Advertisement

Journal of Intelligent Manufacturing

, Volume 30, Issue 8, pp 2835–2852 | Cite as

An immune system based algorithm for cell formation problem

  • Berna H. UlutasEmail author
Article

Abstract

Technological developments enable the design and manufacturing of products tailored to individual consumers. Cellular Manufacturing Systems (CMS) can be considered as to ease flexibility, to reduce setup time, throughput time, work-in-process inventories, and material handling costs. Cell formation problem (CFP) that is one of the critical CMS design problems is the assignment of parts and machines to specific cells based on their similarity. This study introduces a Clonal Selection Algorithm (CSA) with a novel encoding structure that is efficient to solve real-sized problems. Unlike the methods in literature that define the number of cells as a constant number, this algorithm is significant because it can obtain the optimum number of cell to generate best efficacy value. Proposed CSA is tested by using 67 (35 well-known and 32 less-known) test problems. CSA obtains the same 63 best-known optimal solutions, provides solutions for the 3 of the well-known test problem and a new solution for the largest test problem (50 machine 150 part) that was not possible to be solved by the mixed integer linear programming model due to the high computational complexity. Final CSA grouping results are illustrated with figures to attract attention to the singleton and residual cells.

Keywords

Artificial immune systems Cell formation problem Clonal selection algorithm Group technology 

