Skip to main content
SpringerLink
Log in

Neural Network-Based Fuzzy Multi-objective Optimisation for Efficiency Evaluation

  • Conference paper
  • First Online:
Mathematical Modeling and Computational Tools (ICACM 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 320))

Included in the following conference series:

  • 661 Accesses

Abstract

Multi-objective optimisation handles the optimisation of multiple objectives on a multi-dimensional space (Lootsma in Fuzzy Multi-Objective Optimization. Springer, Boston, 1997 [1]). There are various classical methods and a wide variety of genetic algorithms for determining the Pareto-optimal front in MOOP. Most of the MOOP algorithms dealing with fuzzy systems treat fuzzy parameters (Young-Jou and Ching-Lai in Fuzzy multiple objective decision making: Methods and applications, Springer, Berlin, 1994 [2]), fuzzy inequalities (Chuntian in Hydrological Sciences Journal 44(4): 573–582, 1999 [3]) and fuzzy objective function (Young Jou and Ching-Lai in Fuzzy Sets and Systems 54(2): 135–146, 1993 [4]). In this article, an algorithm for multi-objective optimisation using neural network is presented where the variables are fuzzy. The paper deals with the core of the issue that is the fuzzy variables in multi-objective optimisation. Here, the variables are treated as triangular fuzzy variables. The arithmetic on these fuzzy variables is defined, according to the existing available work. As a numerical illustration, the new algorithm has been tested on two fractional functions. The results obtained after implementing the new algorithm using MATLAB code is presented. The algorithm uses neural network to approximate the Pareto front. This proposed algorithm is an illustration of possible optimisation technique in the fuzzy domain using Neural Network.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Lootsma, F.A.: Fuzzy Multi-Objective Optimization. Springer, Boston, MA (1997). https://doi.org/10.1007/978-1-4757-2618-3_7

  2. Young-Jou, L., Ching-Lai, H.: Fuzzy multiple objective decision making: methods and applications (1994)

    Google Scholar 

  3. Chuntian, C.: Fuzzy optimal model for the flood control system of the upper and middle reaches of the yangtze river. Hydrol. Sci. J. 44(4), 573–582 (1999)

    Article  Google Scholar 

  4. Young Jou Lai CLH: Possibilistic linear programming for managing interest rate risk. Fuzzy Sets Syst. 54(2), 135–146 (1993)

    Article  Google Scholar 

  5. Cohon, J.L.: Multicriteria programming: brief review and application. In: Design Optimization, pp. 163–191 (1985)

    Google Scholar 

  6. Charnes, A., Cooper, W.W.: An explicit general solution in linear fractional programming. Nav. Res. Logist. Q. 20(3), 449–467 (1973)

    Google Scholar 

  7. Bitran, G.R., Novaes, A.G.: Linear programming with a fractional objective function. Oper. Res. 21(1), 22–29 (1973). https://doi.org/10.1287/opre.21.1.22

  8. Schaible, S.: Fractional programming. I, duality. Manage. Sci. 22(8), 858–867 (1976). https://doi.org/10.1287/mnsc.22.8.858

  9. Choo, E.U., Atkins, D.R.: Bicriteria linear fractional programming. J. Optim. Theory Appl. 36(2), 203–220 (1982). https://doi.org/10.1007/BF00933830

  10. Buhler, W.: A note on fractional interval programming. Oper. Res. A B 19, 29–36 (1975)

    Google Scholar 

  11. Banks, J.: Handbook of Simulation: Principles, Methodology, Advances, Applications, and Practice. Wiley, Hoboken (1998)

    Google Scholar 

  12. Billingsley, P.: Convergence of Probability Measures. John, Hoboken (2013)

    Google Scholar 

  13. Cabo, M., Possani, E.: Considerations on applying cross entropy methods to the vehicle routing problem. Int. J. Comb. Optim. Probl. Inform. 6(3), 22 (2015)

    Google Scholar 

  14. Grefenstette, J.J.: Optimization of control parameters for genetic algorithms. IEEE Trans. Syst. Man Cybern. 16(1), 122–128 (1986)

    Article  Google Scholar 

  15. Box GE.: Evolutionary operation: a method for increasing industrial productivity. Appl. Stat. 81–101 (1957)

    Google Scholar 

  16. Brent, R.P.: Algorithms for Minimization Without Derivatives. Courier Corporation (2013)

    Google Scholar 

  17. Mifflin JJS Robert: A bracketing technique to ensure desirable convergence in univariate minimization. Math. Program. 43(1–3), 117–130 (1989)

    Article  MathSciNet  Google Scholar 

  18. Robert Mifflin JJS: A rapidly convergent five-point algorithm for univariate minimization. Math. Program. 62(1–3), 299–319 (1993)

    MathSciNet  MATH  Google Scholar 

  19. Box, G.: Wkb on the experimental attainment of optimum condition. J. R. Stat. Soc. Ser. B 13(1), 20 (1951)

    Google Scholar 

  20. George, E.P., Box, N.R.D.: Evolutionary Operation: A Statistical Method for Process Improvement, vol. 67. Wiley, Hoboken (1998)

