Genetic algorithm based fuzzy programming approach for multi-objective linear fractional stochastic transportation problem involving four-parameter Burr distribution | International Journal of System Assurance Engineering and Management
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Genetic algorithm based fuzzy programming approach for multi-objective linear fractional stochastic transportation problem involving four-parameter Burr distribution

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Abstract

In real life situations, it is difficult to handle multi-objective linear fractional stochastic transportation problem. It can’t be solved directly using mathematical programming approaches. In this paper, a solution procedure is proposed for the above problem using a genetic algorithm based fuzzy programming method. The supply and demand parameters of the said problem follow four-parameters Burr distribution. The proposed approach omits the derivation of deterministic equivalent form as required in case of classical approach. In the given methodology, initially the probabilistic constraints present in the problem are tackled using stochastic programming combining the strategy adopted in genetic algorithm. Throughout the problem, feasibility criteria is maintained. Then after, the non-dominated solution are obtained using genetic algorithm based fuzzy programming approach. In the proposed approach, the concept of fuzzy programming approach is inserted in the genetic algorithm cycle. The proposed algorithm has been compared with fuzzy programming approach and implemented on two examples. The result shows the efficacy of the proposed algorithm over fuzzy programming approach.

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References

  • Ali I et al (2019) Multi-objective linear fractional inventory problem under intuitionistic fuzzy environment. Int J Syst Assur Eng Manag 10(2):173–189

    Article  Google Scholar 

  • Ardjmand E et al (2016) Applying genetic algorithm to a new bi-objective stochastic model for transportation, location, and allocation of hazardous materials. Expert Syst Appl 51:49–58

    Article  Google Scholar 

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

    Google Scholar 

  • Burr IW (1942) Cumulative frequency functions. Ann Math Stat 13(2):215–232

    Article  MathSciNet  MATH  Google Scholar 

  • Charles V, Dutta D (2005) Linear stochastic fractional programming with sum of probabilistic fractional objective. Optimization online http://www.optimizationonline.org

  • Charles V et al (1997) E-model for transportation problem of linear stochastic fractional programming. Optimization online. http://www.optimizationonline.org

  • Charles V et al (2011) Stochastic fractional programming approach to a mean and variance model of a transportation problem. Math Probl Eng 2011 Article number 657608

  • Dantzig GB (1955) Linear programming under uncertainty. Manag Sci 1(3 & 4):197–206

    Article  MathSciNet  MATH  Google Scholar 

  • Dutta S et al (2016) Genetic algorithm based fuzzy stochastic transportation programming problem with continuous random variables. Opsearch 53(4):835–872

    Article  MathSciNet  MATH  Google Scholar 

  • Garai T, Garg H (2019) Multi-objective linear fractional inventory model with possibility and necessity constraints under generalised intuitionistic fuzzy set environment. CAAI Trans Intell Technol. https://doi.org/10.1049/trit.2019.0030

    Article  Google Scholar 

  • Garg H (2016) A hybrid PSO-GA algorithm for constrained optimization problems. Appl Math Comput 274:292–305

    MathSciNet  MATH  Google Scholar 

  • Garg H (2018) Analysis of an industrial system under uncertain environment by using different types of fuzzy numbers. Int J Syst Assur Eng Manag 9(2):525–538

    Article  MathSciNet  Google Scholar 

  • Garg H (2019) A hybrid GSA-GA algorithm for constrained optimization problems. Inf Sci 478:499–523

    Article  Google Scholar 

  • Goicoechea A, Lucien D (1987) Nonnormal deterministic equivalents and a transformation in stochastic mathematical programming. Appl Math Comput 21(1):51–72

    MathSciNet  MATH  Google Scholar 

  • Gupta K, Arora SR (2012) An algorithm to find optimum cost time trade of pairs in a fractional capacitated transportation problem with restricted flow. Int J Res Soc Sci 2(2):41

    Google Scholar 

  • Guzel N et al (2012) A solution proposal to the interval fractional transportation problem. Appl Math Inf Sci 6(3):567–571

    MathSciNet  Google Scholar 

  • He C et al (2019) Accelerating large-scale multi-objective optimization via problem reformulation. IEEE Trans Evolut Comput 23(6):949–961

    Article  Google Scholar 

  • Jadhav VA, Doke DM (2016) Solution procedure to solve fractional transportation problem with fuzzy cost and profit coefficients. Int J Math 4(7):1554–1562

