Previous |  Up |  Next

Article

Keywords:
genetic algorithms; transportation problem; fixed charge transportation problem; metaheuristic algorithms
Summary:
In this paper, we consider the fixed-cost transportation problem. This problem is known to be NP-hard. Therefore, various heuristic and metaheuristic approaches have been proposed to find an approximate optimal solution. In this paper, we propose three hybrid algorithms that combine the ideas of metaheuristic and heuristic approaches in different ways. Two of the proposed algorithms consist of the sequential implementation of metaheuristic and heuristic algorithms, while the third one is a full hybrid algorithm designed by completely intertwining these two approaches. Experimental results on medium-size problems show that our proposed full hybrid algorithm provides approximately a 5
References:
[1] Adlakha, V., Kowalski, K.: On the fixed-charge transportation problem. Omega 27 (1999), 3, 381-388. DOI 
[2] Adlakha, V., Kowalski, K.: A simple heuristic for solving small fixed-charge transportation problems. Omega 31 (2003), 3, 205-211. DOI 
[3] Adlakha, V., Kowalski, K., Vemuganti, R. R.: Heuristic algorithms for the fixed-charge transportation problem. Opsearch 43 (2006), 132-151. DOI  | MR 2764169
[4] Adlakha, V., Kowalski, K., Lev, B.: A branching method for the fixed charge transportation problem. Omega 38 (2010), 5, 393-397. DOI  | MR 2764169
[5] Amrahov, S. E., Ar, Y., Tugrul, B., Akay, B. E., Kartli, N.: A new approach to Mergesort algorithm: Divide smart and conquer. Future Generation Computer Systems 157 (2024), 330-343. DOI 
[6] Balinski, M. L.: Fixed-cost transportation problems. Naval Research Logistics Quarterly 8 (1961), 1, 41-54. DOI 
[7] Biswas, A., Roy, S., Mondal, S. P.: Evolutionary algorithm based approach for solving transportation problems in normal and pandemic scenario. Applied Soft Computing 129 (2022), 109576. DOI 
[8] Calvete, H. I., Gale, C, Iranzo, J. A., Toth, P.: A matheuristic for the two-stage fixed-charge transportation problem. Computers Oper. Res. 95 (2018), 113-122. DOI  | MR 3789199
[9] Cosma, O., Pop, P. C., Danciulescu, D.: A novel matheuristic approach for a two-stage transportation problem with fixed costs associated to the routes. Computers Oper. Res. 118 (2020), 104906. DOI  | MR 4067956
[10] Dantzig, G. B.: Linear programming. Oper. Res. 50 (2002), 1, 42-47. DOI  | MR 1885208
[11] Ebrahimnejad, A.: New method for solving fuzzy transportation problems with LR flat fuzzy numbers. Inform. Sci. 357 (2016), 108-124. DOI  | MR 3414360
[12] Eiben, A. E., Smith, A. E.: Introduction to Evolutionary Computing. Springer-Verlag, Berlin, Heidelberg 2015. MR 3379133
[13] El-Sherbiny, M. M., Alhamali, R. M.: A hybrid particle swarm algorithm with artificial immune learning for solving the fixed charge transportation problem. Computers Industr. Engrg. 64 (2013), 2, 610-620. DOI 
[14] Hakim, M., Zitouni, R.: An approach to solve a fuzzy bi-objective multi-index fixed charge transportation problem. Kybernetika 60 (2024), 3, 271-292. DOI  | MR 4777310
[15] Nejad, E. Hazrati, Yigit-Sert, S., Amrahov, S. Emrah: An effective global path planning algorithm with teaching-learning-based optimization. Kybernetika 60 (2024), 3, 293-316. DOI 
[16] Hirsch, W. M., Dantzig, G. B.: The fixed charge problem. Naval Res. Logist. Quarterly 15 (1968), 3, 413-424. DOI  | MR 0258464
[17] Hitchcock, F. L.: Distribution of a product from several sources to numerous locations. J. Math. Physics 20 (1941), 224-230. DOI  | MR 0004469
[18] Hong, J., Diabat, A., Panicker, V. V., Rajagopalan, Sand .: A two-stage supply chain problem with fixed costs: An ant colony optimization approach. Int. J. Product. Econom. 204, (2018), 214-226. DOI 
[19] Hosseini, A., Pishvaee, M. S.: Capacity reliability under uncertainty in transportation networks: An optimization framework and stability assessment methodology. Fuzzy Optim. Decision Making 21 (2022), 3, 479-512. DOI  | MR 4456241
[20] Rani, J. Jansi, Manivannan, A., Dhanasekar, S.: Interval valued intuitionistic fuzzy diagonal optimal algorithm to solve transportation problems. Int. J. Fuzzy Systems 25 (2023), 4, 1465-1479. DOI 
