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Evolving Systems

, Volume 9, Issue 2, pp 169–180 | Cite as

Modality of teaching learning based optimization algorithm to reduce the consistency ratio of the pair-wise comparison matrix in analytical hierarchy processing

  • Prashant Borkar
  • M. V. Sarode
Original Paper
  • 86 Downloads

Abstract

This paper presents an approach to improve the consistency of pair-wise comparison matrix in analytical hierarchy process (AHP) using teaching learning based optimization (TLBO) algorithm. The purpose of this proposed approach to minimize the consistency ratio (CR). Consistency test for the comparison matrix in AHP have been studied rigorously since AHP was introduced in 1970s. However, existing approaches are either too complicated or difficult. Most of them could not preserve the original judgments provided by an expert. To improve the consistency ratio (CR), this research work proposes a simple, effective and efficient method which will minimize the CR to almost zero while preserving the judgment values in pair-wise comparison matrix. The correctness of the proposed method is proved by applying it to two real world case studies reported in literature, namely new product design selection and material selection (work tool combination). The experimentation shows that the proposed approach is efficient and accurate to satisfy the consistency requirements of AHP.

Keywords

Analytical hierarchy process (AHP) Pair-wise comparison matrix Teaching learning based optimization (TLBO) Consistency ratio 

References

  1. Arunachalam R, Mannan M (2000) Machinability of nickel-based high temperature alloys. Mach Sci Technol 4:127–168. doi: 10.1080/10940340008945703 CrossRefGoogle Scholar
  2. Besharati B, Azarm S, Kannan P (2006) A decision support system for product design selection: a generalized purchase modeling approach. Decis Support Syst 42:333–350. doi: 10.1016/j.dss.2005.01.002 CrossRefGoogle Scholar
  3. Borkar P, Sarode M, Malik L (2016) Acoustic signal based optimal route selection problem: performance comparison of multi-attribute decision making methods. KSII Trans Internet Inf Syst 10(2):647–669Google Scholar
  4. Boubekri N, Rodriguez J, Asfour S (2003) Development of an aggregate indicator to assess the machinability of steels. J Mater Process Technol 134:159–165. doi: 10.1016/s0924-0136(02)00446-6 CrossRefGoogle Scholar
  5. Cao D, Leung L, Law J (2008) Modifying inconsistent comparison matrix in analytic hierarchy process: a heuristic approach. Decis Support Syst 44:944–953. doi: 10.1016/j.dss.2007.11.002 CrossRefGoogle Scholar
  6. Chakraborty P, Das S, Roy G, Abraham A (2011) On convergence of the multi-objective particle swarm optimizers. Inf Sci 181:1411–1425. doi: 10.1016/j.ins.2010.11.036 MathSciNetCrossRefzbMATHGoogle Scholar
  7. Chen S, Hwang C (1992) Fuzzy multiple attribute decision making. Lect Notes Econ Math Syst. doi: 10.1007/978-3-642-46768-4 CrossRefzbMATHGoogle Scholar
  8. Costa J (2011) A genetic algorithm to obtain consistency in analytic hierarchy process. BJOPM 8:55–64. doi: 10.4322/bjopm.2011.003 CrossRefGoogle Scholar
  9. Dong Y, Xu Y, Li H (2008) On consistency measures of linguistic preference relations. Eur J Oper Res 189:430–444. doi: 10.1016/j.ejor.2007.06.013 MathSciNetCrossRefzbMATHGoogle Scholar
  10. Dorigo M, Stutzle T (2004) Ant colony optimization. MIT Press, CambridgezbMATHGoogle Scholar
  11. Dravid SV, Utpat LS (2001) Machinability evaluation based on the surface finish criterion. J Inst Eng (India) Prod Eng Div 81:47–51Google Scholar
  12. Efren MM, Mariana EMV, Rubi DCGR (2010) Differential evolution in constrained numerical optimization: an empirical study. Inf Sci 180:4223–4262MathSciNetCrossRefzbMATHGoogle Scholar
  13. Enache S, Strjescu E, Opran C et al. (1995) Mathematical model for the establishment of the materials machinability. CIRP Ann Manuf Technol 44:79–82. doi: 10.1016/s0007-8506(07)62279-3 CrossRefGoogle Scholar
  14. Farmer J, Packard N, Perelson A (1986) The immune system, adaptation, and machine learning. Phys D 22:187–204. doi: 10.1016/0167-2789(86)90240-x MathSciNetCrossRefGoogle Scholar
  15. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–70CrossRefGoogle Scholar