References

  1. Adil, G. K., Rajamani, D., & Strong, D. (1996). Cell formation considering alternate routings. International Journal of Production Research, 34(5), 1361–1380.Google Scholar
  2. Arkat, A., Hosseini, L., & Hosseinabadi, F. M. (2011). Minimization of exceptional elements and voids in the cell Formation problem using a multi-objective genetic algorithm. Expert Systems with Applications, 38, 9597–9602.Google Scholar
  3. Arvindh, B., & Irani, S. A. (1994). Cell formation: The need for an integrated solution of the sub problem. International Journal of Production Research, 32(5), 1197–1218.Google Scholar
  4. Askin, R. G., & Subramanian, S. (1987). A cost-based heuristic for group technology configuration. International Journal of Production Research, 25, 101–113.Google Scholar
  5. Boctor, F. A. (1991). Linear formulation of the machine-part cell formation problem. International Journal of Production Research, 29(2), 343–356.Google Scholar
  6. Boe, W., & Cheng, C. H. (1991). A close neighbor algorithm for designing cellular manufacturing systems. International Journal of Production Research, 29(10), 2097–2116.Google Scholar
  7. Brownlee J. (2011). Clever algorithms: Nature-inspired programming recipes. Creative Commons 280, http://www.cleveralgorithms.com/. Last accessed February 2018.
  8. Brown, E., & Sumichrast, R. (2001). CF-GGA: a grouping genetic algorithm for the cell formation problem. International Journal of Production Research, 36, 3651–3669.Google Scholar
  9. Bychkov, I., & Batsyn, M. (2018). An efficient exact model for the cell formation problem with a variable number of production cells. Computers and Operations Research, 91, 112–120.Google Scholar
  10. Bychkov, I. S., Batsyn, M. V., & Pardalos, P. M. (2014). Exact model for the cell formation problem. Optimization Letters, 8(8), 2203–2210.Google Scholar
  11. Bychkov, I., Batsyn, M., Sukhov, P., & Pardalos, P. M. (2013). Heuristic algorithm for the cell formation problem. Models, algorithms, and technologies for network analysis. Springer Proceedings in Mathematics & Statistics, 59, 43–69.Google Scholar
  12. Carrie, S. (1973). Numerical taxonomy applied to group technology & plant layout. International Journal of Production Research, 11, 399–416.Google Scholar
  13. Chandrasekaran, M. P., & Rajagopalan, R. (1986a). An ideal seed nonhierarchical clustering algorithm for cellular manufacturing. International Journal of Production Research, 24, 451–463.Google Scholar
  14. Chandrasekaran, M. P., & Rajagopalan, R. (1986b). MODROC: An extension of rank order clustering of group technology. International Journal of Production Research, 24(5), 1221–1233.Google Scholar
  15. Chandrasekharan, M. P., & Rajagopalan, R. (1987). ZODIAC: An algorithm for concurrent formation of part-families and machine-cells. International Journal of Production Research, 24(2), 835–850.Google Scholar
  16. Chandrasekharan, M. P., & Rajagopalan, R. (1989). Groupability: Analysis of the properties of binary data matrices for group technology. International Journal of Production Research, 27(6), 1035–1052.Google Scholar
  17. Chan, H. M., & Milner, D. A. (1982). Direct clustering algorithm for group formation in cellular manufacture. Journal of Manufacturing System, 1, 65–75.Google Scholar
  18. Cheng, C., Gupta, Y., Lee, W., & Wong, K. (1998). A TSP-based heuristic for forming machine groups and part families. International Journal of Production Research, 36, 1325–1337.Google Scholar
  19. Dasgupta, D., Ji, Z., & Gonzalez, F. (2003). Artificial immune systems research in the last five years. In Proceedings of the 2003 congress on evolutionary computation conference. Canberra. Australia. (pp. 123–130). December 8–13.Google Scholar
  20. De Castro, L., & Von Zuben, F. J. (1999). Artificial immune systems: Part I: Basic theory & applications. FEEC Univ. Campnas, Campinas, Brasil, ftp://ftp.dca.fee.unicamp.br/pub/docs/vonzuben/tr_dca/trdca0199.pdf. Last accessed January 2018.
  21. Dimopoulos, C., & Mort, N. (2001). A hierarchical clustering methodology based on genetic programming for the solution of simple cell-formation problems. International Journal of Production Research, 39, 1–19.Google Scholar
  22. Dimopoulos, C., & Zalzala, A. (2000). Recent developments in evolutionary computation for manufacturing optimization: problems, solutions, and comparisons. IEEE Transactions on Evolutionary Computatio, 4(2), 93–113.Google Scholar
  23. Farahani, M. H., & Hosseini, L. (2011). An ant colony optimization for the machine-part cell formation problem. International Journal of Computational Intelligence Systems, 4, 486–496.Google Scholar
  24. Goldberg, D. E. (1989). Genetic algorithms: Search, optimization and machine learning. Boston, MA: Addison-Wesley Longman Publishing Co. Inc.Google Scholar
  25. Goncalves, J. F., & Resende, M. G. C. (2004). An evolutionary algorithm for manufacturing cell formation. Computers and Industrial Engineering, 47, 247–273.Google Scholar
  26. Ham I., Hitomi K., & Yoshida T. (1985). Layout planning for group technology. In Group technology. International series in management science/operations research. (pp. 153–169). Dordrecht: Springer.Google Scholar
  27. Harhalakis, G., Ioannou, G., Minis, I., & Nagi, R. (1994). Manufacturing cell formation under random product demand. International Journal of Production Research, 32(1), 47–64.Google Scholar
  28. Hyer, N., & Wemmerlov, U. (1984). Group technology and productivity. Harvard Business Review, 62(4), 140–149.Google Scholar
