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Solution of multi-objective transportation-p-facility location problem with effect of variable carbon emission by evolutionary algorithms


This paper presents an evolutionary approach-based solution of multi-objective transportation-p-facility location problem (MOT-p-FLP) that minimizes overall transportation time, cost of transportation, and carbon emission (CE) from available sites to facility sites by seeking transported product quantities and the facility locations in the Euclidean plane. Genetic algorithm (GA), non-dominated sorting genetic algorithm (NSGA-II and NSGA-III), and modified Self-Adaptive Multi-Population Elitism Jaya Algorithm (SAMPE JA) are utilized to solve the problem. We compared obtained compromise solutions of the problem by evolutionary algorithms with population size, the maximum number of generations, crossover probability, mutation probability, and computational time. Sensitivity analysis for supply, demand, and carbon cap parameters is incorporated in the model’s solution, which helps the decision maker make the appropriate decision. These evolutionary algorithms (NSGA-II and NSGA-III) give Pareto-optimal solutions, and it helps management decide on the selection of p-facility locations. They could transport their product to the facility locations easily, with minimum transport, CE costs, and transportation time. As a result, management can give equal attention to their profit and environment, which helps to build world market credibility. At last, the paper concludes the results.

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  • Ardestani-Jaafari A, Delage E (2018) The value of flexibility in robust location-transportation problems. Transp Sci 52(1):189–209

    Article  Google Scholar 

  • Carlo HJ, David V, Salvat-Dávila GS (2017) Transportation-location problem with unknown number of facilities. Comput Ind Eng 112:212–220

    Article  Google Scholar 

  • Chikumbo O, Goodman E, Deb K (2012) Approximating a multi-dimensional pareto front for a land use management problem: a modified MOEA with an epigenetic silencing metaphor. In: 2012 IEEE congress on evolutionary computation. IEEE, pp 1–9

  • Das SK, Roy SK (2019) Effect of variable carbon emission in a multi-objective transportation-p-facility location problem under neutrosophic environment. Comput Ind Eng 132:311–324

    Article  Google Scholar 

  • Deb K, Jain H (2013) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601

    Article  Google Scholar 

  • Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: International conference on parallel problem solving from nature. Springer, Berlin, pp 849–858

  • Deshmukh M, Moorthy CB (2010) Application of genetic algorithm to neural network model for estimation of wind power potential. Methods 11:12

  • Du S, Tang W, Song M (2016) Low-carbon production with low-carbon premium in cap-and-trade regulation. J Clean Prod 134:652–662

    Article  Google Scholar 

  • Elhedhli S, Merrick R (2012) Green supply chain network design to reduce carbon emissions. Transp Res Part D Transp Environ 17(5):370–379

    Article  Google Scholar 

  • Farahani RZ, SteadieSeifi M, Asgari N (2010) Multiple criteria facility location problems: a survey. Appl Math Model 34(7):1689–1709

    MathSciNet  Article  Google Scholar 

  • Fu G, Kapelan Z, Kasprzyk JR, Reed P (2013) Optimal design of water distribution systems using many-objective visual analytics. J Water Resour Plan Manag 139(6):624–633

    Article  Google Scholar 

  • Gabrel V, Lacroix M, Murat C, Remli N (2014) Robust location transportation problems under uncertain demands. Discret Appl Math 164:100–111

    MathSciNet  Article  Google Scholar 

  • Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach learn 3:95–99

    Article  Google Scholar 

  • Guo Y, Chen ZR, Ruan YL, Zhang J (2012) Application of NSGA-II with local search to multi-dock cross-docking sheduling problem. In: 2012 IEEE international conference on systems, man, and cybernetics (SMC). IEEE, pp 779–784

  • Harris I, Mumford CL, Naim MM (2014) A hybrid multi-objective approach to capacitated facility location with flexible store allocation for green logistics modeling. Transp Res Part E Logist Transp Rev 66:1–22

    Article  Google Scholar 

  • Hitchcock FL (1941) The distribution of a product from several sources to numerous localities. J Math Phys 20(1–4):224–230

    MathSciNet  Article  Google Scholar 

  • Holland J (1975) Adaptation in natural and artificial systems: an introductory analysis with application to biology. In: Control and artificial intelligence, pp 1–19

  • Klibi W, Lasalle F, Martel A, Ichoua S (2010) The stochastic multiperiod location transportation problem. Transp Sci 44(2):221–237

