基于遗传算法的双目标设施布置方法研究
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摘要
随着制造业竞争的加剧,越来越多的人都意识到物流在企业发展中所起到的重要作用,设施布置作为物流的一部分也逐渐为人们所关注。合理的设施布置可以有效的降低物流搬运成本、提高产品质量、缩短订货提前期、优化布置环境。
本文介绍了多种典型设施布置问题的模型、设施布置方法及其求解算法,分析了它们在求解设施布置问题中的优点和不足。在吸收结合这些模型和方法的基础上,针对它们的不足,提出了含墙体及通道的双目标设施布置方法。首先,在传统设施布置模型和SLP方法的基础上,结合企业的实际布置需要,提出了含墙体及通道的双目标设施布置模型;然后,运用改进后的遗传算法对其进行求解,通过多次迭代得出候选方案,供决策者选择。
本文所建立的含墙体及通道的双目标设施布置模型有很强的系统性和实用性。首先,模型所要解决的设施面积不等、设施形状不规则的连续型设施布置问题更加符合现实布置要求,加入墙体及通道后更增加了模型的实用性;其次,模型在传统的设施布置模型的基础上加入非物流相关关系的目标,能够使布置在物料搬运成本和非物流相关性两方面都得到优化;所采用的图论中最短路问题的Dijkstra’s方法求解带通道的设施间距离,比直线距离、矩形距离等计算方式更加能够准确、客观的表示设施间的实际距离,从而保证最终优化结果的准确性。在遗传算法的设计上针对不同的染色体及染色体区段运用不同的遗传操作,确保算法的有效性和全局优化性;采用修正操作解决解码过程中空白区域的问题,提高了设施布置面积的利用率。最后在实证研究部分运用C#语言编写遗传算法程序实现算法的设计和运算,得出优化方案,在结果分析的基础上得出该算法的优越性结论。
Nowadays, more and more people have realized the importance of logistics in enterprises in the competitive environment of the manufacturing industry. So does the facility layout problem. Reasonable facility layout can reduce the transportation costs of logistics, improve the quality of products, shorten the lead time, and improve the working environment effectively.
This paper describes several classical facility layout problems, and discuses the methods and the algorithms to these problems. By analyzing the advantages and disadvantages of these approaches, this paper proposes a bi-criteria mathematic model for the facility layout problems with inner walls and passages. First, establishes a bi-criteria layout model that has walls and passages based on the traditional facility layout models and SLP method combining the actual needs of enterprises. Then, gives some candidate solutions maked by the improved genetic algorithm for decision-makers to choose.
The model this paper proposes has highly systematic and practical use. First, the continuous layout problem of unequal area and irregular shape of facilities is more practical than others, and it is better when adding the factors of inner walls and passages; Second, it is more optimized when concerning material handing costs together with nonmaterial relation requirements; the shortest path and distance between two facilities is calculated using Dijkstra’s algorithm of graph theory, and it is more accurate and objective than traditional methods of straight line or rectangular distance. For the design of the proposed genetic algorithm, different genetic operation is imposed on different chromosomes and segments to ensure the effectiveness and overall optimization of the algorithm; by using the refinement operation in the proposed algorithm, this paper has handled void spaces generated during the decoding process, and improved the utilization of the layout area. Finally, in the part of the empirical study, this paper uses C# language to achieve the genetic algorithm, and draw solutions of the genetic algorithm which can prove the superiority of the algorithm.
