2007年外文翻譯--用遺傳算法解決設(shè)施布局問題（節(jié)選）

1、<p>　　2100英文單詞，12000英文字符，中文3700字</p><p>　　文獻出處：Mihajlovi? I, ?ivkovi? ?, ?trbac N. Using genetic algorithms to resolve facility layout problem[J]. Serbian Journal of Management, 2007, 2(1): 35-46.</p

2、><p>　　USING GENETIC ALGORITHMS TO RESOLVE FACILITY LAYOUT PROBLEM</p><p>　　University of Belgrade, Technical Faculty at Bor,</p><p>　　Vojske Jugoslavije 12, 19210 Bor, Serbia</p>

3、;<p>　　(Received 12 May 2006; accepted 23 July 2006)</p><p>　　Abstract: The component layout problem requires efficient search of large, discontinuous spaces. The efficient layout planning of a produc

4、tion site is a fundamental task to any project undertaking. This paper describes a genetic algorithm (GA) to solve the problem of optimal facilities layout in manufacturing system design so that material-handling costs a

5、re minimized. The performance of the proposed heuristic is tested over problems selected from the literature. Computational results indicate t</p><p>　　Keywords: facility layout; flexible manufacturing; stoc

6、hastic programming</p><p>　　1. INTRODUCTION</p><p>　　Component layout plays an important role in the design and usability of many engineering products. The layout problem is also classified unde

7、r the headings of packing, packaging, configuration, container stuffing, pallet loading or spatial arrangement in the literature. The problem involves the placement of components in an available space such that a set of

8、objectives</p><p>　　can be optimized while satisfying optional spatial of performance constraints.</p><p>　　Current tools available in practice to designers to aid in the general mechanical layo

9、ut process mostly remain at the stages of physical or electronic models with the assistance of manual adjustment and visual feedback.</p><p>　　The difficulty in automating the mechanical and electromechanica

10、l layout processes stems from: (1) the modeling of the design objectives and constraints; (2) the constraints; (3) the identification of appropriate optimization search strategies.</p><p>　　A number of desig

11、n goals can be modeled as layout objectives. In addition, a set of constrains often has to be satisfied to ensure the applicability of the layouts. Efficient calculations of objectives and constraints are necessary to so

12、lve the layout problems in reasonable time since the analysis of objectives and constraints can be computationally expensive and a large number of evaluations may be required to achieve convergence. The search space of t

13、he layout problem is non-linear and multimo</p><p>　　The layout goals are usually formulated as objective functions. The objectives may reflect the cost, quality, performance and service requirements. Variou

14、s constraints may be necessary to specify spatial relationships between components. The specifications of components, objectives,</p><p>　　constraints, and topological connections define a layout problem and

15、 an optimization search algorithm takes the problem formulation and identifies promising solution by evaluating design alternatives and evolving design states. Analysis of objectives and constraints vary from problem<

16、/p><p>　　to problem. However, the optimization search technique and geometric representation and the resulting interference evaluation are problem independent and are,thus, the focus for a generic layout tool[1

17、].</p><p>　　The primary objective of the design problem is to minimize the costs associatedwith production and materials movement layout, semiconductor manufacturing andservice center layout. For US manufact

18、urers,between 20% and 50% of total operating expenses are spent on material handling and an appropriate facilities design can reduce these costs by at least 10%-30% [2,3].</p><p>　　Altering facility designs

19、due to incorrect decisions, forecasts or assumptions usually involves considerable cost, time and disruption of activities. On the other hand,good design decisions can reap economic and operational benefits for a long –t

20、ime period. Therefore, the critical aspects are designs that translate readily into physical reality and designs that are "robust" to departures from assumptions.</p><p>　　The project manager or pl

21、anner usually performs the task of preparing the layout based on his/her own knowledge and expertise. Apparently, this could result in layouts that differ significantly from one person to another. To put this task into m

22、ore perspective, researchers have introduced different approaches to systematically plan the layout of production sites [4,5]</p><p>　　Facility layout planning can generally be classified according to two ma

23、in aspects: (1) method of facility assignment and (2) layout planning technique.</p><p>　　Mathematical techniques usually involve the identification of one or more goals that the sought layout should strive

24、to achieve. A widely used goal is the minimization of transportation costs on site. These goals are commonly interpreted to what mathematicians term "objective functions". This objective function is then optimi