    Google Scholar 

  • Jagannathan R (1974) Chance-constrained programming with joint constraints. Oper Res 22(2):358–372

    Article  MathSciNet  MATH  Google Scholar 

  • Jain S, Nitin A (2013) An inverse transportation problem with the linear fractional objective function. Adv Model Optim 15(3):677–687

    MATH  Google Scholar 

  • Javaid S et al (2017) A model for uncertain multi-objective transportation problem with fractional objectives. Int J Oper Res 14(1):11–25

    MathSciNet  Google Scholar 

  • Khurana A, Arora SR (2006) The sum of a linear and a linear fractional transportation problem with restricted and enhanced flow. J Interdiscip Math 9(2):373–383

    Article  MathSciNet  MATH  Google Scholar 

  • Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin, pp 205–234

    Book  Google Scholar 

  • Pradhan A, Biswal MP (2015) Computational methodology for linear fractional transportation problem. In: Proceedings of the 2015 winter simulation conference. IEEE Press, pp 3158–3159

  • Rani D et al (2016) Multi-objective non-linear programming problem in intuitionistic fuzzy environment: optimistic and pessimistic view point. Expert Syst Appl 64:228–238

    Article  Google Scholar 

  • Sadia S et al (2016) Multiobjective capacitated fractional transportation problem with mixed constraints. Math Sci Lett 5(3):235–242

    Article  Google Scholar 

  • Safi M, Seyyed MG (2017) Uncertainty in linear fractional transportation problem. Int J Nonlinear Anal Appl 8(1):81–93

    MATH  Google Scholar 

  • Sivri M et al (2011) A solution proposal to the transportation problem with the linear fractional objective function. In: 4th international conference on modeling, simulation and applied optimization (ICMSAO), Kualalumpur, Malasia. IEEE Press, pp 1–9

  • Swarup K (1966) Transportation technique in linear fractional functional programming. J R Naval Sci Serv 21(5):256–260

    Google Scholar 

  • Syarif A, Gen M (2000) Genetic algorithm for nonlinear side constrained transportation problem. In: Proceedings of international conference on computers, Beijing, China

  • Tadikamalla PR (1980) A look at the Burr and related distributions. Int Stat Rev/Rev Int Stat 48:337–344

    Article  MathSciNet  MATH  Google Scholar 

  • Tian Y et al (2017) Effectiveness and efficiency of non-dominated sorting for evolutionary multi-and many-objective optimization. Complex Intell Syst 3(4):247–263

    Article  Google Scholar 

  • Trivedi A et al (2017) A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Trans Evol Comput 21(3):440–462

    Google Scholar 

  • Vignaux GA, Michalewicz Z (1991) A genetic algorithm for the linear transportation problem. IEEE Trans Syst Man Cybern 21(2):445–452

    Article  MathSciNet  MATH  Google Scholar 

  • Yari G, Tondpour Z (2017) The new Burr distribution and its application. Math Sci 11(1):47–54

    Article  MathSciNet  MATH  Google Scholar 

  • Yinzhen L, Kenichi I (1999) Solving multi-objective transportation problem by spanning tree-based genetic algorithm. IEICE Trans Fundam Electron Commun Comput Sci 82(12):2802–2810

    Google Scholar 

  • Zhu H, Huang GH (2011) SLFP: a stochastic linear fractional programming approach for sustainable waste management. Waste Manag (Oxford) 31(12):2612–2619

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, KIIT, Deemed to be University, Bhubaneswar, Odisha, 751024, India

    Adane Abebaw Gessesse, Rajashree Mishra & Mitali Madhumita Acharya

  2. Department of Mathematics, NIT Silchar, Silchar, Assam, 788010, India

    Kedar Nath Das

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  1. Adane Abebaw Gessesse
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  2. Rajashree Mishra
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  3. Mitali Madhumita Acharya
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  4. Kedar Nath Das
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Correspondence to Adane Abebaw Gessesse.

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Abebaw Gessesse, A., Mishra, R., Acharya, M.M. et al. Genetic algorithm based fuzzy programming approach for multi-objective linear fractional stochastic transportation problem involving four-parameter Burr distribution. Int J Syst Assur Eng Manag 11, 93–109 (2020). https://doi.org/10.1007/s13198-019-00928-0

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