本文介绍了多种典型设施布置问题的模型、设施布置方法及其求解算法,分析了它们在求解设施布置问题中的优点和不足。在吸收结合这些模型和方法的基础上,针对它们的不足,提出了含墙体及通道的双目标设施布置方法。首先,在传统设施布置模型和SLP方法的基础上,结合企业的实际布置需要,提出了含墙体及通道的双目标设施布置模型;然后,运用改进后的遗传算法对其进行求解,通过多次迭代得出候选方案,供决策者选择。
本文所建立的含墙体及通道的双目标设施布置模型有很强的系统性和实用性。首先,模型所要解决的设施面积不等、设施形状不规则的连续型设施布置问题更加符合现实布置要求,加入墙体及通道后更增加了模型的实用性;其次,模型在传统的设施布置模型的基础上加入非物流相关关系的目标,能够使布置在物料搬运成本和非物流相关性两方面都得到优化;所采用的图论中最短路问题的Dijkstra’s方法求解带通道的设施间距离,比直线距离、矩形距离等计算方式更加能够准确、客观的表示设施间的实际距离,从而保证最终优化结果的准确性。在遗传算法的设计上针对不同的染色体及染色体区段运用不同的遗传操作,确保算法的有效性和全局优化性;采用修正操作解决解码过程中空白区域的问题,提高了设施布置面积的利用率。最后在实证研究部分运用C#语言编写遗传算法程序实现算法的设计和运算,得出优化方案,在结果分析的基础上得出该算法的优越性结论。
Nowadays, more and more people have realized the importance of logistics in enterprises in the competitive environment of the manufacturing industry. So does the facility layout problem. Reasonable facility layout can reduce the transportation costs of logistics, improve the quality of products, shorten the lead time, and improve the working environment effectively.
This paper describes several classical facility layout problems, and discuses the methods and the algorithms to these problems. By analyzing the advantages and disadvantages of these approaches, this paper proposes a bi-criteria mathematic model for the facility layout problems with inner walls and passages. First, establishes a bi-criteria layout model that has walls and passages based on the traditional facility layout models and SLP method combining the actual needs of enterprises. Then, gives some candidate solutions maked by the improved genetic algorithm for decision-makers to choose.
The model this paper proposes has highly systematic and practical use. First, the continuous layout problem of unequal area and irregular shape of facilities is more practical than others, and it is better when adding the factors of inner walls and passages; Second, it is more optimized when concerning material handing costs together with nonmaterial relation requirements; the shortest path and distance between two facilities is calculated using Dijkstra’s algorithm of graph theory, and it is more accurate and objective than traditional methods of straight line or rectangular distance. For the design of the proposed genetic algorithm, different genetic operation is imposed on different chromosomes and segments to ensure the effectiveness and overall optimization of the algorithm; by using the refinement operation in the proposed algorithm, this paper has handled void spaces generated during the decoding process, and improved the utilization of the layout area. Finally, in the part of the empirical study, this paper uses C# language to achieve the genetic algorithm, and draw solutions of the genetic algorithm which can prove the superiority of the algorithm.
引文
[1]王家善,设施规划与设计,北京:机械工业出版社,1995,34~54
[2]Koopmans T-C, Beckmann M, Assignment problems and the location of economic activities Econometrical, 1957, 25(1):53~76
[3]Meller R-D, Gau K-Y, Facility layout objective functions and robust layouts, International Journal of Production Research, 1996, 34(10):2727~2742
[4]Armour G-C, BuOa E-S, A heuristic algorithm and simulation approach to relative location of facilities, International Journal of Management Science, 1963, 9(1):294~309
[5]Seehof J-M, Evans W-O, Automated layout design program, Journal of Industrial Engineering, 1967, 18:690~695
[6]Lee R, Moore J-M, CORELAP-computerized relationship layout planning, Journal of Industrial Engineering, 1967, 18(3):195~200
[7] Khalil T-M, Facilities relative allocation technique (FRAT), International Journal of Production Research, 1973, 11(1):183~194
[8]Tompkins J-A, Reed R-J, An applied model for the facilities design problem, International Journal of Production Research, 1976,14(5):583~595
[9]Scriabin M, Vergin R-C, A cluster analytic approach to facility layout, International Journal of Management Science, 1985, 31(1):33~49