25、zed under problem-specific constraints to</p><p>　　produce the desired layout. Systems utilizing knowledge-based techniques, in contrast, provide rules that assist planners in layout planning rather than per

26、form the process based purely on a specified optimization goal(s). </p><p>　　Usually the selected fitness function is the minimum total costs of handling of work pieces. In general, those costs are the sum o

27、f the transport costs (these are proportional to the intensity of the flow and distances) and other costs</p><p>　　.An effective facility layout design reduces. manufacturing lead-time, and increases the thr

28、oughput, hence increases overall productivity and efficiency of the plant. The major types of arrangements in manufacturing systems are the process, the flow line or single line, the multi-line, the semi-circular and the

29、 loop layout. The selection of a specific layout defines the way in which parts move from one machine to another machine. The selection of the machine layout is affected by a number of fac</p><p>　　The probl

30、em in machine layout design is to assign machines to locations within a given layout arrangement such that a given performance measure is optimized. The measure used here is the minimization of material handling cost. Th

31、is problem belongs to the non-polynomial hard (NP-hard) class. The problem complexity increases exponentially with the number of possible machine locations.</p><p>　　2. LAYOUT SPACE CHARACTERISTICS AND SOLUT

32、ION APPROACHES</p><p>　　The problem of plant layout involves distributing different departments,equipment, and physical resources as best as possible in the facility, in order to provide greater efficiency i

33、n the production of goods or services.The aims to be achieved when dealing with a problem of the above type can generally be described from two stances. On the one hand, many researchers describe the problem as one of op

34、timizing product flow, from the raw material stage through to the final product. This is achieved</p><p>　　On the other hand, layout can be considered as a design problem. Seen from this angle, solving the p

35、roblem involves not only collecting the quantitative information mentioned above, but also qualitative information, for instance, how different departments are related from the point of view of adjacency. </p><

36、;p>　　The layout space is defined as the mathematical representation of the space of configurations mapped against the cost per configuration. Deterministic algorithms are unable to navigate such a space for globally n

37、ear-optimal solutions, and stochastic algorithms are usually required for solutions of good quality. </p><p>　　The manner of arranging of working devices largely depends on the type of production. NP-hard pr

38、oblems are unsolvable in polynomial time [7](Kusiak 1990). Accurate mathematical solutions do not exist for such problem. The complexity of such problems increases exponentially</p><p>　　with the number of d

39、evices. For instance, a flexible manufacturing system (FMS) consisting of N machines will comprise a solution space with the size N. The problem is theoretically solvable also by testing all possibilities (i.e., random s

40、earching) but practical experience shows that in such</p><p>　　manner of solving the capabilities of either the human or the computer are fast exceeded.For arranging the devices in the FMS the number of poss

41、ible solutions is equal to the number of permutations of N elements. When N is large, it is difficult, if not impossible, to produce the optimal solution within a reasonable time, even with support of a powerful computer

42、. With today's computation power of modern computers it is possible to search for the optimum solution by examining the total space of s</p><p>　　3. LAYOUT SEARCH ALGORITHMS</p><p>　　The lay

43、out problem can have different formulations, but it is usually abstracted as an optimization problem. An assignment of the coordinates and orientations of components that minimizes the cost and satisfies certain placemen

44、t requirements is sought. The problem can be viewed as a generalization of the quadratic assignment problem and therefore belongs to the class of NP-hard problems [9]. Consequently it is highly unlikely that exact soluti

45、on to the general layout problem can be obtained in a</p><p>　　. Heuristic techniques were introduced to seek near-optimal solutions at reasonable computational time for large problems covering several kno

46、wn methods such as improvement, construction and hybrid methods, and graph-theory methods [10]. However, the area of</p><p>　　researches is still always interesting for many researchers, since today the prob

47、lems are solved by new methods and with the possibility of application of much greater computation capacity of modern computers. A variety of optimization algorithms have been applied to the layout problem. Some of the a

48、pproaches may be efficient for specific types of problems, but often placerestrictions on component geometry, allowable degrees-of-freedom, and the objective function formulation. Others are applicab</p><p>

49、　　The target of all methods is the minimum transport costs, but they differ in exactingness, particularly in the length of the procedure. However, it cannot be decided with certainty which basic method and/or method of i

50、mprovement of the layout is the best.</p><p>　　4. Genetic algorithms</p><p>　　Genetic algorithms (GAs) can be defined as meta-heuristics based on the evolutionary</p><p>　　process o

