototypes can be cost prohibitive. @RISK allows engineers to simulate thousands of different outcomes on models without the cost and time associated with physical simulation. @RISK is helpful at each stage of a DFSS implementation in the same way as the DMAIC steps. Using @RISK for DFSS gives engineers the following benefits: •Experiment with different designs / Design of Experiments•Identify CTQs•Predict process capability•Reveal product design constraints•Cost estimation•Project selection – using RISKOptimizer to find the optimal portfolio•Statistical tolerance analysis•Resource allocation – using RISKOptimizer to maximize efficiency@RISK and Lean Six Sigma@RISK is the perfect companion for the synergy of Lean manufacturing and Six Sigma. “Quality only” Six Sigma models may fail when applied to reducing variation in a single process step, or to processes which do not add value to the customer. For example, an extra inspection during the manufacturing process to catch defective units may be recommended by a Six Sigma analysis. The waste of processing defective units is eliminated, but at the expense of adding inspection which is itself waste. In a Lean Six Sigma analysis, @RISK identifies the causes of these failures. Furthermore, @RISK can account for uncertainty in both quality (ppm) and speed (cycle time) metrics.@RISK provides the following benefits in Lean Six Sigma analysis:•Project selection – using RISKOptimizer to find the optimal portfolio•Value stream mapping•Identification of CTQs that drive variation•Process optimization•Uncover and reduce wasteful process steps•Inventory optimization – using RISKOptimizer to minimize costs•Resource allocation – using RISKOptimizer to maximize efficiency@RISK | Six Sigma GuideUsing @RISK for Six Sigma@RISK’s standard simulation capabilities have been enhanced for use in Six Sigma modeling through the addition of four key features. These are:1. The RiskSixSigma property function for entering specification limits and target values forsimulation outputs.2. Six Sigma statistics functions, including process capability indices such as RiskCpk, RiskCpmand others which return Six Sigma statistics on simulation results directly in spreadsheet cells.3. Columns in the Results Summary window that provide Six Sigma statistics on simulationresults in table form.4. Markers on graphs of simulation results that display specification limits and the target value. The standard features of @RISK, such as entering distribution functions, fitting distributions to data, running simulations and performing sensitivity analyses, are also applicable to Six Sigma models.RiskSixSigma Property FunctionIn an @RISK simulation the RiskOutput function identifies a cell in a spreadsheet as a simulation output. A distribution of possible outcomes is generated for every output cell selected. These probability distributions are created by collecting the values calculated for a cell for each iteration of a simulation.When Six Sigma statistics are to be calculated for an output, the RiskSixSigma property function should be entered as an argument to the RiskOutput function. This property function specifies the lower specification limit, upper specification limit, target value, long term shift, and the number of standard deviations for the Six Sigma calculations for an output. These values are used in calculating Six Sigma statistics displayed in the Results window and on graphs for the output. For example:=RiskOutput(“Part Height”,,RiskSixSigma(0.88,0.95,0.915,1.5,6))specifies an LSL of 0.88, a USL of 0.95, target value of 0.915, long term shift of 1.5, and a number of standard deviations of 6 for the output Part Height. You can also use cell referencing in the RiskSixSigma property function.These values are used in calculating Six Sigma statistics displayed in the Results window and as markers on graphs for the output.When @RISK detects a RiskSixSigma property function in an output, it automatically displays the available Six Sigma statistics on the simulation results for the output in the Results Summary window and adds markers for the entered LSL, USL and Target values to graphs of simulation results for the output.You can type the RiskOutput function, together with the RiskSixSigma function, directly into the cell’s formula, or you can have @RISK help you do this using the user interface.@RISK | Six Sigma Guide From the Add Output dialog, click the Settings/Actions button at the bottom of the window and select ‘Sho w Advanced Properties’:The Six Sigma tab of the dialog contains fields for configuring all the options:Clicking the OK button will add the RiskOutput function, together with the RiskSixSigma function, to the ce ll’s formula.The options available in the Six Sigma tab are:Calculate Capability Metrics for This Output - Specifies that capability metrics will be calculated and displayed in reports and graphs for the output. These metrics will use the entered LSL, USL and Target values.LSL, USL and Target - Sets the LSL (Lower Specification Limit), USL (Upper Specification Limit) and Target values for the output.Use Long Term Shift and Shift -Specifies an optional shift for calculation of long-term capability metrics.