ABOUT OF THE ANNEALING METHOD USING FOR THE TRAVELING SALESMAN PROBLEM SOLUTION WITH THE FUZZY TIME PERCEPTION
Authors: Ivohin E. V. , Adzhubey L. T. , Makhno M. F. , Rets V. O. 
Published: December 2024

Context. The article considers a technique for the use of fuzzy numbers and the annealing method for solving the traveling salesman problem, which is formulated as the problem of finding a route to visit a given number of cities without repetitions with a minimum duration of movement. The task of formalizing the algorithm for solving the traveling salesman problem by the annealing method using fuzzy numbers for subjective time perception is posed. The use of fuzzy numbers to increase the accuracy to represent real-world circumstances is proposed.
Objective. The goal of the work is to develop an algorithm for solving the traveling salesman problem based on the implementation of the annealing method with fuzzy numbers representing the subjective time perception for traveling between the cities with the minimum perceived duration of movement along the route.
Method. This paper proposes a method for solving the traveling salesman problem by the annealing method with fuzzy numbers for subjective time perception. A scheme for formalizing the procedure for solving the traveling salesman problem with the minimal perceived duration of movement along the route is described. A variant of the original traveling salesman problem is proposed, which consists in using fuzzy numbers to represent the uncertainty and subjective time perception in traveling between cities as opposed to regular crisp numbers to show regular distance and/or time of traveling. The results of the proposed algorithm for calculating solutions to the traveling salesman problem with minimization of the perceived duration of movement are presented, the obtained solutions are compared with the solutions found by other heuristic methods.
Results. The method for solving the traveling salesman problem using the annealing method with fuzzy numbers for subjective time perception is developed. A variant of the original traveling salesman problem is proposed, which consists in using fuzzy numbers to represent the uncertainty and subjective time perception in traveling between cities as opposed to regular crisp numbers to show regular distance and/or time of traveling. The application of fuzzy numbers makes it possible to perform calculation over possibly uncertain or subjective data, making results more accurate in the case of realistic deviations from the expected mean values in distance coverage. The results of the proposed algorithm for calculating solutions to the traveling salesman problem with minimization of the perceived duration of movement are presented, the obtained solutions are compared with the solutions found by other heuristic methods.
Conclusions. The paper considers a method for formalizing the algorithm for solving the traveling salesman problem using fuzzy numbers for subjective time perception. The use of fuzzy numbers to increase the accuracy to represent real-world circumstances is proposed. The scheme for formalizing the procedure for solving the traveling salesman problem with the minimal perceived duration of movement along the route is described. A variant of the original traveling salesman problem is proposed, which consists in using fuzzy numbers to represent the uncertainty and subjective time perception in traveling between cities as opposed to regular crisp numbers to show regular distance and/or time of traveling.