Dynamic multiscale region search algorithm using vitality selection for traveling salesman problem

• Dynamic multiscale region search using vitality selection is proposed for TSP.
• Dynamic-variable and multiscale search rules are different from strong-fixed rules.
• Vitality selection selects an individual by its progress, not only by its fitness.
• The objective of vitality selection is to maximize the match of other operators.

Traveling salesman problem (TSP) is a classical mathematical model. Many industry, network, and engineering optimization problems on expert and intelligent system are able to be expressed by using TSP-based mathematical model, such as production planning, vehicle routing, resource scheduling, and so on. Vitality selection (VS) is proposed as a new modification scheme based on delete-oldest selection for TSP. The evaluation criterion of individuals in VS is the individual-made progress in the local successive generations. This is different from the pure fitness criterion. Theoretical comparison and behavior feature analysis demonstrate that VS is effective to avoid the premature convergence and escape from the local optimum. On the other hand, dynamic multiscale region search algorithm (DMRSA) using VS is proposed. DMRSA is characterized by the subregion-segmentation and the selected-city methods. These methods for one individual are not only dynamic in one generation, but also variable from the first generation to the last generation. These dynamic-variable search rules are effective to improve the performance of the local search, and different from variable neighborhood search. To demonstrate the effectiveness of DMRSA, experiments about the convergence, the percentage deviation of the average solution to the best known solution, and the average execution time were done. We compared DMRSA with 9 compared algorithms for 27 TSP instances of TSPLIB. DMRSA found the 22 best known solutions for 27 TSP instances. The experiment-proof robustness and adaptability of DMRSA is trustworthy for solving TSP-based mathematical model applications on expert and intelligent system.