@RISK | Six Sigma GuideUpper/Lower X Bound - The number of standard deviations to the right or the left of the mean for calculating the upper or lower X-axis values.Six Sigma Statistics Functions@RISK includes a set of Six Sigma statistics functions which can be entered directly into a spreadsheet model to perform Six Sigma calculations. For example, consider the simple model shown below:Cell C15 contains a RiskOutput function with a RiskSixSigma property function:=RiskOutput(C14,,,RiskSixSigma(C4,C5,C6,0,6)) +RiskNormal(C10,C11)The green cells in column C contain the following Six Sigma statistics functions:=RiskCpk(C15)=RiskPNC(C15)=RiskDPM(C15)These statistics functions, like other @RISK statistics functions, show relevant results only after a simulation has been run. They rely on the parameter values (LSL, USL, and so on) in the RiskSixSigma property function in cell C15 for their values.Note also in this screenshot how the graph of the output in C15 shows the LSL, Target, and USL as markers. These markers also rely on information provided by the RiskSixSigma property function in cell C15.@RISK | Six Sigma Guide The complete list of Six Sigma statistic function can be found on @RISK’s Function menu:Six Sigma and the Results Summary Window@RISK’s Results Summary window summarizes the results of your model and displays thumbnail graphs and summary statistics for your simulated output cells and input distributions. When @RISK detects a RiskSixSigma property function in an output, it also will automatically display the available Six Sigma statistics for the simulation results for any output that utilizes Six Sigma.@RISK | Six Sigma GuideThis table can be exported to Excel, the printer, or a PDF file by clicking the Export button in the bottom right corner of the window.Clicking the Table Settings item from the Settings/Actions menu displays a dialog from which you can customize which statistics to display in the window:Six Sigma Markers on GraphsWhen @RISK detects a RiskSixSigma property function in an output, it adds markers for the LSL, USL and Target values to graphs of simulation results for the output. It also adds Six Sigma statistics to the statistics grid to the right of the graph.@RISK | Six Sigma GuideYou can configure the display of both the markers and the grid from by choosing the Graph Formatting Options item on the Settings/Action menu.@RISK | Six Sigma GuideSix Sigma Example ModelsA number of examples models that demonstrate the use o f Six Sigma can be found on Palisade’s website. Please visit https:///models/ and search for Six Sigma (results pictured below).。

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– Convexity gives: (1) local optimal global optimal, (2) duality (certificates of optimality or unboundedness)
• • • •
Linear -> Second-order Cone -> Semidefinite Deterministic vs Stochastic vs Robust Finite vs Semi-Infinite vs Infinite Dimensional Calculus of Variations / Optimal Control / Dynamic Programming
Usage
• • • • Operations Research Design Control Imaging / Signal Processing
– Imaging is boarder than “taking a picture”. It refers to the generation and representation of an object in a visual way, subject to analysis and understanding.
Formulation
An Example
What is a Solution
• Solution = Optimal Solution = Global Solution = Global Minimizer / Maximizer • Global minimizer: best of all feasible • Local minimizer: best of all in a certain neighborhood
– local = global – Existence of a dual solution
– Variables – Objective – Feasible set
• Other names: math programming (planning), energy minimization
Major Subfields
This is not an exact partition! • Continues (feasible set is a continuum) vs Discrete • Linear vs Quadratic vs Nonlinear vs Integer vs MixedInteger vs Combinatorial • Convex vs Non-convex
• chastic Economics / Finance Medical Treatment Management Planning
Everyday Use of Optimization
• Commuting
– Shortest / quickest / simplest paths
Methods
• • • • • • • • • • Combinatorial Derivative-Free First-Order Conjugate Gradient Second-Order (Newton / Quasi-Newton) Simplex Ellipsoid / Interior-Point Line Search Direct / Patterned Search Meta Heuristics (Genetic / Tabu / Ant Colony …)
•
Recognize a Solution
• Recognize a local solution for unconstrained probs
– First-order condition – Second-order necessary / sufficient condition
• Constrained problems also asks for feasibility • For convex problems
• Time management
– Make study most efficient, maximize relaxation time
• Investing
– Maximize return, minimize risk
• Spending
– Find the best price / value
A Brief Introduction to Optimization
Wotao YIN
What is Optimization
• Something different people define it in very different way, and it is widely abused • Mathematically, optimization is to minimize or maximize a function by choosing the values of variables from within an allowed set. • 3 fundamental elements