[10]Drezner Z, A heuristic procedure for the layout of a large number of facilities, International Journal of Management Science, 1987, 33(7):907~915
[11]Hassan M-M-D, Hogg G-L, Smith D-R, SHAPE: a construction algorithm for area placement evaluation. International Journal of Production Research, 1986, 24(5):1283~1295
[12]Tam K-Y, Li S-G, A hierarchical approach to the facility layout problem, International Journal of Production Research, 1991, 29(1):165~184
[13]van Camp D-J, Carter M-W, Vannelli A, A nonlinear optimization approach for solving facility layout problems, European Journal of Operational Research, 1991, 57(2):174~189
[14]Tam K-Y, A simulated annealing algorithm for allocating space to manufacturing cells, International Journal of Production Research, 1992, 30(1):63~87
[15]Tam K-Y, Genetic algorithms, function optimization and facility layout design, European Journal of Operational Research, 1992, 63(2):322~346
[16]Goetschalckx M, An interactive layout heuristic based on hexagonal adjacency graphs, European Journal of Operational Research, 1992, 63:304~321
[17]Kim J-Y, Kim Y-D, Graph theoretic heuristics for unequal-sized facility layout problems, International Journal of Management Science, 1995, 23(4):391~401
[18]王俊峰,M台设备单行布置问题的一种新解法,安徽工学院学报,1995,14 (3):82~87
[19]张毕西,刘永清,多对象生产单元设备双行布置优化分析,北京航空航天大学学报,1999,27(5):34~45
[20]王定益,王丽亚,一种改进遗传算法在生产车间设备布局中的应用,计算机工程与应用,2005,14:190~193
[21]吴永忠,吴永明,袁红亮,家族保护遗传算法解决设备布局问题的研究,计算机工程,2005,31(6):186~188
[22]李广强,霍军周,膝弘飞,并行混合遗传算法及其在布局设计中的应用,计算机工程,2003,29(17):6~8
[23]R J Dakin, A tree-search algorithm for mixed integer programming problems, The Computer Journal, 1965, 8(3):250~255
[24]邱枫,基于单亲遗传算法的设备布局问题研究:[硕士学位论文],天津;天津大学,2007
[25]Gilmore P C, Optimal and suboptimal algorithms for the quadratic assignment problem, Journal of the Society for Industrial and Applied Mathematic, 1962, 10: 305~313
[26]Lawler E L, The quadratic assignment problem, Management Science, 1963, 9:586~599
[27]Bazaraa M S, Computerized layout design: A branch and bound approach, AIIE Transactions, 1975, 7(4):432~437
[28]Gomory R E, Outline of an algorithm for integer solutions to linear problem, Bulletin of the American Mathematical Society, 1958, 64(5):54~65
[29]Burkad R E, Bonninger T, A heuristic for quadratic Boolean program with applications to quadratic assignment problems, European Journal of Operational Research, 1983, 13:374~386
[30]Wimmert R J, A mathematical method for equipment location, The Journal of Industrial Engineering, 1958, 9:498~505
[31]Bazaraa M S, Kirca O, A branch-and-bound-based heuristic for solving the QAP, Naval Research Logistics Quarterly, 1983, 30:287~304
[32]Tompkins J A, Reed R Jr, An applied model for the facilities design problem, International Journal of Productions Research, 1973, 14(5):583~595
[33]Scriabin M, Vergin R C, A cluster-analytic approach to facility layout, Management Science, 1985, 31(1):33~49
[34]R E Burkard, F Rendl, A Thermodynamically motivated simulation procedure for combinatorial optimization problems, European Journal of Operational Research, 1984, 17:169~174
[35]V. Madhusudanan Pillai, Bhavani Sankar Gudivada, A Simulated Annealing Algorithm for Linear Sequencing of Machines for Layout Design, Sixth Int. Conf. on Opers. and Quant. Management, 2005, August 9-11:435~442
[36]Heragu S S, ALFA A S, Experimental analysis of simulated annealing based algorithms for the layout problem, European journal of operational research,1992, 57(2):190~202
[37]苗玉彬,刘成良,赵爽等,基于人机交互的遗传退火算法及其有履带起重机布局设计中的应用,中国机械工程,2004,15(3):238~241
[38]F Glover, Tabu Search-PartⅠ,Operations Research Society of America, 1989, 1(3):190~206
[39]Alan R. McKendall, Jr. J.R. Jaramillo, A tabu search heuristic for the dynamic space allocation problem, Computers& Operations Rearch, 2006, (3):768~789
[40]Holland J H, Adaptation in Natural and Artificial Systems, MIT Press, 1975.10~46
