An Effective Heuristic Algorithm for the Traveling-Salesman Problem

This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem. The procedure is based on a general approach to heuristics that is believed to have wide applicability in combinatorial optimization problems. The procedure produces optimum solutions for all problems tested, “classical” problems appearing in the literature, as well as randomly generated test problems, up to 110 cities. Run times grow approximately as n²; in absolute terms, a typical 100-city problem requires less than 25 seconds for one case (GE635), and about three minutes to obtain the optimum with above 95 per cent confidence.