Geometric Approaches to Solving the Traveling Salesman Problem

Abstract

Two geometric approaches to solving sequencing problems are described and tested. Both methods have yielded optimal or near optimal solutions in problems where the optimal is known. Further, these methods have the advantage of being programmable, with execution in relatively short computation times, even for large problems. (The largest tested was composed of 318 cities.) One of these methods (the largest angle method) can be used to generate tours without any computation, if the number of cities is less than 25 or so, giving the practitioner an effective "back of the envelope method" of finding solutions. The results include applications to problems previously reported in the literature as well as several original large problems. The tours, their costs and computation times are presented.