HEURISTIC APPROACH TO THE SOFTWARE IMPLEMENTATION OF LITTLE'S METHOD USING THE TRAVELER'S PROBLEM AS AN EXAMPLE

The travelling salesman problem has been considered as one of the most popular optimization problems. This problem consists in finding the most advantageous route that passes through each of the specified cities only once. The criterion of the route profitability (i.e. the shortest and cheapest one) and the corresponding distance matrices (in kilometers) are applied using the conditions of this problem. It is known that the route must pass through each city only once, in which case the solution is among Hamiltonian cycles. In order to use a mathematical means to solve a problem, it is presented in the form of a mathematical model. The travelling salesman problem is represented as a model on a graph, that is, using the vertices and edges between them. The authors propose the use of the heuristic method to solve this problem. To do this, the software implementation of Little's algorithm, which chooses a set with a minimum boundary for partition from all possible branches, rather than from two resulting from the last partition, has been improved. The heuristic approach is used to the choice of the set with a limit of no more than minimal. The program realization has been demonstrated based on the example of driving between the cities of Ukraine given by the real distance matrix (in kilometers). It has been found that the speed of work of the software implementation of Little’s modified algorithm, developed by the authors, is much higher, which makes it possible to use the latter instead of the complete re-selection method.