The Metric Travelling Salesman Problem: Pareto-optimal Heuristic Algorithms
The Metric Travelling Salesman Problem is a subcase of the Travelling Salesman Problem (TSP), where the triangle inequality holds. It is a key problem in combinatorial optimization. Solutions of the Metric TSP are generally used for costs minimization tasks in logistics, manufacturing and genetics. Since this problem is NP-hard, heuristic algorithms providing near optimal solutions in polynomial time will be considered. The aim of this article is to find Pareto optimal heuristics for Metric TSP under criteria of error rate and run time efficiency. Two real-life kinds of inputs are intercompared - VLSI Data Sets based on very large scale integration schemes and National TSPs that use geographic coordinates. There is a classification of algorithms for Metric TSP in the article. Feasible heuristics and their prior estimates are described. The details of the research methodology are provided. Finally, results and prospective research are discussed.