  16. Girsang A, Tsai C, Yang C (2014a) Ant algorithm for modifying an inconsistent pairwise weighting matrix in an analytic hierarchy process. Neural Comput Appl 26:313–327. doi: 10.1007/s00521-014-1630-0 CrossRefGoogle Scholar
  17. Girsang AS, Tsai CW, Yang CS (2014b) Ant colony optimization for reducing the consistency ratio in comparison matrix. In: Proceedings of the International Conference on Advances in Engineering and Technology (ICAET’14), pp 577–582Google Scholar
  18. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, ReadingzbMATHGoogle Scholar
  19. Haque B, Belecheanu R, Barson R, Pawar K (2000) Towards the application of case based reasoning to decision-making in concurrent product development (concurrent engineering). Knowl Based Syst 13:101–112. doi: 10.1016/s0950-7051(00)00051-4 CrossRefGoogle Scholar
  20. Hsiao S, Chou J (2004) A creativity-based design process for innovative product design. Int J Ind Ergon 34:421–443. doi: 10.1016/j.ergon.2004.05.005 CrossRefGoogle Scholar
  21. Iida Y (2009) Ordinality consistency test about items and notation of a pairwise comparison matrix in AHP. In: Proceedings of the International Symposium on the Analytic Hierarchy ProcessGoogle Scholar
  22. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report-TR06. Erciyes UniversityGoogle Scholar
  23. Karen A, Yildiz A, Kaya N et al (2006) Hybrid approach for genetic algorithm and Taguchi’s method based design optimization in the automotive industry. Int J Prod Res 44:4897–4914. doi: 10.1080/00207540600619932 CrossRefzbMATHGoogle Scholar
  24. Keeney R, Raiffa H (1976) Decisions with multiple objectives; preferences and values tradeoffs. Wiley, New YorkzbMATHGoogle Scholar
  25. Kennedy J, Eberhart R (1995) Particle Swarm Optimization. In: Proceedings of IEEE International Conference on Neural Networks, pp 1942–1948Google Scholar
  26. Kim K, Kang M, Kim J et al (2002) A study on the precision machinability of ball end milling by cutting speed optimization. J Mater Process Technol 130–131:357–362. doi: 10.1016/s0924-0136(02)00824-5 CrossRefGoogle Scholar
  27. Kulak O, Kahraman C (2005) Multi-attribute comparison of advanced manufacturing systems using fuzzy vs. crisp axiomatic design approach. Int J Prod Econ 95:415–424. doi: 10.1016/j.ijpe.2004.02.009 CrossRefGoogle Scholar
  28. Li H, Ma L (2007) Detecting and adjusting ordinal and cardinal inconsistencies through a graphical and optimal approach in AHP models. Comput Oper Res 34:780–798. doi: 10.1016/j.cor.2005.05.010 CrossRefzbMATHGoogle Scholar
  29. Lin C, Wang W, Yu W (2008) Improving AHP for construction with an adaptive AHP approach (A3). Autom Constr 17:180–187. doi: 10.1016/j.autcon.2007.03.004 CrossRefGoogle Scholar
  30. Lin M, Lee Y, Ho T (2011) Applying integrated DEA/AHP to evaluate the economic performance of local governments in China. Eur J Oper Res 209:129–140. doi: 10.1016/j.ejor.2010.08.006 CrossRefGoogle Scholar
  31. Liu J, Tang L (1999) A modified genetic algorithm for single machine scheduling. Comput Ind Eng 37:43–46. doi: 10.1016/s0360-8352(99)00020-0 CrossRefGoogle Scholar
  32. Lo C, Wang P, Chao K (2006) A fuzzy group-preferences analysis method for new-product development. Expert Syst Appl 31:826–834. doi: 10.1016/j.eswa.2006.01.005 CrossRefGoogle Scholar
  33. Maddulapalli A, Azarm S, Boyars A (2007) Sensitivity analysis for product design selection with an implicit value function. Eur J Oper Res 180:1245–1259. doi: 10.1016/j.ejor.2006.03.055 CrossRefzbMATHGoogle Scholar
  34. Morehead M, Huang Y, Ted Hartwig K (2007) Machinability of ultrafine-grained copper using tungsten carbide and polycrystalline diamond tools. Int J Mach Tools Manuf 47:286–293. doi: 10.1016/j.ijmachtools.2006.03.014 CrossRefGoogle Scholar
  35. Ong S, Chew L (2000) Evaluating the manufacturability of machined parts and their setup plans. Int J Prod Res 38:2397–2415. doi: 10.1080/00207540050031832 CrossRefzbMATHGoogle Scholar
  36. Ozer M (2005) Factors which influence decision making in new product evaluation. Eur J Oper Res 163:784–801. doi: 10.1016/j.ejor.2003.11.002 CrossRefzbMATHGoogle Scholar
  37. Passino K (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst Mag 22:52–67. doi: 10.1109/mcs.2002.1004010 CrossRefGoogle Scholar