51、f natural systems [11]. Since their inception, they have been applied to numerous optimization problems with highly acceptable results. </p><p>　　GAs are new approach to solving complex problems such as dete

52、rmination of facility layout. GAs became known through work of John Holland in the 1960s [11]. The GAs contain the elements of the methods of blind searching for the solution and of directed and stochastic searching and

53、thus give compromise between the utilization and searching for solution. At the beginning, the search in the entire search space and afterwards, by means of crossover, they search only in the surrounding of the promisin&

54、lt;/p><p>　　The starting point in GA presented in this work was an initial population of solutions (which was randomly generated). Process shop layout and its randomly generated chromosome are shown on figure1.

55、 This population undergoes a number of transformations designed to improve the solutions provided. Such transformations are made in the main loop of the algorithm, and have three basic stages: selection, reproduction, an

56、d replacement, as discussed below. Each of the selection-transformation cycles tha</p><p>　　5. CONCLUSION</p><p>　　This paper proposes an approach using GAs to solve facility layout problems. Al

57、gorithm presented here has theoretical aspect that is finding an ideal workstations position in short time as well as practical significance of saving financials needed for transportation costs in concrete production sys

58、tems. The proposed GA approach produces the optimal machine layout, which minimizes the total material handling cost. The effectiveness of the proposed approach has been examined by using three benchma</p><p&g

59、t;　　problem with less number of iterations. The solutions for the example studied were calculated in reasonably short time on standard PC equipment. Only demerit of GA presented in this work, compared to results presente

60、d by Chan and Tansri [13], Mak, Wong and Chan [14] and El-Baz [6] is that number of trials needed to obtain first optimum is to some extent larger, still overall number of iterations is much lesser (40995 < 63200), wi

61、th same number of experiments. </p><p>　　References</p><p>　　1. Cagan J., Shimida K., Yin S., A Survey of computational approaches to three-dimensional layout problems. Computer-Aided Design, 2

62、002, 34, 597-611.</p><p>　　2. Maller R.D., Gau K.Y., The facility layout problem: recent and emerging trends and perspectives. Journal of Manufacturing Systems, 1996, 15,351-66.</p><p>　　3. Tam

63、K.Y., Genetic algorithms, function optimization, and facility layout design. European Journal of Operational Research, 1992, 63, 322-46.</p><p>　　4. Yeh I.C., Construction-site layout using annealed network.

64、J.Comput.Civ.Eng.,ASCE , 1995,9, 201-208.</p><p>　　5. Cheung S.O., Tong T.K.L., Tam C.M., Site precast yard layout arrangement through genetic algorithms. Autom. Constr., 2002 11, 35-46.</p><p>

65、　　6. El-Baz M. Adel, A genetic algorithm for facility layout problems of different manufacturing environments. Computers and Industrial Engineering, 2004, 47, 233-246.</p><p>　　7. Kusiak A., Intelligent Manu

66、facturing Systems, 1990 (Prentice - Hall Inc.: New Jersey).</p><p>　　8. Ficko M., Brezocnik M., Balic J., Designing the layout-and multiple-rows flexible manufacturing system by genetic algorithms. Journal o

67、f Materials Processing Technology, 2004, 157 150-158.</p><p>　　9. De Bont F., Aerts E., Meehen P., O`Brien C., Placement of shapeable blocks. Philips Journal of Research 1988, 43, 1-22.</p><p>

68、　　10. Kusiak A., Heragy S., The facility layout problem. Eur. J. Operat. Res., 1987, 29, 229-251.</p><p>　　11. Holland H.J., Adaptation in Natural and Artificial Systems, 1975 (University of Michigan Press:

69、 Ann Arbor).</p><p>　　12. Heng L., Love P.E.D., Genetic Search for solving Construction Site-Level Unequal-Area Facility Layout Problems. Automation in Construction, 2000, 9, 217-226.</p><p>　　1

70、3. Chan K.C., Tansri H., A study of genetic crossover operations on the facility layout problem. Computers and Industrial Engineering, 1994, 26(3),537-550.</p><p>　　14. Mak K.L., Wong Y.S., Chan T.S., A gene

71、tic algorithm for facility layout problems. Journal of Computer Integrated Manufacturing Systems, 1998, 1(1-2), 113-123.</p><p>　　用遺傳算法解決設(shè)施布局問題</p><p>　　摘要:設(shè)施布局問題需要大量的，離散空間的有效研究。生產(chǎn)現(xiàn)場有效的布局規(guī)劃對于任何項