  29. Islam, K. M. S., & Sarker, B. R. (2000). A similarity coefficient measure and machine parts grouping in cellular manufacturing systems. International Journal of Production Research, 38(3), 699–720.Google Scholar
  30. Islier, A. A. (2001). Forming manufacturing cells by using genetic algorithm. Anadolu University Journal of Science and Technology, 2, 137–157.Google Scholar
  31. Islier, A. A. (2005). Group technology by ants. International Journal of Production Research, 43(5), 913–932.Google Scholar
  32. James, T., Brown, E. C., & Keeling, K. B. (2007). A hybrid grouping genetic algorithm for the cell formation problem. Computers and Operations Research, 34, 2059–2079.Google Scholar
  33. Joines, J., Culberth, C. T., & King, R. E. (1996). Manufacturing cell design: an integer programming model employing genetic algorithms. IEE Transactions, 28, 69–85.Google Scholar
  34. Kamel, M., Ghenniwa, H., & Liu, T. (1994). Machine assignment and part-families formation using group technology. Journal of Intelligent Manufacturing, 5, 225–234.Google Scholar
  35. King, J. R. (1980). Machine-component grouping in production flow analysis: An approach using a rank order clustering algorithm. International Journal of Production Research, 18(2), 213–232.Google Scholar
  36. King, J. R., & Nakornchai, V. (1982). Machine-component group formation in group technology: Review and extension. International Journal of Production Research, 20(2), 117–133.Google Scholar
  37. Kumar, C. S., & Chandrasekharan, M. P. (1990). Grouping efficacy: A quantitative criterion for goodness of block diagonal forms of binary matrices in group technology. International Journal of Production Research, 28, 233–243.Google Scholar
  38. Kumar, K. R., Kusiak, A., & Vannelli, A. (1986). Grouping of parts and components in flexible manufacturing systems. European Journal of Operations Research, 24, 387–397.Google Scholar
  39. Kumar, K. R., & Vannelli, A. (1987). Strategic subcontracting for efficient disaggregated manufacturing. International Journal of Production Research, 25(12), 1715–1728.Google Scholar
  40. Kusiak, A., & Cho, M. (1992). Similarity coefficient algorithm for solving the group technology problem. International Journal of Production Research, 30, 2633–2646.Google Scholar
  41. Kusiak, A., & Chow, W. (1987). Efficient solving of the group technology problem. Journal of Manufacturing Systems, 6(2), 117–124.Google Scholar
  42. Lee, H., Malavi, C. O., & Ramachandran, S. (1992). A self-organizing neural network approach for the design of cellular manufacturing systems. Journal of Intelligent Manufacturing, 3, 325–332.Google Scholar
  43. Li, M. L. (2003). The algorithm for integrating all incidence matrices in multidimensional group technology. International Journal Production Economics, 86, 121–131.Google Scholar
  44. Mahdavi, I., Paydar, M. M., Solimanpur, M., & Heidarzade, A. (2009). Genetic algorithm approach for solving a cell formation problem in cellular manufacturing. Expert Systems with Applications, 36, 6598–6604.Google Scholar
  45. Malavi, C. O., & Ramachandran, S. (1991). Neural network-based design of cellular manufacturing systems. Journal of Intelligent Manufacturing, 2, 305–314.Google Scholar
  46. McCormick, W. T., Schweitzer, P. J., & White, T. W. (1972). Problem decomposition and data reorganization by a clustering technique. Operations Research, 20, 993–1009.Google Scholar
  47. Moon, Y. B. (1992). Establishment of a neurocomputing model for part family/machine group identification. Journal of Intelligent Manufacturing, 3, 173–182.Google Scholar
  48. Moon, Y. B., & Chi, S. C. (1992). Generalized part family formation using neural network techniques. Journal of Manufacturing Systems, 11(3), 149–159.Google Scholar
  49. Mosier, C. T., & Taube, L. (1985a). The facets of group technology & their impact on implementation. Omega, 13(6), 381–391.Google Scholar
  50. Mosier, C. T., & Taube, L. (1985b). Weighted similarity measure heuristics for the group technology machine clustering problem. Omega, 13(6), 577–583.Google Scholar
  51. Nagi, R., Harhalakis, G., & Proth, J. M. (1990). Multiple routeings and capacity considerations in group technology applications. International Journal of Production Research, 28(12), 1243–1257.Google Scholar
  52. Nair, G. J. (1999). Accord: A bicriterion algorithm for cell formation using ordinal and ratio level data. International Journal of Production Research, 37(3), 539–556.Google Scholar
  53. Onwubalu, G. C. (1999). Design of parts for cellular manufacturing using neural network-based approach. Journal of Intelligent Manufacturing, 10, 251–265.Google Scholar
  54. Onwubalu, G. C., & Mutingi, M. (2001). A genetic algorithm approach to cellular manufacturing systems. Computers and Industrial Engineering, 39, 125–44.Google Scholar
  55. Pa Rkin, R. E., & Li, M. L. (1997). The multi-dimensional aspects of a group technology algorithm. International Journal of Production Research, 35(8), 2345–2358.Google Scholar
  56. Papaionnaou, G., & Wilson, J. M. (2010). The evolution of cell formation problem methodologies based on recent studies (1997–2008): Review and directions for future research. European Journal of Operational Research, 206, 509–521.Google Scholar
  57. Sandbothe, R. A. (1998). Two observations on the grouping efficacy measure for goodness of block diagonal forms. International Journal of Production Research, 36(11), 3217–3222.Google Scholar
  58. Sarker, B. R., & Khan, M. (2001). A comparison of existing grouping eciency measures and a new weighted grouping eciency measure. IIE Transactions, 33, 11–27.Google Scholar