[41]M.Solimanpur, Prem Vrat, Ravi Shankar. An ant algorithm for the single row layout problem in flexible manufacturing systems, Computers& Operations Research, 2005, (32):583~598
[42]张亚南,阚树林,王越,用蚁群算法解决动态设施布置问题,工业工程,2007,(3):107~111
[43]J. D. Bagley, The Behavior of Adaptive System Which Employ Genetic and Correlation Algorithm, Dissertation Abstracts International, 1967, 28(12):8~89
[44]J. H. Holland, Adaptation in Natural and Artisficial Systems, The university of Michigan press, 1975
[45]D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning. Adaptation Wesley Publishing, 1989
[46]M. Adel, A genetic algorithm for facility layout problems of different manufacturing environments, Computers& Industrial Engineering, 2004, (11):233~246
[47]K. L. Mak, Y. S. Wong, F. T. S. Chan, A genetic algorithm for facility layout problems, Computer Integrated Manufacturing Systems, 1998, (3):113~127
[48]Ponnambalam S G, Ramkumar V.A, genetic Algorithm for the Design of a Single–row Layout in Automated Manufacturing Systems, International Journal of Advanced Manufacturing Technology, 2001, 18(7):512~519
[49]G. Q. Zhang, K. K. Lai, Combining path relinking and genetic algorithms for the multiple-level warehouse layout problem, European Journal of Operational Research, 2006, 169(2):413~425
[50]Gomez A, Fernandez Q, Dela Fuente, Garcia D, Using Genetic Algorithms to Resolve Layout Problems in Facilities Where there are Aisles, International Journal of Production Economics, 2003, 84(3):271~282
[51]Lee K Y, Rob M I, Jeong H S, An Improved Genetic Algorithm for Multi-floor Facility Layout Problems Having Inner Structure Walls and Passages, Computer Operations Research, 2003, 30(1):117~138
[52]Young Hae Lee, Moon Hwan Lee, A shape-based block layout approach to facility layout problems using hybrid genetic algorithm, Computers& Industrial Engineering, 2002, 42(2):237~248
[53]G. Aiello, M. Enea, G. Galante, A multi-objective approach to facility layout problem by genetic search algorithm and Electre method, Robotics and Computer-Integrated Manufacturing, 2006, 22(5):447~455
[54]王丽薇,遗传算法的研究与应用:[博士学位论文],哈尔滨,哈尔滨工业大学,1994
[55]李郝林,杨敏,基于生物遗传算法的车间布局优化算法,机械制造与研究,2001(4):35~38
[56]姚冠新,刘正刚,设施布置问题的非线性目标规划模型及其遗传算法,江苏理工大学学报,2001,(2):57~61
[57]龚全胜,李世其,基于遗传算法的制造系统设备布局设计,计算机工程与应用,2004,26:202~205
[58]申建刚,王理,邱珮强,基于遗传算法的设备布置优化算法,北京航空航天大学学报,2009,35(10):1241~1244
[59]朱颢,曾益坤,基于多层遗传算法的柔性Job Shop调度问题的研究,微型机与应用,2009,28(15):68~71
[60]Goldberg. D, Genetic Algorithms in Search Optimization and Machine Learning, Addison-Wesley, Reading, MA, 1989
[61]玄光男,承润伟,遗传算法与工程设计(汪定伟等),北京:科学出版社,2000
[62]Koopmans T C, Beckman M, Assignment problems and the location of economic activities, Econometrica, 1957, 25:53~76
[63]钟建平,制造企业设施布局优化方法研究:[硕士学位论文],重庆;重庆大学,2009
[64]Kusiak A, Heragu S S, The facility layout problem, European Journal of Operational Research, 1987, 29:229~251
[65]Lawler E L, The quadratic assignment problem, Management Science,1963, 9:586~599
[66]Bazaraa M S, Sherali M D, Benders’partitioning scheme applied to a new formulation of the quadratic assignment problem, Naval Research Logistics Quarterly, 1980, 27(1):29~41
[67]黄小荣,基于遗传算法的双阶段设施布置方法研究:[硕士学位论文],天津;天津大学,2008
[68]Foulds L R, Robinson D F, A strategy for solving the plant layout problem, Operations Research Quarterly, 1976, 27(4):845~855
[69]张承谦,SLP及其在调整生产布局中的应用,运筹与管理,1995,4(4):45~50
[70]刘旺盛,兰培真,系统布置设计——SLP法的改进研究,权威论坛,2006(11):90~94
[71]杨建华,彭丽静,杨永清,基于SLP和SHA结合的企业物流系统平面再布置设计,物流与采购研究,2009,530(19):8~13
[72]吴育华,杜纲,管理科学基础,天津:天津大学出版社,2006.113~120
[73]王凌等,车间调度及其遗传算法,北京:清华大学出版社,2006.44~56
[74]Cohon J-L, Multi-objective programming and planning, New York: Academic Press, 1978
[75]De Jong K A, An Analysis of the Behavior of a Class of Genetic Adaptive Systems: [Ph. D Dissertation], University of Michigan, 1975
[76]Jomikow C Z, Michalewicz Z, An Experimental Comparison of Binary and Floating Point Representations in Genetic Algorithm, Morgan Kaufmann,1991,31~36.
