Utilizing new approaches to address the fuzzy fixed charge transportation problem

References

• Gen M., Cheng R. Genetic algorithms and engineering optimization. New York: Wiley; 2000.
   Google Scholar
• Clover F., Klingman D., Phillips NV. Network models in optimization and their applications in practice. New York (NY): John Wiley; 1992.
   Google Scholar
• Firoozi Z, Ariafar S. A supply chain network design model for random-lifetime products. J Ind Prod Eng. 2017;34:113–123.10.1080/21681015.2016.1237384
   Web of Science ®Google Scholar
• Golmohamadi S, Tavakkoli-Moghaddam R, Hajiaghaei-Keshteli M. Solving a fuzzy fixed charge solid transportation problem using batch transferring by new approaches in meta-heuristic. Electron Notes Discrete Math. 2017;58:143–150.10.1016/j.endm.2017.03.019
   Google Scholar
• Rahmaniani R, Shafia MA. A study on maximum covering transportation network design with facility location under uncertainty. J Ind Prod Eng. 2013;30:78–93.10.1080/21681015.2013.785447
   Google Scholar
• Nourmohamadi Shalke P, Paydar MM, Hajiaghaei-Keshteli M. Sustainable supplier selection and order allocation through quantity discounts. Int J Manage Sci Eng Manage. 2018;13(1):1–13.
   Google Scholar
• Samadi A, Mehranfar N, Fathollahi Fard AM, et al. Heuristic-based metaheuristics to address a sustainable supply chain network design problem. J Ind Prod Eng. 2018:1–16.10.1080/21681015.2017.1422039
   Google Scholar
• Klose A. Algorithms for solving the single-sink fixed-charge transportation problem. Comput Oper Res. 2008;35:2079–2092.10.1016/j.cor.2006.10.011
   Web of Science ®Google Scholar
• Adlakha V, Kowalski K. A simple heuristic for solving small fixed-charge transportation problems Omega. Int J Manage Sci. 2003;31:205–211.
   Web of Science ®Google Scholar
• Gottlieb J, Paulmann L. Genetic algorithms for the fixed charge transportation problem. Proceedings of IEEE International Conference on Evolutionary Computation; Anchorage, 1998:330–335.
   Google Scholar
• Sun M, Aronson JE, Mckeown PG, et al. A tabu search heuristic procedure for the fixed charge transportation problem. Eur J Operational Res. 1998;106:441–456.10.1016/S0377-2217(97)00284-1
   Web of Science ®Google Scholar
• Ida K, Tohyama H, Teramatsu C, et al. A genetic algorithm for fixed charge transportation problem. Proceedings of the Fifth Asia-Pacific Industrial Engineering Management Systems; Australia, 2004:1–32.
   Google Scholar
• Liu L, Yang X, Mu H, et al. The fuzzy fixed charge transportation problem and genetic algorithm. Fifth Int Conf Fuzzy Syst Knowl Discovery. 2008;5:208–212.
   Google Scholar
• Yang L, Liu L. Fuzzy fixed charge solid transportation problem and algorithm. Appl Soft Comput. 2007;7:879–889.10.1016/j.asoc.2005.11.011
   Web of Science ®Google Scholar
• Steinberg DI. The fixed charge problem. Naval Res Logistics Q. 1970;17:217–235.10.1002/(ISSN)1931-9193
   Google Scholar
• Gen M, Kumar A, Ryul Kim J. Recent network design techniques using evolutionary algorithms. Int J Prod Econ. 2005;98:251–261.10.1016/j.ijpe.2004.05.026
   Web of Science ®Google Scholar
• Jo J, Li Y, Gen M. Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Comput Ind Eng. 2007;53:290–298.10.1016/j.cie.2007.06.022
   Web of Science ®Google Scholar
• Hajiaghaei-Keshteli M, Molla-Alizadeh-Zavardehi S, Tavakkoli-moghaddam R. Addressing a nonlinear fixed-charge transportation problem using a spanning tree-based genetic algorithm. Comput Ind Eng. 2010;59:259–271.10.1016/j.cie.2010.04.007
   Web of Science ®Google Scholar
• Othman Z, Rostamian Delavar MR, Behnam S, et al. Adaptive genetic algorithm for fixed-charge transportation problem. International Multi Conference of Engineers & Computer Sciences (IMECS); 2011 Mar 16–18.
