Mutation transit search algorithm introducing black hole swallowing strategy to solve p-hub location allocation problem

The p-Hub allocation problem is a classic problem in location assignment, which aims to optimize the network by placing Hub devices and allocating each demand node to the corresponding Hub. A mutation Transit search (TS) algorithm with the introduction of the black hole swallowing strategy was proposed to solve the p-Hub allocation problem. Firstly, the mathematical model for the p-Hub allocation problem is established. Six mutation operators specifically designed for p-Hub allocation problem are introduced to enhance the algorithm’s ability to escape local optima. Additionally, the black hole swallowing strategy was incorporated into TS algorithm so as to accelerate its convergence rate while ensuring sufficient search in the solution space. The improved TS algorithm was applied to optimize three p-Hub location allocation problems, and the simulation results are compared with those of the basic TS algorithm. Furthermore, the improved TS algorithm is compared with the Honey Badger Algorithm (HBA), Sparrow Search Algorithm (SSA), Harmony Search Algorithm (HS), and Particle Swarm Optimization (PSO) to solve three of p-Hub allocation problems. Finally, the impact of the number of Hubs on the cost of three models was studied, and the simulation results validate the effectiveness of the improved TS algorithm.