72、目都是根本任務(wù)。本文介紹了一種遺傳算法（GA）來解決制造系統(tǒng)的設(shè)施布局設(shè)計的最優(yōu)化，使材料處理成本最小化。通過文獻中選的問題對啟發(fā)式算法的性能進行了測試。計算結(jié)果表明，該方法相比，許多現(xiàn)有的算法在這方面產(chǎn)生更好的效果。與現(xiàn)有的許多研究方法相比，該方法在此領(lǐng)域的效果更好。</p><p>　　關(guān)鍵詞：設(shè)施布局；敏捷制造；隨機規(guī)劃</p><p><b>　　1引言</b>

73、;</p><p>　　元件布局在許多工程產(chǎn)品的設(shè)計和可用性方面都扮演著很重要的角色。布局問題也歸類在包裝，包裝，配置，集裝箱，貨盤裝載或空間等文獻的標題下。這個問題涉及的組件放置在一個可用的空間中，使得一組目標可以優(yōu)化，同時滿足性能約束的可選的空間。</p><p>　　目前在一般的機械布局過程中，設(shè)計師可以利用的工具大多還停留在手動調(diào)節(jié)和視覺反饋的協(xié)助下的物理或電子模型階段。</

74、p><p>　　機械和機電布局流程自動化的困難源于：（1）造型的設(shè)計目標和約束；（2）的限制；（3）確定適當?shù)膬?yōu)化搜索策略。</p><p>　　許多的設(shè)計目標可以建模如布局目標。此外，一組的限制往往必須被滿足，以確保布局的適用性。在合理的時間內(nèi)，高效的計算目標和約束條件是解決的布局問題所必需的，然而分析目標和約束條件的需要大量的計算和評估才能得到交點。布局問題的搜索空間是非線性的和多模式，確

75、定一個合適的算法來導(dǎo)航空間和找到質(zhì)量好的解決方案是至關(guān)重要的。</p><p>　　通常布局目標制定成目標函數(shù)。目標可能反映了成本，質(zhì)量，性能和服務(wù)的要求。各種約束可能是必要的指定組件之間的空間關(guān)系，元件的規(guī)格，目標，約束，拓撲連接定義一個布局的問題，優(yōu)化搜索算法的問題，通過評估設(shè)計方案和不斷變化的設(shè)計狀態(tài)來制定和確定可行的解決方案。目標的分析和約束的變化從一個問題到另一個問題，然而，優(yōu)化搜索技術(shù)、幾何表示和結(jié)果

76、干擾評價都是獨立的課題，因此，一個通用的布局工具成為了焦點。</p><p>　　設(shè)計問題的主要目的是與生產(chǎn)及物料運動的布局，半導(dǎo)體制造和服務(wù)中心的布局，盡量減少成本。美國制造商的總經(jīng)營開支的20％至50％之間，用于材料處理和適當?shù)脑O(shè)施設(shè)計，至少可以減少這些成本10％-30％。</p><p>　　由于不正確的決策改變設(shè)備設(shè)計，預(yù)測或假定通常涉及大量的成本，時間和破壞活動。另一方面，良好的

77、設(shè)計決策，就可以收獲長期的經(jīng)濟和經(jīng)營效益。因此，關(guān)鍵的環(huán)節(jié)是設(shè)計，容易翻譯成物理現(xiàn)實和是“健壯”從假設(shè)出發(fā)的設(shè)計。</p><p>　　項目經(jīng)理或策劃者通常是在他/她自己的知識和專業(yè)技能的基礎(chǔ)上執(zhí)行編制布局的任務(wù)。很明顯，這可能會導(dǎo)致從一個人到另一個人布局明顯不同的結(jié)果。為了把這個任務(wù)分解成更多的角度，研究人員已經(jīng)推出了系統(tǒng)地規(guī)劃生產(chǎn)現(xiàn)場布局的不同的方法。</p><p>　　設(shè)施布局規(guī)劃