    Article  Google Scholar 

  • Mahapatra DR, Roy SK, Biswal MP (2013) Multi-choice stochastic transportation problem involving extreme value distribution. Appl Math Model 37(4):2230–2240

    MathSciNet  Article  Google Scholar 

  • Maity G, Roy SK, Verdegay JL (2016) Multi-objective transportation problem with cost reliability under uncertain environment. Int J Comput Intell Syst 9(5):839–849

    Article  Google Scholar 

  • Martínez-Vargas A, Domínguez-Guerrero J, Andrade ÁG, Sepúlveda R, Montiel-Ross O (2016) Application of NSGA-II algorithm to the spectrum assignment problem in spectrum sharing networks. Appl Soft Comput 39:188–198

    Article  Google Scholar 

  • Oreski S, Oreski D, Oreski G (2012) Hybrid system with genetic algorithm and artificial neural networks and its application to retail credit risk assessment. Expert Syst Appl 39(16):12605–12617

    Article  Google Scholar 

  • Phanden R, Demir H, Gupta R (2018) Application of genetic algorithm and variable neighborhood search to solve the facility layout planning problem in job shop production system. In: 2018 7th international conference on industrial technology and management (ICITM). IEEE, pp 270–274

  • Ramesh S, Kannan S, Baskar S (2012) Application of modified NSGA-II algorithm to multi-objective reactive power planning. Appl Soft Comput 12(2):741–753

    Article  Google Scholar 

  • Rao RV (2019) Jaya: an advanced optimization algorithm and its engineering applications. Springer International Publishing, New York City, pp 1–58

    Google Scholar 

  • Roy SK, Maity G, Weber GW, Gök SZA (2017) Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal. Ann Oper Res 253(1):599–620

    MathSciNet  Article  Google Scholar 

  • Sabbagh MS, Ghafari H, Mousavi SR (2015) A new hybrid algorithm for the balanced transportation problem. Comput Ind Eng 82:115–126

    Article  Google Scholar 

  • Saif A, Elhedhli S (2016) A Lagrangian heuristic for concave cost facility location problems: the plant location and technology acquisition problem. Optim Lett 10(5):1087–1100

    MathSciNet  Article  Google Scholar 

  • Schaffer JD (1986) Some experiments in machine learning using vector evaluated genetic algorithms (artificial intelligence, optimization, adaptation, pattern recognition). Vanderbilt Univ., Nashville, TN (USA), pp 1–55

  • Soyel H, Tekguc U, Demirel H (2011) Application of NSGA-II to feature selection for facial expression recognition. Comput Electr Eng 37(6):1232–1240

    Article  Google Scholar 

  • Srinivas N, Deb K (1994) Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248

    Article  Google Scholar 

  • Tsai CC, Huang HC, Chan CK (2011) Parallel elite genetic algorithm and its application to global path planning for autonomous robot navigation. IEEE Trans Ind Electron 58(10):4813–4821

    Article  Google Scholar 

  • Turken N, Carrillo J, Verter V (2017) Facility location and capacity acquisition under carbon tax and emissions limits: to centralize or to decentralize? Int J Prod Econ 187:126–141

    Article  Google Scholar 

  • Vikhar PA (2016) Evolutionary algorithms: a critical review and its future prospects. In: 2016 International conference on global trends in signal processing, information computing and communication (ICGTSPICC). IEEE, pp 261–265

  • Wang S, Zhao D, Yuan J, Li H, Gao Y (2019) Application of NSGA-II algorithm for fault diagnosis in power system. Electr Power Syst Res 175:105893

    Article  Google Scholar 

  • Wu P, Jin Y, Shi Y, Shyu H (2017) The impact of carbon emission costs on manufacturers’ production and location decision. Int J Prod Econ 193:193–206

    Article  Google Scholar 

  • Yeh WC, Chuang MC (2011) Using multi-objective genetic algorithm for partner selection in green supply chain problems. Expert Syst Appl 38(4):4244–4253

    Article  Google Scholar 

  • Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms—a comparative case study. In: International conference on parallel problem solving from nature. Springer, Berlin, pp 292–301

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Correspondence to Dhruvrajsinh O. Vansia.

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Vansia, D.O., Dhodiya, J.M. Solution of multi-objective transportation-p-facility location problem with effect of variable carbon emission by evolutionary algorithms. Soft Comput 25, 9993–10005 (2021).

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  • MOT-p-FLP
  • Genetic algorithm
  • Non-dominated sorting algorithms
  • Self-Adaptive Multi-Population Elitism Jaya Algorithm