[77]Cheng R and Gen M, Genetic search for facility layout design under inter-flows uncertainty, Japanese Journal of Fuzzy Theory and Systems, 1996,8(2):335～346
[78]Rosenblatt M, The dynamics of plant layout, Management Science, 1986, (32):76~86
[2]Koopmans T-C, Beckmann M, Assignment problems and the location of economic activities Econometrical, 1957, 25(1):53~76
[3]Meller R-D, Gau K-Y, Facility layout objective functions and robust layouts, International Journal of Production Research, 1996, 34(10):2727~2742
[4]Armour G-C, BuOa E-S, A heuristic algorithm and simulation approach to relative location of facilities, International Journal of Management Science, 1963, 9(1):294~309
[5]Seehof J-M, Evans W-O, Automated layout design program, Journal of Industrial Engineering, 1967, 18:690~695
[6]Lee R, Moore J-M, CORELAP-computerized relationship layout planning, Journal of Industrial Engineering, 1967, 18(3):195~200
[7] Khalil T-M, Facilities relative allocation technique (FRAT), International Journal of Production Research, 1973, 11(1):183~194
[8]Tompkins J-A, Reed R-J, An applied model for the facilities design problem, International Journal of Production Research, 1976,14(5):583~595
[9]Scriabin M, Vergin R-C, A cluster analytic approach to facility layout, International Journal of Management Science, 1985, 31(1):33~49
[10]Drezner Z, A heuristic procedure for the layout of a large number of facilities, International Journal of Management Science, 1987, 33(7):907~915
[11]Hassan M-M-D, Hogg G-L, Smith D-R, SHAPE: a construction algorithm for area placement evaluation. International Journal of Production Research, 1986, 24(5):1283~1295
[12]Tam K-Y, Li S-G, A hierarchical approach to the facility layout problem, International Journal of Production Research, 1991, 29(1):165~184
[13]van Camp D-J, Carter M-W, Vannelli A, A nonlinear optimization approach for solving facility layout problems, European Journal of Operational Research, 1991, 57(2):174~189
[14]Tam K-Y, A simulated annealing algorithm for allocating space to manufacturing cells, International Journal of Production Research, 1992, 30(1):63~87
[15]Tam K-Y, Genetic algorithms, function optimization and facility layout design, European Journal of Operational Research, 1992, 63(2):322~346
[16]Goetschalckx M, An interactive layout heuristic based on hexagonal adjacency graphs, European Journal of Operational Research, 1992, 63:304~321
[17]Kim J-Y, Kim Y-D, Graph theoretic heuristics for unequal-sized facility layout problems, International Journal of Management Science, 1995, 23(4):391~401
[18]王俊峰,M台设备单行布置问题的一种新解法,安徽工学院学报,1995,14 (3):82~87
[19]张毕西,刘永清,多对象生产单元设备双行布置优化分析,北京航空航天大学学报,1999,27(5):34~45
[20]王定益,王丽亚,一种改进遗传算法在生产车间设备布局中的应用,计算机工程与应用,2005,14:190~193
[21]吴永忠,吴永明,袁红亮,家族保护遗传算法解决设备布局问题的研究,计算机工程,2005,31(6):186~188
[22]李广强,霍军周,膝弘飞,并行混合遗传算法及其在布局设计中的应用,计算机工程,2003,29(17):6~8
[23]R J Dakin, A tree-search algorithm for mixed integer programming problems, The Computer Journal, 1965, 8(3):250~255
[24]邱枫,基于单亲遗传算法的设备布局问题研究:[硕士学位论文],天津;天津大学,2007
[25]Gilmore P C, Optimal and suboptimal algorithms for the quadratic assignment problem, Journal of the Society for Industrial and Applied Mathematic, 1962, 10: 305~313