78、的分類一般根據(jù)兩個主要的特征：（1）設(shè)施分配方法（2）布局規(guī)劃技術(shù)設(shè)施布局規(guī)劃。</p><p>　　數(shù)學(xué)技術(shù)通常包括一個或多個目標的識別尋求的布局要努力實現(xiàn)。一種被廣泛使用的目標是盡量減少現(xiàn)場的運輸成本。這些目標通常數(shù)學(xué)家被解釋為“目標函數(shù)”，然后根據(jù)問題的具體限制，優(yōu)化該目標函數(shù)生產(chǎn)所需的布局。系統(tǒng)利用知識為基礎(chǔ)的技術(shù)，相反，提供協(xié)助規(guī)劃者布局規(guī)劃的規(guī)則，而不是完全基于一個指定的優(yōu)化目標的執(zhí)行過程。</

79、p><p>　　通常情況下選擇的合格函數(shù)是搬運工件的最低總成本。在一般情況下，這些費用是運輸成本的總和（這些是成比例的流的強度和距離）及其他成本。</p><p>　　一個有效的設(shè)備布局設(shè)計可以降低生產(chǎn)交貨時間，并提高了吞吐量，從而提高整體的生產(chǎn)力和效率的工廠。制造系統(tǒng)中主要的布置類型有：流線或單線，多線，半圓形和環(huán)路布局。選擇一個特定的布局意味著哪些部分從一臺機器移動到另一臺機器的方式。設(shè)備

80、布局的選擇受多個因素的影響，即機器的數(shù)量，可用的空間，操作序列的相似性和使用的材料處理系統(tǒng)。有許多類型的材料搬運設(shè)備，包括自動搬運車，輸送系統(tǒng)，機器人，和其他。材料搬運設(shè)備的選擇對于一個現(xiàn)代制造工廠中的設(shè)計是很重要的。</p><p>　　整機布局設(shè)計中的問題是分配一個給定的布局的位置，如給定的性能指標等是優(yōu)化的。這里使用的措施要盡量減少材料處理成本。這個問題屬于非多項式硬盤（NP-hard）類的。問題復(fù)雜性的增

81、加與可能的機器位置的數(shù)目呈倍數(shù)關(guān)系。</p><p>　　2布局空間特性和解決方法</p><p>　　工廠布局的問題，涉及分配不同的部門，設(shè)備，和物理資源在設(shè)施中盡可能的最優(yōu)化，為了在產(chǎn)品或服務(wù)方面提供更大的效率，實現(xiàn)的目標是在處理上述的問題時可以從兩個角度進行描述。一方面，許多研究人員描述該問題的作為一個優(yōu)化的產(chǎn)品流，從原材料階段到最終產(chǎn)品。這是通過總的材料處理成本最小化。在這個意義上

82、解決問題，需要知道部門之間的距離（通常是從他們的重心），部門與部門之間的旅行的數(shù)目，以及單位成本。</p><p>　　另一方面，布局可以被認為是一個設(shè)計問題。從這個角度來看，解決這個問題不僅涉及收集上述的量化信息也包括定性信息，例如，不同的部門是如何從圖鄰接點有關(guān)。</p><p>　　布局空間被定義為映射針對每個配置的成本的配置空間的數(shù)學(xué)表達式。確定性算法是無法接近最優(yōu)的解決方案為全球

83、導(dǎo)航這樣的空間，并隨機算法通常需要良好的質(zhì)量的解決方案。</p><p>　　安排的工作裝置的方式，在很大程度上取決于生產(chǎn)的類型。 NP-hard的問題在多項式時間是不可解（Kusiak1990）。精確的數(shù)學(xué)解決方案不存在這樣的問題。這樣問題的復(fù)雜性與設(shè)備的數(shù)量呈倍數(shù)關(guān)系。比如，一個靈活的制造系統(tǒng)（FMS）組成的N機器將包括解空間的大小N.理論上是可解的問題也通過測試所有的可能性（即，隨機搜索），但實際經(jīng)驗表明，

84、不管是人類還是計算機解決能力的方式都超過安排在FMS中的設(shè)備的數(shù)目可能的解決方案是等于排列的N個元素的數(shù)目。當N很大時，它是困難的，在合理的時間內(nèi)產(chǎn)生最佳的解決方案是不可能的，即使有一個功能強大的計算機的支持。以今天的現(xiàn)代計算機的計算能力尋找檢查某處總空間尺寸為10的最優(yōu)解決方案是可能的。在大尺寸的問題的情況下使用復(fù)雜的解決方法是必要的，而在研究解決空間要以某種限制自己的方式，并利用可能已經(jīng)研究的解決方案。</p><