[21] Jawahar, N., Balaji, A. N.: A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge. Eur. J. Oper. Res. 194 (2009), 2, 496-537. DOI 
[22] Jawahar, N., Gunasekaran, A., Balaji, N.: A simulated annealing algorithm to the multi-period fixed charge distribution problem associated with backorder and inventory. Int. J. Prod. Res. 50 (2012), 9, 2533-2554. DOI 
[23] Jo, J. B., Li, Y., Gen, M.: Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers Industr. Engrg. 53 (2007), 2, 290-298. DOI 
[24] Kartlı, N., Bostancı, E., Guzel, M. S.: A new algorithm for the initial feasible solutions of fixed charge transportation problem. In: 2022 7th International Conference on Computer Science and Engineering (UBMK), IEEE 2022, pp. 82-85. DOI  | MR 4567841
[25] Kartli, N., Bostanci, E., Guzel, M. S.: A new algorithm for optimal solution of fixed charge transportation problem. Kybernetika 59 (2023), 1, 45-63. DOI  | MR 4567841
[26] Kartli, N., Bostanci, E., Guzel, M. S.: Heuristic algorithm for an optimal solution of fully fuzzy transportation problem. Computing 106 (2024), 10, 3195-3227. DOI  | MR 4794582
[27] Kartli, N.: A Metaheuristic Algorithm for the Fixed Charge Transportation Problem. In 2024 9th International Conference on Computer Science and Engineering (UBMK) IEEE (2024) 1030–1033. DOI:10.1109/UBMK63289.2024.10773580 DOI 
[28] Lotfi, M. M., Tavakkoli-Moghaddam, R.: A genetic algorithm using priority-based encoding with new operators for fixed charge transportation problems. Appl. Soft Comput. 13 (2013), 5, 2711-2726. DOI 
[29] Mardanya, D., Roy, S. K.: New approach to solve fuzzy multi-objective multi-item solid transportation problem. RAIRO Oper. Res. 57 (2023), 1, 99-120. DOI  | MR 4534569
[30] Mirjalili, S.: Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput. Appl. 27 (2016) 1053-1073. DOI 
[31] Mohammed, A. S., Amrahov, S. E., Celebi, F. V.: Bidirectional conditional insertion sort algorithm; An efficient progress on the classical insertion sort. Future Generation Computer Systems 71 (2017), 102-112. DOI 
[32] Mondal, A., Roy, S. K.: Behavioural threeway decision making with Fermatean fuzzy Mahalanobis distance: Application to the supply chain management problems. Appl. Soft Computing 151 (2024), 111182. DOI 
[33] Panicker, V. V., Vanga, R., Sridharan, R.: Ant colony Optimization algorithm for distribution-allocation problem in a two-stage supply chain with a fixed transportation charge. Int. J. Prod. Res. 51 (2013), 3, 698-717. DOI 
[34] Paojiyah, A. N. S., Az'zahra, A. P., Aulia, V. F., Wulan, E. R.: Penerapan Dragonfly Optimization Algorithm (DOA) untuk Menyelesaikan Fixed Charge Transportation Problem (FCTP). KUBIK: Jurnal Publikasi Ilmiah Matematika 9 (2024), 2, 187-197.
[35] Pop, P. C., Sabo, C., Biesinger, B., Hu, B., Raidl, G. R.: Solving the two-stage fixed charge transportation problem with a hybrid genetic algorithm. Carpathian J. Math. 33 (2017), 3, 365-371. DOI 10.37193/CJM.2017.03.11 | MR 3728059
[36] Raj, K. A. A. D., Rajendran, C.: A genetic algorithm for solving the fixed-charge transportation model: two-stage problem. Comput. Oper. Res. 39 (2012), 9, 2016-2032. DOI 
[37] Rao, R. V., Savsani, V. J., Vakharia, D.: Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems. Computer-aided Design 43 (2011), 303-315. DOI  | MR 2847014
[38] Saikia, B., Dutta, P., Talukdar, P.: An advanced similarity measure for Pythagorean fuzzy sets and its applications in transportation problem. Artif. Intell. Rev. 56 (2023), 11, 12689-12724. DOI 
[39] Sandhiya, S., Dhanapal, A.: Solving neutrosophic multi-dimensional fixed charge transportation problem. Contemp. Math. 5 (2024), 3, 3601-3624. DOI 
[40] Singh, G., Singh, A.: Extension of particle swarm optimization algorithm for solving transportation problem in fuzzy environment. Appl. Soft Comput. 110 (2021), 107619. DOI 
[41] Shivani, Chauhan, D., Rani, D.: A feasibility restoration particle swarm optimizer with chaotic maps for two-stage fixed-charge transportation problems. Swarm Evolutionary Comput. 91 (2024), 101776. DOI 
[42] Sun, M., Aronson, J. E., Mckeown, P. G., Drinka, D.: Tabu search heuristic procedure for the fixed charge transportation problem. Eur. J. Oper. Res. 106 (1998), 2-3, 411-456.
Partner of
EuDML logo