ПРО РАЦІОНАЛЬНІ МЕТОДИ ПОШУКУ ОПТИМАЛЬНИХ МАРШРУТІВ У НЕЧІТКИХ ЗАДАЧАХ КОМІВОЯЖЕРА

Context. This paper presents the results of a study on the use of triangular fuzzy numbers for determining time-optimal routes in the traveling salesman problem under fuzzy representations of travel duration in a transportation network. To formalize the uncertainty and imprecision of input data – associated with the subjectivity in estimating the time intervals required to travel between individual cities-triangular fuzzy numbers are employed. Various approaches to solving fuzzy traveling salesman problems are examined.Objective. The goal of the work is to develop algorithms for solving the fuzzy traveling salesman problem based on the implementation of the Bellman-Zadeh parametric optimization methods, the use of a two-criteria approach with a given weight function and the refinement of the scheme for calculating the center of gravity of the membership function graph for a given curve density.Method. The article considers methods for solving the fuzzy 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 travel time. The parameters of the problem for formalizing the uncertainty and inaccuracy of input data associated with the influence of subjectivity in assessing the duration of time intervals required to travel between individual cities are presented as fuzzy triangular numbers. Different approaches to solving fuzzy traveling salesman problems are considered. The application of the Bellman-Zadeh method, methods taking into account refinements of defuzzified data, and methods based on a multicriteria approach is formalized. Computational experiments are carried out.Results. Rational algorithms for solving the fuzzy traveling salesman problem based on the Bellman-Zadeh parametric optimization model, multicriteria approach and methods for refining the results of defuzzification of fuzzy data have been developed. In the conducted numerical experiments on solving the traveling salesman problem, fuzzy input data are based on the method for calculating the center of gravity (CoG), the center of gravity of homogeneous and non-homogeneous curves, which are determined by the membership function and the specified reliability values of subjective data. A comparison of the results obtained based on solving the crisp traveling salesman problem and the results based on defuzzified duration values for the fuzzy traveling salesman problem is carried out, according to the results of which the dependence of the solution on the defuzzification method is confirmed.Conclusions. The article considers the method of formalizing the algorithm for solving the fuzzy traveling salesman problem with the minimum duration of movement along the route based on the Belman-Zadeh method, methods taking into account the refinements of defuzzified data and methods based on the multicriteria approach. Fuzzy triangular numbers are used to formalize the uncertainty of the input data when assessing the duration of movement between individual towns of the transport network. It was made a conclusion about the feasibility of using fuzzy numbers when solving fuzzy traveling salesman problems in real conditions of logistics transportation