Skip to main content
SpringerLink
Log in

Genetic Algorithm-Based Fuzzy Programming Method for Multi-objective Stochastic Transportation Problem Involving Three-Parameter Weibull Distribution

  • Conference paper
  • First Online:
Proceedings of the Fifth International Conference on Mathematics and Computing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1170))

Abstract

In real-life situations, it is difficult to handle multi-objective stochastic transportation problems. It can’t be solved directly using traditional mathematical programming approaches. In this paper, we proposed a solution procedure to handle the above problem. The proposed solution procedure is a hybridization of the evolutionary algorithm called a genetic algorithm and a classical mathematical programming technique called fuzzy programming method. This hybrid approach is called a genetic algorithm-based fuzzy programming method. The supply and demand parameters of the constraints follow a three-parameter Weibull distribution. To complete the proposed problem a total of three steps are required. Initially, the probabilistic constraints are handled using stochastic simulation. Then, we checked the feasibility of probability constraints by the stochastic programming with the genetic algorithm without deriving the deterministic equivalents. Then, the genetic algorithm-based fuzzy programming method is considered to generate non-dominated solutions for the given problem. Finally, a numerical case study is presented to illustrate the methodology.

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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ardjmand, E., Young II, W.A., Weckman, G.R., Bajgiran, O.S., Aminipour, B., Park, N.: Applying genetic algorithm to a new bi-objective stochastic model for transportation, location, and allocation of hazardous materials. Expert Syst. Appl. 51, 49–58 (2016)

    Google Scholar 

  2. Bartkute, V., Sakalauskas, L.: The method of three-parameter Weibull distribution estimation. ACUTM 12, 65–78 (2008)

    MathSciNet  MATH  Google Scholar 

  3. Bharathi, K., Vijayalakshmi, C.: Optimization of multi-objective transportation problem using evolutionary algorithms. Glob. J. Pure Appl. Math. 12(2), 1387–1396 (2016)

    Google Scholar 

  4. Biswal, M., Samal, H.: Stochastic transportation problem with Cauchy random variables and multi choice parameters. J. Phys. Sci. 17(11), 117–130 (2013)

    MathSciNet  Google Scholar 

  5. Hitchcock, F.L.: The distribution of a product from several sources to numerous localities. J. Math. Phys. 20, 224–230 (1941)

    Article  MathSciNet  Google Scholar 

  6. Holland, J.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Application to Biology. Control and Artificial Intelligence. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  7. Karthy, T., Ganesan, K.: Multi-objective transportation problem - genetic Algorithm approach. Int. J. Pure Appl. Math. 119(9), 343–350 (2018)

    Google Scholar 

  8. Krishnamoorthy, K.: Handbook of sTatistical Distributions with Applications. CRC Press, Boca Raton (2016)

    Google Scholar 

  9. Mahapatra, D.R., Roy, S.K., Biswal, M.: Stochastic based on multi-objective transportation problems involving normal randomness. Adv. Model. Optim. 12(2), 205–223 (2010)

    MathSciNet  MATH  Google Scholar 

  10. Mousa, A.A., Geneedy, H.M., Elmekawy, A.Y.: Efficient evolutionary algorithm for solving multiobjective transportation problem. J. Nat. Sci. Math. 4(1), 77–102 (2010)

    Google Scholar 

  11. Quddoos, A., ull Hasan, M.G., Khalid, M.M.: Multi-choice stochastic transportation problem involving general form of distributions. SpringerPlus 3(1), 565–574 (2014)

    Google Scholar 

  12. Roy, S.K.: Multi-choice stochastic transportation problem involving weibull distribution. IJOR 21(1), 38–58 (2014)

    Article  MathSciNet  Google Scholar 

  13. Roy, K., Maity, G., Weber, G.W., Gök, S.Z.A.: Conic scalarization approach to solve multichoice multi-objective transportation problem with interval goal. Ann. Oper. Res. 253(1), 599–620 (2017)

    Article  MathSciNet  Google Scholar 

  14. Roy, S.K., Ebrahimnejad, A., Verdegay, J.L., Das, S.: New approach for solving intuitionistic fuzzy multi-objective transportation problem. Sādhanā, 43(1), 3 (2018)

    Google Scholar 

  15. Sanjay, D., Acharya, S., Rajashree, M.: Genetic algorithm based fuzzy stochastic transportation programming problem with continuous random variables. Opsearch 53(4), 835–872 (2016)

    Article  MathSciNet  Google Scholar 

  16. Trivedi, A., Srinivasan, D., Sanyal, K., Ghosh, A.: A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Trans. Evol. Comput. 21(3), 440–462 (2017)

    Google Scholar 

  17. Zaki, S.A., Mousa, A.A.A., Geneedi, H.M., Elmekawy, A.Y.: Efficient multiobjective genetic algorithm for solving transportation, assignment, and transshipment problems. Appl. Math. 3(1), 92–99 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, School of Applied Sciences, KIIT Deemed to be University, Bhubaneswar, 751024, India

    Adane Abebaw Gessesse & Rajashree Mishra

Authors
  1. Adane Abebaw Gessesse
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rajashree Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adane Abebaw Gessesse .

Editor information

Editors and Affiliations

  1. Department of Information Technology, Maulana Abul Kalam Azad University of Technology, Haringhata, West Bengal, India

    Debasis Giri

  2. Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, UK

    Anthony T. S. Ho

  3. Indian Institute of Technology Madras, Chennai, India

    S. Ponnusamy

  4. Department of Information Management, National Taiwan University of Science and Technology, Taipei City, Taiwan

    Nai-Wei Lo

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Abebaw Gessesse, A., Mishra, R. (2021). Genetic Algorithm-Based Fuzzy Programming Method for Multi-objective Stochastic Transportation Problem Involving Three-Parameter Weibull Distribution. In: Giri, D., Ho, A.T.S., Ponnusamy, S., Lo, NW. (eds) Proceedings of the Fifth International Conference on Mathematics and Computing. Advances in Intelligent Systems and Computing, vol 1170. Springer, Singapore. https://doi.org/10.1007/978-981-15-5411-7_11

Download citation

Publish with us

Policies and ethics

Search

Navigation