   Google Scholar
• Bit AK. Fuzzy programming with hyperbolic membership functions for multi-objective capacitated solid transportation problem. J Fuzzy Math. 2005;13:373–385.
   Google Scholar
• Bit AK, Biswal MP, Alam SS. Fuzzy programming approach to multiobjective solid transportation problem. Fuzzy Sets Syst. 1993;57:183–194.10.1016/0165-0114(93)90158-E
   Web of Science ®Google Scholar
• Bit AK, Biswal MP, Alam SS. An additive fuzzy programming model for multiobjective transportation problem. Fuzzy Sets Syst. 1993;57:313–319.10.1016/0165-0114(93)90026-E
   Web of Science ®Google Scholar
• Li L, Lai KK. A fuzzy approach to the multiobjective transportation problem. Comput Oper Res. 2000;27:43–57.10.1016/S0305-0548(99)00007-6
   Web of Science ®Google Scholar
• Samanta B, Roy TK. Multiobjective entropy transportation model with trapezoidal fuzzy number penalties, sources, and destinations. J Transp Eng. 2005;131:419–428.10.1061/(ASCE)0733-947X(2005)131:6(419)
   Google Scholar
• Omar MS, Samir AA. A parametric study on transportation problem under fuzzy environment. J Fuzzy Math. 2003;11:115–124.
   Google Scholar
• Chanas S, Kuchta D. A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy Sets Syst. 1996;82:299–305.10.1016/0165-0114(95)00278-2
   Web of Science ®Google Scholar
• Kapur JN, Kesavan HK. Entropy optimization principles with applications. San Diego (CA): Academic Press; 1992.10.1007/978-94-011-2430-0
   Google Scholar
• Ojha A, Das B, Mondal SK, et al. An entropy based solid transportation problem for general fuzzy costs and time with fuzzy equality. Math Comput Model. 2009;50:166–178.10.1016/j.mcm.2009.04.010
   Web of Science ®Google Scholar
• Lotfi MM, Tavakkoli-Moghaddam R. A genetic algorithm using priority-based encoding with new operators for fixed charge transportation problems. Appl Soft Comput. 2013;13:2711–2726.10.1016/j.asoc.2012.11.016
   Web of Science ®Google Scholar
• Tari FG, Hashemi Z. A priority based genetic algorithm for nonlinear transportation costs problems. Comput Ind Eng. 2016;96:86–95.10.1016/j.cie.2016.03.010
   Web of Science ®Google Scholar
• Cheraghalipour A, Paydar MM, Hajiaghaei-keshteli M. An integrated approach for collection center selection in reverse logistic. Int J Eng Trans A. 2017;30:1005–1016.
   Google Scholar
• Kowalski K, Lev B. On step fixed-charge transportation problem. Omega. 2008;36:913–917.10.1016/j.omega.2007.11.001
   Web of Science ®Google Scholar
• El-Sherbiny MM. Alternate mutation based artificial immune algorithm for step fixed charge transportation problem. Egypt Inf J. 2012;13:123–134.10.1016/j.eij.2012.05.003
   Google Scholar
• Altassan KM, El-Sherbiny MM, Sasidhar B. Near optimal solution for the step fixed charge transportation problem. Appl Math Inf Sci. 2013;7:661–669.10.12785/amis/072L41
   Google Scholar
• Molla-Alizadeh-Zavardehi S, Nezhad SS, Tavakkoli-Moghaddam R, et al. Solving a fuzzy fixed charge solid transportation problem by metaheuristics. Math Comput Model. 2013;57:1543–1558.10.1016/j.mcm.2012.12.031
   Google Scholar
• Molla-Alizadeh-Zavardehi S, Mahmoodirad A, Rahimian M. Step fixed charge transportation problems via genetic algorithm. Indian J Sci Technol. 2014;7:949–954.
   Google Scholar
• Sanei M, Mahmoodirad A, Niroomand S, et al. Step fixed-charge solid transportation problem: a Lagrangian relaxation heuristic approach. Comput Appl Math. 2015;36:1–21.
