A knowledge-based genetic algorithm for a capacitated fuzzy p-hub centre network under uncertain information

In real applications of hub networks, the travel times may vary due to traffic, climate conditions, and land or road type. To facilitate this difficulty, in this paper, the travel times are assumed to be characterized by trapezoidal fuzzy variables to present a fuzzy capacitated single allocation p-hub centre transportation (FCSApHCP) with uncertain information. The proposed FCSApHCP is redefined into its equivalent parametric integer non-linear programming problem using credibility constraints. The aim is to determine the location of p capacitated hubs and the allocation of centre nodes to them in order to minimize the maximum travel time in a hub-and-centre network under uncertain environments. As the FCSApHCP is NP-hard, a novel approach called knowledge-based genetic algorithm (KBGA) is developed to solve it. This algorithm utilizes 2 knowledge modules to gain good and bad knowledge about hub locations and then saves them in a good and bad hub memory, respectively. As there is no benchmark available to validate the results obtained, a genetic algorithm with multiparent crossover is designed to solve the problem as well. Then, the algorithms are tuned to solve the problem, based on which their performances are analysed and then compared together statistically. The applicability of the proposed approach and the solution methodologies are demonstrated. Finally, sensitivity analyses on the discount factor in the network and the memory sizes of the proposed KBGA are conducted to provide more insights. The results show that appropriate values of memory sizes can enhance the convergence and save population diversity of KBGA simultaneously.