COMPARATIVE ANALYSIS OF THE APPLICATION OF HEURISTIC ALGORITHMS FOR SOLVING THE TSP PROBLEM

Abstract

The need to solve the traveling salesman problem (TSP) often arises when solving practically significant optimization problems, such as problems in the field of economics, logistics in the widest range of applications, in chains of technical programs. Quite often, the specifics of these problems require obtaining a solution that is as close to the exact value as possible. But the TSP problem is NP-complex, that is, its exact solution can be obtained only in exponential time. Therefore, it is not efficient to solve the TSP problem by the full search algorithm in the presence of a large number of vertices of the graph. However, there are various heuristic algorithms that allow finding a rational solution to this problem with a large number of vertices in a time acceptable for the relevant subject area. In this work, the problem of the traveling salesman is defined as a mathematical programming task of finding the shortest path for the movement of a traveling salesman (traveling salesman), the goal of which is to visit all the objects involved in the task in the shortest time and with minimal costs. Appropriate adaptations of the heuristic algorithms, namely the genetic algorithm and the ant colony algorithm, were developed in the MATLAB environment. A computational experiment was performed on the same input sample, a comparative analysis of the performance of two heuristic algorithms, and the effectiveness of the use of heuristic algorithms for solving NP-complex problems was proven.