85、;p><b>　　3布局搜索算法</b></p><p>　　布局的問題可以有不同的配方，但它通常是抽象為一個優(yōu)化問題。尋求成本降至最低成本，并滿足一定的放置要求的元件坐標和方向的分配。這個問題可以被看作是一個推廣的二次分配問題，因此屬于NP-hard問題之類的。因此它準確的解決總體布局的問題是極不可能的，可以得到的量的時間范圍內(nèi)的大小的問題中的一個多項式，導(dǎo)致大問題的計算時間望而卻步

86、。啟發(fā)式算法通常用來生成可以接受的解決方案。將要討論的，一般的算法通常需要一定程度的（隨機的）干擾以避免局部最優(yōu)解。在過去三年已經(jīng)提出了各種模型和解決方法。</p><p>　　介紹了在合理的計算時間內(nèi)針對大問題用啟發(fā)式技術(shù)尋求接近最優(yōu)的解決方案，覆蓋幾個公知的方法，如改善，建筑和混合方法，圖的理論方法。然而，許多研究人員認為區(qū)域研究仍然是很有趣的，因為今天的問題通過新方法和現(xiàn)代計算機強大的計算能力的應(yīng)用都解決了

87、。各種的優(yōu)化算法已應(yīng)用于的布局問題。一些方法對于特定類型的問題可能是有效率的，但往往在部件的幾何形狀，允許程度的自由，制定目標函數(shù)受到限制。其他適用于更廣泛的問題，望而卻步計算時間長，但可能需要解決簡單的問題。布局算法根據(jù)設(shè)計空間探索使用的搜索策略可以分為不同的類別。</p><p><b>　　4遺傳算法</b></p><p>　　遺傳算法（GAS）可以被定義為基

88、于進化的元啟發(fā)式自然生態(tài)系統(tǒng)的過程。自成立以來，已應(yīng)用于許多優(yōu)化問題的高度可以接受的結(jié)果。遺傳算法是新的方法來解決復(fù)雜的問題，如設(shè)施布局的決策。遺傳算法通過20世紀60年代在約翰荷蘭起作用被廣為人知。遺傳算法包含的元素的盲目搜索的解決的方法，定向和隨機的搜索，從而得到解決和搜索之間的妥協(xié)的利用率。開始在整個搜索空間的搜索后，通過交叉，他們只搜索周圍有前途的解決方案。因此，遺傳算法隨機的，但定向搜索定位的全局最優(yōu)解。</p>

89、<p>　　遺傳算法的起點是在這項工作中提出的解決方案（這是隨機生成的）是一個初始種群。工藝店的布局和隨機產(chǎn)生的染色體上圖所示。這一種群經(jīng)歷了許多旨在改善提供的解決方案的轉(zhuǎn)換。這樣的轉(zhuǎn)換是由在該算法的主循環(huán)中，有三個基本階段：選擇，復(fù)制，和替換，如下面所討論的：每一個選擇的人口經(jīng)歷的轉(zhuǎn)型周期，構(gòu)成了一代人的希望，幾代人一定次數(shù)后，人口將發(fā)展對最佳的解決方案的問題，或者至少是接近最佳的解決方案。選擇階段由采樣的初始種群，從而獲

90、得一個新的與相同數(shù)量的人口作為最初的一個個人。這個階段的目的是提高人口素質(zhì)有利于更充分的一個特定的問題（一個人的素質(zhì)是衡量通過計算其健身，式（1），這表明一個好的解決方案是使用）的個人。</p><p><b>　　5結(jié)論</b></p><p>　　本文提出了一種方法，使用遺傳算法解決設(shè)備布局問題。這里介紹的算法在很短的時間找到一個理想的工作站位置具有重要的理論方面

91、意義，在節(jié)約混凝土生產(chǎn)系統(tǒng)所需的運輸成本財務(wù)狀況具有現(xiàn)實意義。建議的的GA方法產(chǎn)生最佳的機器布局，最大限度地減少了總材料處理成本。已審查通過使用三個基準問題所提出的方法的有效性。比較結(jié)果表明，該方法是有效的，并具有獲得的最佳設(shè)備布局解決方案較高的機會</p><p>　　問題的迭代次數(shù)少。在相當短的時間標準PC設(shè)備的解決方案，例如研究進行了計算。只有GA提出在這項工作中的缺點，比Chan和Tansri提出的結(jié)果，