Iranian Institute of Industrial Engineering Journal of Industrial and Systems Engineering 1735-8272 12 1 2019 01 06 Addressing a fixed charge transportation problem with multi-route and different capacities by novel hybrid meta-heuristics 167 184 78694 EN Mohammad Bagher Fakhrzad Industrial Engineering Department, Yazd University, Yazd, Iran F. Goodarzian Industrial Engineering Department, Yazd University, Yazd, Iran A. M. Golmohammadi Industrial Engineering Department, Yazd University, Yazd, Iran Journal Article 2018 04 03 In most real world application and problems, a homogeneous product is carried from an origin to a destination by using different transportation modes (e.g., road, air, rail and water). This paper investigates a fixed charge transportation problem (FCTP), in which there are different routes with different capacities between suppliers and customers. To solve such a NP-hard problem, four meta-heuristic algorithms include Red Deer Algorithm (RDA), Stochastic Fractal Search(SFS), Genetic Algorithm (GA), and Simulated Annealing (SA) and two new hybrid meta-heuristics include hybrid RDA & GA (HRDGA) algorithm and Hybrid SFS & SA (HSFSA) algorithm are utilized. Regarding the literature, this is the first attempt to employ such optimizers to solve a FCTP. To tune up their parameters of algorithms, various problem sizes are generated at random and then a robust calibration is applied by using the Taguchi method. The final output shows that Simulated Annealing (SA) algorithm is the better than other algorithms for small-scale, medium-scale, and large-scale problems. As such, based on the Gap value of algorithms, the results of LINGO software shows that it reveals a better outputs in comparison with meta-heuristic algorithms in small-scale and simulated annealing algorithm is better than other algorithms in large-scale and medium-scale problems. Finally, a set of computational results and conclusions are presented and analyzed. https://www.jise.ir/article_78694_08866b4db1d8a7285d46ef30c3d9feae.pdf