One Approach to Solving the Fuzzy Traveling Salesman Problem Based on a Multicriteria Approach

The aim of this work is to develop methods for solving fuzzy traveling salesman problems based on a multi-criteria approach. The paper considers options for solving multi-criteria traveling salesman problems, methods for reducing the problem to a single-criteria problem, and approaches to forming a compromise route using Prim's algorithm. The paper considers methods for solving a fuzzy problem of finding the fastest route with fuzzy specified values of travel time on a transport system. Fuzzy triangular numbers are used to represent the duration. The fuzzy traveling salesman problem is considered as a multi-criteria problem, for which the convolution method with confidence weighting coefficients is used. A discrete version of setting the weighting coefficients and a continuous analog are considered. Membership indicators of the values of the carrier of each fuzzy number are taken into account. The results of applying the developed method for solving real traveling salesman problems are proposed, and an analysis of the effect of the increase in travel time on the final form of the route is carried out. The developed approach can be used to solve the problem of optimizing transportation in a transport network, taking into account the uncertainty of traffic parameters and indicators of subjective confidence of a traveling salesman regarding the effective choice of travel time costs