Computer tools for solving the traveling salesman problem

Abstract

The task of the traveling salesman, which is to find the shortest or least costly circular route, is one of the most common optimization problems that need to be solved in various fields of practice. The article analyzes and demonstrates various methods for solving this problem using a specific example: heuristic (the nearest neighbor method, the most profitable neighbor method), metaheuristic (evolutionary algorithm), methods of mathematical programming. In addition to classic exact methods (which are difficult to use for large-scale tasks based on existing software) and heuristic methods, the article suggests using the innovative features of the commercially available MS Excel software using a meta-heuristic base. To find the optimal solution using exact methods, the Excel (Solver) software package was used, as well as the specialized GAMS software package. Comparison of different approaches to solving the traveling salesman problem using a practical example showed that the use of traditional heuristic approaches (the nearest neighbor method or the most profitable neighbor method) is not difficult from a computational point of view, but does not provide solutions that would be acceptable in modern conditions. The use of MS Excel for solving the problem using the methods of mathematical programming and metaheuristics enabled us to obtain an optimal solution, which led to the conclusion that modern tools are an appropriate addition to solving the traveling salesman problem while maintaining the quality of the solution.

Genetic Algorithm Approach for Optimal Cyclic Tour Round the State Capitals in Nigeria’s Niger Delta Region

“…A simple formulation of the TSP model based on the model of Taha (2017) and Pekár et al (2020) is as follows:…”

“…Routing models, according to Pekár et al (2020), are one of the most common discrete and combinatorial optimization problems in practice. They are models used in organizing a collection of things like positions, job schedules, towns, places, and so on, into orders or paths that could sometimes form all points into a single sequence or requiring several routes Danusaputro et al (1990).…”