A hybrid algorithm based on state-adaptive slime mold model and fractional-order ant system for the travelling salesman problem

The ant colony optimization (ACO) is one efficient approach for solving the travelling salesman problem (TSP). Here, we propose a hybrid algorithm based on state-adaptive slime mold model and fractional-order ant system (SSMFAS) to address the TSP. The state-adaptive slime mold (SM) model with two targeted auxiliary strategies emphasizes some critical connections and balances the exploration and exploitation ability of SSMFAS. The consideration of fractional-order calculus in the ant system (AS) takes full advantage of the neighboring information. The pheromone update rule of AS is modified to dynamically integrate the flux information of SM. To understand the search behavior of the proposed algorithm, some mathematical proofs of convergence analysis are given. The experimental results validate the efficiency of the hybridization and demonstrate that the proposed algorithm has the competitive ability of finding the better solutions on TSP instances compared with some state-of-the-art algorithms.