    Google Scholar 

  21. Xiaoli Zhang, Y.W., Zhou, Qinghua: An efficient pattern search method. J. Appl. Math. Phys. 1(04), 68 (2013)

    Article  Google Scholar 

  22. Swan, W.J.: Report on Development of New Direct Search Method of Optimisation. Tech. Rep, ICI Ltd. (1964)

    Google Scholar 

  23. Fletcher, R.: Practical Methods of Optimization. Wiley, Hoboken (2013)

    Google Scholar 

  24. Gill, P.E., Murray, W., Wright, M.H.: Practical optimization. Academic press (1981)

    Google Scholar 

  25. Gabay, D.: Reduced quasi-newton methods with feasibility improvement for nonlinearly constrained optimization. In: Algorithms for Constrained Minimization of Smooth Nonlinear Functions, pp. 18–44. Springer, New York (1982)

    Google Scholar 

  26. Adams, L.M., Nazareth, J.L., et al. (1996) Linear and Nonlinear Conjugate Gradient-Related Methods, vol. 85. Siam

    Google Scholar 

  27. Zangwill, W.I.: Nonlinear programming: a unified approach. Prentice-Hall (1969)

    Google Scholar 

  28. Engau, A.: Interactive decomposition-coordination methods for complex decision problems. In: Handbook of Multicriteria Analysis, pp. 329–365. Springer, New York (2010)

    Google Scholar 

  29. Geue, F.: An improved n-tree algorithm for the enumeration of all neighbors of a degenerate vertex. Ann. Oper. Res. 46(2), 361–391 (1993)

    Article  MathSciNet  Google Scholar 

  30. Maeda, T.: Second order conditions for efficiency non-smooth multi objective optimisation. J. Optim. Theory Appl. 122(3), 139–153 (2004)

    Article  Google Scholar 

  31. Ricardo Feced, M.A.M., Zervas, Michalis N.: An efficient inverse scattering algorithm for the design of nonuniform fiber bragg gratings. IEEE J. Quantum Electron. 35(8), 1105–1115 (1999)

    Article  Google Scholar 

  32. Ulungu, E.L. Teghem, J.: The two phases method- an efficient process to solve bi-objective combinatorial optimisation problems. Foundaions Comput. Decis. Sci. 20(2), 149–165 (1995)

    Google Scholar 

  33. Lai, J.Y.: Imost: interactive multiple objective system technique. J. Oper. Res. Soc. 46(8), 958–976 (1995)

    Article  Google Scholar 

  34. Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1(1), 45–55 (1978)

    Article  MathSciNet  Google Scholar 

  35. Kannan, D., Khodaverdi, R., Olfat, L., Jafarian, A., Khodaverdi, A..: Integrated fuzzy multi criteria decision making method and multi-objective programming approach for supplier selection and order allocation in a green supply chain. J. Clean. 47, 355–367 (2013). https://www.sciencedirect.com/science/article/pii/S0959652613000590

  36. Carlsson, C.: Fuzzy multiple criteria decision making: recent developments. Fuzzy Sets Syst. 78(2), 139–153 (1996). https://www.sciencedirect.com/science/article/pii/0165011495001654

  37. Cheng, C.H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst. 95(3), 307–317 (1998). https://doi.org/10.1016/S0165-0114(96)00272-2

    Article  MathSciNet  MATH  Google Scholar 

  38. Herrera, F., Lozano, M.: Fuzzy genetic algorithms: issues and models. Tech. Rep. (1994) https://pdfs.semanticscholar.org/8595/aedf2e923018a1d1fac85bec28c0c309445a.pdf

  39. Schaefer, G., Nakashima, T.: Michigan vs. pittsburgh style ga optimisation of fuzzy rule bases for gene expression analysis. Int. J. Fuzzy. Syst. Appl. 3(4), 60–72 (2013). https://doi.org/10.4018/ijfsa.2013100105

  40. Fortemps MR (1996) Ranking and defuzzification methods based on area compensation. https://www.sciencedirect.com/science/article/pii/0165011495002731

  41. Nielsen, M.: Neural networks and deep learning (2015). http://static.latexstudio.net/article/2018/0912/neuralnetworksanddeeplearning.pdf

  42. Barron, A.: Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inf. Theory (1993)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CER, Mathematics Department, Indian Institute of Technology Kharagpur, Kharagpur, India

    Debasish Roy

Authors
  1. Debasish Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Debasish Roy .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India

    Somnath Bhattacharyya

  2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India

    Jitendra Kumar

  3. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India

    Koeli Ghoshal

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Roy, D. (2020). Neural Network-Based Fuzzy Multi-objective Optimisation for Efficiency Evaluation. In: Bhattacharyya, S., Kumar, J., Ghoshal, K. (eds) Mathematical Modeling and Computational Tools. ICACM 2018. Springer Proceedings in Mathematics & Statistics, vol 320. Springer, Singapore. https://doi.org/10.1007/978-981-15-3615-1_26

Download citation

Publish with us

Policies and ethics

Search

Navigation