  59. Seifoddini, H. (1989). Single linkage versus average linkage clustering in machine cells formation applications. Computers and Industrial Engineering, 16(3), 419–426.Google Scholar
  60. Seifoddini, H., & Djassemi, M. (1991). The production data based similarity coefficient versus Jaccard’s similarity coefficient. Computers Industrial Engineering, 21, 263–266.Google Scholar
  61. Seifoddini, H., & Djassemi, M. (1996). The threshold value of a quality index for formation of cellular manufacturing systems. International Journal of Production Research, 34(12), 3401–3416.Google Scholar
  62. Seifoddini, H., & Wolfe, P. M. (1986). Application of the similarity coefficient method in group technology. IIE Transactions, 18(3), 266–270.Google Scholar
  63. Shargal, M., Shekhar, S., & Irani, S. A. (1995). Evaluation of search algorithms and clustering efficiency measures for machine-part matrix clustering. IIE Transactions, 27(1), 43–59.Google Scholar
  64. Srinivasan, G. (1994). A clustering algorithm for machine cell formation in group technology using minimum spanning trees. International Journal of Production Research, 32(9), 2149–2158.Google Scholar
  65. Srinivasan, G., Narendran, T., & Mahadevan, B. (1990). An assignment model for the part-families problem in group technology. International Journal of Production Research, 28(1), 145–152.Google Scholar
  66. Stanfel, L. (1985). Machine clustering for economic production. Engineering Costs and Production Economics, 9, 73–78.Google Scholar
  67. Talbi, E. (2009). Metaheuristics: From design to implementation (p. 267). New Jersey: Wiley.Google Scholar
  68. Tunnukij, T., & Hicks, C. (2009). An enhanced grouping genetic algorithm for solving the cell formation problem. International Journal of Production Research, 47(7), 1989–2007.Google Scholar
  69. Ulutas, B., & Sarac, T. (2009). A clonal selection algorithm for cell formation problem with alternative routings. In \(4^{{\rm th}}\)international conference of group technology/cellular manufacturing 2009 (GT/CM 2009), 16–18 February 2009 (pp. 10–14). Japan: Kitakyishu.Google Scholar
  70. Ulutas, B. (2015). Assessing the number of cells for a cell formation problem. IFAC Proceedings Volumes, 48(3), 1122–1127.Google Scholar
  71. Ulutas, H. B., & Islier, A. A. (2007). A parameter setting for clonal selection algorithm in facility layout problems. In O. Gervasi & M. Gavrilova (Eds.), LNCS Springer (pp. 886–899). Berlin: Springer. 4705/2007.Google Scholar
  72. Ulutas, H. B., & Islier, A. A. (2009). A clonal selection algorithm for dynamic facility layout problems. Journal of Manufacturing Systems, 28(4), 123–131.Google Scholar
  73. Ulutas, B., & Islier, A. A. (2009). The performance of clonal selection algorithm for cell formation problem compared to other nature based methods, 4th International Conference of Group Technology/Cellular Manufacturing 2009 (GT/CM 2009), 16–18 February 2009 (pp. 15–22). Japan: Kitakyishu.Google Scholar
  74. Ulutas, B. H., & Kulturel-Konak, S. (2011). A review of clonal selection algorithm and its applications. Artificial Intelligence Review, 36(2), 117–138.Google Scholar
  75. Ulutas, H. B., & Kulturel-Konak, S. (2012). An artificial immune system based algorithm to solve unequal area facility layout problem. Expert Systems with Applications, 39(5), 5384–5395.Google Scholar
  76. Ulutas, H. B., & Kulturel-Konak, S. (2013). Assessing hypermutation operators of clonal selection algorithm for the unequal area facility layout problem. Engineering Optimization, 45(3), 375–395.Google Scholar
  77. Viswanathan, S. (1996). A new approach for solving the P-median problem in group technology. International Journal of Production Research, 34(10), 2691–2700.Google Scholar
  78. Waghodekar, P. H., & Sahu, S. (1984). Machine-component cell formation in group technology, MACE. International Journal of Production Research, 22, 937–948.Google Scholar
  79. Wemmerlov, U., & Hyer, N. (1989). Cellular manufacturing in the US industry: a survey of users. International Journal of Production Research, 27(9), 1511–1530.Google Scholar
  80. Won, Y., & Kim, S. (1997). Multiple criteria clustering algorithm for solving the group technology problem with multiple process routings. Computers and Industrial Engineering, 32(1), 207–220.Google Scholar
  81. Xiangyong, L., Baki, M. F., & Aneja, Y. P. (2010). An ant colony optimization metaheuristic for machine-part cell formation problem. Computers and Operations Research, 37, 2071–2081.Google Scholar
  82. Yang, M. S., & Yang, J. H. (2008). Machine-part cell formation in group technology using a modified ART1 method. European Journal of Operations Research, 188(1), 140–152.Google Scholar
  83. Yasuda, K., Hu, L., & Yin, Y. (2005). A grouping genetic algorithm for the multi-objective cell formation problem. International Journal of Production Research, 43(4), 829–853.Google Scholar
  84. Zolfaghari, S., & Liang, M. (1997). An objective-guided ortho-synapse Hopfield network approach to machine grouping problems. International Journal of Production Research, 35(10), 2773–2792.Google Scholar
  85. Zolfaghari, S., & Liang, M. (2002). Comparative study of simulated annealing, genetic algorithms and tabu search for binary and comprehensive machine-grouping problems. International Journal of Production Research, 40, 2141–2158.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial EngineeringEskisehir Osmangazi UniversityEskisehirTurkey

Personalised recommendations