  38. Peng Y, Kou G, Wang G et al (2011a) Ensemble of software defect predictors: an AHP-based evaluation method. Int J Inf Tech Decis Mak 10:187–206. doi: 10.1142/s0219622011004282 CrossRefGoogle Scholar
  39. Peng Y, Wang G, Kou G, Shi Y (2011b) An empirical study of classification algorithm evaluation for financial risk prediction. Appl Soft Comput 11:2906–2915. doi: 10.1016/j.asoc.2010.11.028 CrossRefGoogle Scholar
  40. Peng Y, Wang G, Wang H (2012) User preferences based software defect detection algorithms selection using MCDM. Inf Sci 191:3–13. doi: 10.1016/j.ins.2010.04.019 CrossRefGoogle Scholar
  41. Rao R (2005) Machinability evaluation of work materials using a combined multiple attribute decision making method. Int J Adv Manuf Technol 28:221–227Google Scholar
  42. Rao R (2007) Decision making in the manufacturing environment using graph theory and fuzzy multiple attribute decision making. Springer series in advanced manufacturingGoogle Scholar
  43. Rao R (2011) Advanced modeling and optimization of manufacturing processes. Springer series in advanced manufacturing. doi: 10.1007/978-0-85729-015-1
  44. Rao R (2013a) Decision making in manufacturing environment using graph theory and fuzzy multiple attribute decision making methods, vol 2. Springer series in advanced manufacturingGoogle Scholar
  45. Rao R (2013b) Decision making in manufacturing environment using graph theory and fuzzy multiple attribute decision making methods. Springer series in advanced manufacturing. doi: 10.1007/978-1-4471-4375-8
  46. Rao R (2015) Teaching learning based optimization and its engineering applications. Springer, LondonGoogle Scholar
  47. Rao R (2016) Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int J Ind Eng Comput 7:19–34Google Scholar
  48. Rao R, Patel V (2012b) An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems. Int J Ind Eng Comput 3:535–560. doi: 10.5267/j.ijiec.2012.03.007 Google Scholar
  49. Rao R, Patel V (2013b) Multi-objective optimization of heat exchangers using a modified teaching–learning-based optimization algorithm. Appl Math Modell 37:1147–1162. doi: 10.1016/j.apm.2012.03.043 MathSciNetCrossRefzbMATHGoogle Scholar
  50. Rao R, Patel V (2013c) Multi-objective optimization of two stage thermoelectric cooler using a modified teaching–learning-based optimization algorithm. Eng Appl Artif Intell 26:430–445CrossRefGoogle Scholar
  51. Rao R, Savsani V, Vakharia D (2012a) Teaching–learning-based optimization: an optimization method for continuous non-linear large scale problems. Inf Sci 183:1–15. doi: 10.1016/j.ins.2011.08.006 MathSciNetCrossRefGoogle Scholar
  52. Saaty TL (2001) Deriving the AHP 1–9 scale from first principles. In: ISAHP 2001 Proceedings, BernGoogle Scholar
  53. Saaty TL (2003) Decision-making with the AHP: why is the principal eigenvector necessary. Eur J Oper Res 145(1):85–91MathSciNetCrossRefzbMATHGoogle Scholar
  54. Saaty TL (2005) Theory and applications of the analytic network process: decision making with benefits, opportunities, costs and risks. RWS Publications, Pittsburgh (ISBN 1-888603-06-2) Google Scholar
  55. Saaty TL (2006) The analytic network process, decision making with the analytic network process. Int Ser Oper Res Manag Sci 95:1–26Google Scholar
  56. Šalak A, Vasilko K, Selecká M, Danninger H (2006) New short time face turning method for testing the machinability of PM steels. J Mater Process Technol 176:62–69CrossRefGoogle Scholar
  57. Shi W, Shen Q, Kong W, Ye B (2007) QSAR analysis of tyrosine kinase inhibitor using modified ant colony optimization and multiple linear regression. Eur J Med Chem 42:81–86CrossRefGoogle Scholar
  58. Suh NP (2001) Axiomatic design: advances and applications. Oxford University Press, New YorkGoogle Scholar
  59. Yang I, Wang W, Yang T (2012) Automatic repair of inconsistent pairwise weighting matrices in analytic hierarchy process. Autom Constr 22:290–297. doi: 10.1016/j.autcon.2011.09.004
  60. Yildiz AR (2009) A novel hybrid immune algorithm for global optimization in design and manufacturing. Rob Comput Integr Manuf 25:261–270CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringGHRCENagpurIndia
  2. 2.Department of Computer Science and EngineeringGovernment Polytechnic YawatmalYawatmalIndia

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