Gravitational search algorithm for step fixed charge transportation problems

Document Type : Original Article

Author

Department of Mathematics, Kashan Branch, Islamic Azad University, Kashan, Iran

Abstract

Step fixed-charge transportation problem is an extended version of the fixed charge transportation problem, is one of the most important problems in transportation research area. To tackle such an NP-hard problem, we present Gravitational Search Algorithm (GSA). We solve the randomly generated problems by GSA and also with Genetic Algorithm (GA) to compare them. The obtained results show the proficiency of GSA comparison with GA.

Keywords


Altassan, Kh, El-Sherbiny, M.M., Bokkasam, S. (2012).  In handling the step fixed charge transportation problem (ICDeM2012), Kedah, Malaysia, March 15–18.
Balinski, M. L. (1961). Fixed cost transportation problems. Naval Research Logistic Quarterly, 8(1):  41–54.
Baranifar, S. (2018). A credibility-constrained programming for closed-loop supply chain network design problem under uncertainty. Annals of Optimization Theory and Practice, 1(1), 69-83.
El-Sherbiny, M. M. (2012). Alternate mutation based artificial immune algorithm for step fixed charge transportation problem, Egyptian Informatics Journal, 13 (2), 123–134.
Kowalski, K., Lev, B. (2008). On step fixed-charge transportation problem, OMEGA, 36(5):913-917.
Mahmoodirad, A., Hassasi, H., Tohidi, Gh, Sanei, M., Molla-Alizadeh-Zavardehi, S. (2013). Step Fixed Charge Transportation Problems with Fuzzy Numbers, Scientific Journal of Mechanical and Industrial Engineering, 2(3), 50-56.
Mahmoodirad, A., Sanei, M. (2016). Solving a multi-stage multi-product solid supply chain network design problem by meta-heuristics. Scientia Iranica, 23 (3), 1429-1440.
Molla-Alizadeh-Zavardehi S., Hajiaghaei-Keshteli, M., Tavakkoli-moghaddam, R. (2011). Solving a capacitated fixed-charge transportation problem by artificial immune and genetic algorithms with a Prüfer number representation, Expert Systems with Applications, 38, 10462–10474.
Molla-Alizadeh-Zavardehi, S., Sanei, M.,  Soltani, R., Mahmoodirad., A. (2014). Solving a step fixed charge transporation problem by a spanning tree-based memetic algorithm, International Journal of Mathematical Modelling & Computations, 4 (2), 181-191.
Molla-Alizadeh-Zavardehi, S., Mahmoodirad, A., Rahimian, M. (2014). Step Fixed Charge Transportation Problems via Genetic Algorithm, Indian Journal of Science and Technology, 7 (7), 949-954.
Mosallaeipour, S., Mahmoodirad, A., Niroomand,S., Vizvari, B. (2018). Simultaneous selection of material and supplier under uncertainty in carton box industries: a fuzzy possibilistic multi-criteria approach. Soft computing, 22 (9), 2891–2905.
Rajabi, F., Najafi, S., Hajiaghaei-Keshteli, M., Molla-Alizadeh-Zavardehi, S. (2013). Solving fuzzy step fixed charge transportation problems via metaheuristics, International Journal of Research in Industrial Engineering, 2, 24-34.
Rashedi, E., Nezamabadi-pour, H., Saryazdi, S. (2009). GSA: a gravitational search algorithm, Information Sciences, 179 (13), 2232-2248.
 Sanei, M., Hassasi, H., Mahmoodirad, A., Rahimian, M.  (2014). Fixed-Charge Transportation Problem with Fuzzy Costs, Journal of Applied Science and Agriculture, 9 (9), 1-8. 
Taghaodi, R., Kardani, F. (2018). Linear programming problem with generalized interval-valued fuzzy numbers. Annals of Optimization Theory and Practice, 1(2), 1-9.