Bi-objective Optimization of a Multi-product multi-period Fuzzy Possibilistic Capacitated Hub Covering Problem: NSGA-II and NRGA Solutions
محورهای موضوعی : تکتونواستراتیگرافی
Zahra Rajabi
1
(Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran)
Soroush Avakh Darestani
2
(Department of Industrial Engineering, , Qazvin Branch, IslamicAzad University, Qazvin, Iran)
کلید واژه: Multi-product, Hub covering location, Meta heuristic algorithms, The hierarchical, Fuzzy possibilistic multi-objective,
چکیده مقاله :
The hub location problem is employed for many real applications, including delivery, airline and telecommunication systems and so on. This work investigates on hierarchical hub network in which a three-level network is developed. The central hubs are considered at the first level, at the second level, hubs are assumed which are allocated to central hubs and the remaining nodes are at the third level. In this research, a novel multi-product multi-objective model for capacitated hierarchical hub location problem with maximal covering under fuzzy condition first is suggested. Cost, time, hub and central hub capacities are considered as fuzzy parameters, whereas manyparameters are uncertainty and indeterministic in the real world. To solve the proposed fuzzy possibilistic multi-objective model, first, the model is converted to the equivalent auxiliary crisp model by hybrid method and then is solved by two meta-heuristic algorithms such as Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Non-Dominated Ranked Genetic Algorithm (NRGA) using MATLAB software The statistical results report that there is no significant difference between means of two algorithms exception CPU time criteria. In general, in order to show efficiency of two algorithms, we used Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), the resultsclearly show that the efficiency of NRGA is better than NSGA-II and finally, figures are achieved by MATLAB software that analyze the conflicting between two objectives.
Aljadaan, O., Rajamani, L., &Rao, C. (2008). Non-Dominated ranked genetic algorithm for solving constrained multi-objective optimization problems. Journal of Theoretical and Applied Information Technology, 640- 651.
Calik, H., Alumur, S., Kara, B., &Karasan, O. (2009). A tabu-search heuristic for the hub covering problem over incmplete hub networks.Computers & Operation Research, 3088-3096.
Campbell, J. (1994). Integer programming formulations of discrete hub location problems.European Journal of Operational Research, 72, 387-405.
Correia, I., Nickel, S., &Saldanha-da-Gama, F. S. (2013). Multi-product Capacitated Single-Allocation Hub Location Problems: Formulation and Inequalities. Networks and Spatial Economics, 1-25.
Correia, I., Nickel, S. and Saldanha-da Gama, F. (2018). A stochastic multi-priod capacitated multiple allocation hub location problem: Formulation and inequalities. Omega, 74, 122-138.
Davari, S., &Zarandi, M. H. F. (2013).The Single-Allocation Hierarchical Hub-Median Problem with Fuzzy Flows. Paper presented at the Proceedings of the 5th International Workshop Soft Computing Applications (SOFA)(pp. 165-181), Heidelberg: Springer-Verlag.
Damgacioglu, H., EvinOzdemirel, N. and Iyigun, C. (2015 A genetic algorithm for the uncapacitated single allocation planer hub location problem. Computer and Operations Research, 62, 224-236.
Deb, K., Pratap, A., Agarwal, S., &Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary computation, 6(2), 182-197.
Dukkanci, k., Kara, B. (2017).Rouring and scheduling decisions in the hierarchical hub location problem.Computer and Operations Research, 85, 45-57.
Ernast, A., Jiang, H., &Krishnamoorthy, M. (2005). Reformulation and computational results for uncapacitated single and multiple allocation hub covering problem. Unpublished Report, CSIRO Mathematical and Information Sciences. Australia.
Gelareh, S., Nickel, S. (2015). Multi-priod hub location problems in transportation.Transportation Research Part E: Logistics and Transportation Review, 75, 67-94.
Ghodratnama, A., Tavakkoli-Moghaddam, R., &Azaron, A. (2013).A fuzzy possibilistic bi-objective hub covering problem considering production facilities, time horizons and transporter vehicles.International Journal of Advanced Manufacturing Technology, 66, 187-206.
Jimenez, M. (1996).Ranking fuzzy numbers through the comparison of its expected intervals.International Journal of Uncertainty, Fuzziness and Knowledge Based Systems, 4(4), 379-388.
Jimenez, M., Arenas, M., Bilbao, A., & Rodriguez, M. V. (2007). Linear programming with fuzzy parameters:An interactive method resolution. European Journal of Operational Research, 177, 1599-1609.
Kara, B., &Tansel, B. (2003). The Single-Assignment Hub Covering Problem: Models and Linearizations. The Journal of the Operational Research Society, 54(1), 59-64.
Karimi, H., &Bashiri, M. (2011).Hub covering location problems with different coverage types.ScientiaIranica, 1571-1578.
Karimi, M., Eydi, A. R. and Korani, E. (2014). Modeling of the Capacitated Single Allocation Hub Location Problem with a Hierarchical Approch .International Journal of Engineering, 27(4), 573-586.
Korani, E., &Sahraeian, R. (2013).The hierarchical hub covering problem with an innovative allocation procedure covering radiuses.ScientiaIranica, 20(6), 2138-2160.
Mohammadi, M., Jolai, F., &Tavakkoli-Moghaddam, R. (2013).Solving a new stochastic multi-model p-hub covering location problem considering risk by a novel multi-objective algorithm.Applied Mathematical Modelling, 37, 10053-10073.
Parra, M. A., Terol, A. B., Galdish, B. P., &Uria, M. V. (2005). Solving a multiobjectivepossibilistic problem through compromise programming.European Journal of Operational Research, 164, 748-759.
Pishvaee, M. S., &Torabi, S. A. (2010). A possibilistic programming approach for closed-loop supply chain network design under uncertainty. Fuzzy Sets and Systems, 161, 2668-2683.
Randall, M. (2008). Solution approaches for the capacitated single allocation hub location problem using ant colony optimization. Computational Optimization and Applications, 39 (2), 239-261.
Taghipourian, F., Mahdavi, I., Mahdavi-Amiri, N., &Makui, A. (2012).A fuzzy programming approach for dynamic virtual hub location problem.Applied Mathematical Modelling, 36, 3257-3270.
Tavakkoli-Moghaddam, R., Ghalipour-Kanani, Y., &Shahramifar, M. (2013). A Multi-objective Imperialist Competitive Algorithm for a Capacitated Single-allocation Hub Location Problem International Journal of Engineering, 26(6), 605-620.
Wagner, B. (2008). Model formulation for hub covering problems.Journal of the Operational Research Society, 932-938.
Yaman, H. (2009). The hierarchical hub median problem with single assignment.Transportation Research Part B, 43, 643-658.