[26]Lawler E L, The quadratic assignment problem, Management Science, 1963, 9:586~599
[27]Bazaraa M S, Computerized layout design: A branch and bound approach, AIIE Transactions, 1975, 7(4):432~437
[28]Gomory R E, Outline of an algorithm for integer solutions to linear problem, Bulletin of the American Mathematical Society, 1958, 64(5):54~65
[29]Burkad R E, Bonninger T, A heuristic for quadratic Boolean program with applications to quadratic assignment problems, European Journal of Operational Research, 1983, 13:374~386
[30]Wimmert R J, A mathematical method for equipment location, The Journal of Industrial Engineering, 1958, 9:498~505
[31]Bazaraa M S, Kirca O, A branch-and-bound-based heuristic for solving the QAP, Naval Research Logistics Quarterly, 1983, 30:287~304
[32]Tompkins J A, Reed R Jr, An applied model for the facilities design problem, International Journal of Productions Research, 1973, 14(5):583~595
[33]Scriabin M, Vergin R C, A cluster-analytic approach to facility layout, Management Science, 1985, 31(1):33~49
[34]R E Burkard, F Rendl, A Thermodynamically motivated simulation procedure for combinatorial optimization problems, European Journal of Operational Research, 1984, 17:169~174
[35]V. Madhusudanan Pillai, Bhavani Sankar Gudivada, A Simulated Annealing Algorithm for Linear Sequencing of Machines for Layout Design, Sixth Int. Conf. on Opers. and Quant. Management, 2005, August 9-11:435~442
[36]Heragu S S, ALFA A S, Experimental analysis of simulated annealing based algorithms for the layout problem, European journal of operational research,1992, 57(2):190~202
[37]苗玉彬,刘成良,赵爽等,基于人机交互的遗传退火算法及其有履带起重机布局设计中的应用,中国机械工程,2004,15(3):238~241
[38]F Glover, Tabu Search-PartⅠ,Operations Research Society of America, 1989, 1(3):190~206
[39]Alan R. McKendall, Jr. J.R. Jaramillo, A tabu search heuristic for the dynamic space allocation problem, Computers& Operations Rearch, 2006, (3):768~789
[40]Holland J H, Adaptation in Natural and Artificial Systems, MIT Press, 1975.10~46
[41]M.Solimanpur, Prem Vrat, Ravi Shankar. An ant algorithm for the single row layout problem in flexible manufacturing systems, Computers& Operations Research, 2005, (32):583~598
[42]张亚南,阚树林,王越,用蚁群算法解决动态设施布置问题,工业工程,2007,(3):107~111
[43]J. D. Bagley, The Behavior of Adaptive System Which Employ Genetic and Correlation Algorithm, Dissertation Abstracts International, 1967, 28(12):8~89
[44]J. H. Holland, Adaptation in Natural and Artisficial Systems, The university of Michigan press, 1975
[45]D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning. Adaptation Wesley Publishing, 1989
[46]M. Adel, A genetic algorithm for facility layout problems of different manufacturing environments, Computers& Industrial Engineering, 2004, (11):233~246
[47]K. L. Mak, Y. S. Wong, F. T. S. Chan, A genetic algorithm for facility layout problems, Computer Integrated Manufacturing Systems, 1998, (3):113~127
[48]Ponnambalam S G, Ramkumar V.A, genetic Algorithm for the Design of a Single–row Layout in Automated Manufacturing Systems, International Journal of Advanced Manufacturing Technology, 2001, 18(7):512~519