   Google Scholar
• Sadeghi-Moghaddam S, Hajiaghaei-Keshteli M, Mahmoodjanloo M. New approaches in metaheuristics to solve the fixed charge transportation problem in a fuzzy environment. Neural Comput Appl. 2017:1–21.
   Google Scholar
• Birbil Şİ, Fang SC. An electromagnetism-like mechanism for global optimization. J Global Optim. 2003;25:263–282.10.1023/A:1022452626305
   Web of Science ®Google Scholar
• Naji-Azimi Z, Toth P, Galli L. An electromagnetism metaheuristic for the unicost set covering problem. Eur J Operational Res. 2010;205:290–300.10.1016/j.ejor.2010.01.035
   Web of Science ®Google Scholar
• Debels D, De Reyck B, Leus R, et al. A hybrid scatter search/electromagnetism meta-heuristic for project scheduling. Eur J Operational Res. 2006;169:638–653.10.1016/j.ejor.2004.08.020
   Web of Science ®Google Scholar
• Maenhout B, Vanhoucke M. An electromagnetic meta-heuristic for the nurse scheduling problem. J Heuristics. 2007;13:359–385.10.1007/s10732-007-9013-7
   Web of Science ®Google Scholar
• Tsou CS, Kao CH. Multi-objective inventory control using electromagnetism-like meta-heuristic. Int J Prod Res. 2008;46:3859–3874.10.1080/00207540601182278
   Web of Science ®Google Scholar
• Chang PC, Chen SH, Fan CY. A hybrid electromagnetism-like algorithm for single machine scheduling problem. Expert Syst Appl. 2009;36:1259–1267.10.1016/j.eswa.2007.11.050
   Web of Science ®Google Scholar
• Davoudpour H, Hadji Molana M. Solving flow shop sequencing problem for deteriorating jobs by using electromagnetic algorithm. J Appl Sci. 2008;8:4121–4128.
   Google Scholar
• Schwefel H. Evolution and optimum seeking. New York (NY): Wiley; 1995.
   Google Scholar
• Gen M, Cheng R. Genetic algorithms and engineering design. New York: Wiley; 1997.
   Google Scholar
• Hajiaghaei-Keshteli M, Aminnayeri M. Keshtel Algorithm (KA); a new optimization algorithm inspired by Keshtels’ feeding. Proceeding in IEEE Conference on Industrial Engineering and Management Systems. 2013:2249–2253.
   Google Scholar
• Cheraghalipour A, Hajiaghaei-keshteli M. Tree Growth Algorithm (TGA): an effective metaheuristic algorithm inspired by trees behavior. 13th International Conference on Industrial Engineering; 2017 Feb 23; Babolsar: 1–8
   Google Scholar
• Birbil SI, Fang SC, Sheu RL. On the convergence of a population-based global optimization algorithm. J Global Optim. 2004;30:301–318.10.1007/s10898-004-8270-3
   Web of Science ®Google Scholar
• Holland JH. Adaptation in natural and artificial systems. Ann Arbor: University of Michigan Press; 1975.
   Google Scholar
• Kirkpatrick S, Gelatt CD, Vecchi MP. Optimization by simulated annealing. Science. 1983;220:671–680.10.1126/science.220.4598.671
   PubMed Web of Science ®Google Scholar
• Fard AMF, Hajiaghaei-Keshteli M. A tri-level location-allocation model for forward/reverse supply chain. Appl Soft Comput. 2017;62:328–346.
   Web of Science ®Google Scholar
• Fard AMF, Gholian-Jouybari F, Paydar MM, et al. A bi-objective stochastic closed-loop supply chain network design problem considering downside risk. Ind Eng Manage Syst. 2017;16:342–362.
   Web of Science ®Google Scholar
• Golshahi-Roudbaneh A, Hajiaghaei-Keshteli M, Paydar MM. Developing a lower bound and strong heuristics for a truck scheduling problem in a cross-docking center. Knowledge-based Syst. 2017;129:17–38.10.1016/j.knosys.2017.05.006
   Web of Science ®Google Scholar
• Hajiaghaei-Keshteli M. The allocation of customers to potential distribution centers in supply chain networks: GA and AIA approaches. App Soft Comput. 2011;11:2069–2078.10.1016/j.asoc.2010.07.004
   Web of Science ®Google Scholar