Addressing a fixed charge transportation problem with multi-route and different capacities by novel hybrid meta-heuristics

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 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.