[49]G. Q. Zhang, K. K. Lai, Combining path relinking and genetic algorithms for the multiple-level warehouse layout problem, European Journal of Operational Research, 2006, 169(2):413~425
[50]Gomez A, Fernandez Q, Dela Fuente, Garcia D, Using Genetic Algorithms to Resolve Layout Problems in Facilities Where there are Aisles, International Journal of Production Economics, 2003, 84(3):271~282
[51]Lee K Y, Rob M I, Jeong H S, An Improved Genetic Algorithm for Multi-floor Facility Layout Problems Having Inner Structure Walls and Passages, Computer Operations Research, 2003, 30(1):117~138
[52]Young Hae Lee, Moon Hwan Lee, A shape-based block layout approach to facility layout problems using hybrid genetic algorithm, Computers& Industrial Engineering, 2002, 42(2):237~248
[53]G. Aiello, M. Enea, G. Galante, A multi-objective approach to facility layout problem by genetic search algorithm and Electre method, Robotics and Computer-Integrated Manufacturing, 2006, 22(5):447~455
[54]王丽薇,遗传算法的研究与应用:[博士学位论文],哈尔滨,哈尔滨工业大学,1994
[55]李郝林,杨敏,基于生物遗传算法的车间布局优化算法,机械制造与研究,2001(4):35~38
[56]姚冠新,刘正刚,设施布置问题的非线性目标规划模型及其遗传算法,江苏理工大学学报,2001,(2):57~61
[57]龚全胜,李世其,基于遗传算法的制造系统设备布局设计,计算机工程与应用,2004,26:202~205
[58]申建刚,王理,邱珮强,基于遗传算法的设备布置优化算法,北京航空航天大学学报,2009,35(10):1241~1244
[59]朱颢,曾益坤,基于多层遗传算法的柔性Job Shop调度问题的研究,微型机与应用,2009,28(15):68~71
[60]Goldberg. D, Genetic Algorithms in Search Optimization and Machine Learning, Addison-Wesley, Reading, MA, 1989
[61]玄光男,承润伟,遗传算法与工程设计(汪定伟等),北京:科学出版社,2000
[62]Koopmans T C, Beckman M, Assignment problems and the location of economic activities, Econometrica, 1957, 25:53~76
[63]钟建平,制造企业设施布局优化方法研究:[硕士学位论文],重庆;重庆大学,2009
[64]Kusiak A, Heragu S S, The facility layout problem, European Journal of Operational Research, 1987, 29:229~251
[65]Lawler E L, The quadratic assignment problem, Management Science,1963, 9:586~599
[66]Bazaraa M S, Sherali M D, Benders’partitioning scheme applied to a new formulation of the quadratic assignment problem, Naval Research Logistics Quarterly, 1980, 27(1):29~41
[67]黄小荣,基于遗传算法的双阶段设施布置方法研究:[硕士学位论文],天津;天津大学,2008
[68]Foulds L R, Robinson D F, A strategy for solving the plant layout problem, Operations Research Quarterly, 1976, 27(4):845~855
[69]张承谦,SLP及其在调整生产布局中的应用,运筹与管理,1995,4(4):45~50
[70]刘旺盛,兰培真,系统布置设计——SLP法的改进研究,权威论坛,2006(11):90~94
[71]杨建华,彭丽静,杨永清,基于SLP和SHA结合的企业物流系统平面再布置设计,物流与采购研究,2009,530(19):8~13
[72]吴育华,杜纲,管理科学基础,天津:天津大学出版社,2006.113~120
[73]王凌等,车间调度及其遗传算法,北京:清华大学出版社,2006.44~56
[74]Cohon J-L, Multi-objective programming and planning, New York: Academic Press, 1978
[75]De Jong K A, An Analysis of the Behavior of a Class of Genetic Adaptive Systems: [Ph. D Dissertation], University of Michigan, 1975
[76]Jomikow C Z, Michalewicz Z, An Experimental Comparison of Binary and Floating Point Representations in Genetic Algorithm, Morgan Kaufmann,1991,31~36.
[77]Cheng R and Gen M, Genetic search for facility layout design under inter-flows uncertainty, Japanese Journal of Fuzzy Theory and Systems, 1996,8(2):335～346
[78]Rosenblatt M, The dynamics of plant layout, Management Science, 1986, (32):76~86