Hybrid evolutionary fuzzy learning scheme in the applications of traveling salesman problems

This study develops a hybrid evolutionary fuzzy learning algorithm that automatically determines the near optimal traveling path in large-scale traveling salesman problems (LSTSPs). Identifying solutions for LSTSPs is one of the most complicated topics in the field of global combinatorial optimization problems. The proposed hybrid evolutionary fuzzy learning scheme combines the advantages of the adaptive fuzzy C-means (FCM), simple MAX–MIN merging concept, simulated annealing (SA) learning algorithm and an efficient table transform-based particle swarm optimization (TPSO). This study uses the proposed method to deal with the large-size TSP routing system.The evolutionary TPSO learning algorithm is applied to optimize the traveling table, which in turn extracts the appropriate traveling table sequence codes for approaching the shorter traveling path. The SA local optimal learning algorithm works after the TPSO learning scheme, using three operators to acquire the optimal traveling solution, inversion, translation and switching. The other considerable notation is to divide the large-scale cities into suitable subgroup cities to improve the efficiency of training machine. The popular FCM algorithm is a valid unsupervised clustering method that identifies the relational grades of a given traveling city dataset, separating them into popular categories. Based on the critical issue in maximal city number to break the city nodes of the traveling loop, and reconnect suitable nodes again with the minimal distance searching procedure, the proposed simple but powerful MAX–MIN merging algorithm to rebuild the new traveling path. Various sizes of TSP testing instances reveal that the developed hybrid evolutionary fuzzy learning algorithm achieves better results than other learning methods in both the quality of routing and computing time.