Good triangulations yield good tours

Adam N. Letchford, Nicholas A. Pearson
2008 Computers & Operations Research  
Consider the following heuristic for planar Euclidean instances of the traveling salesman problem (TSP): select a subset of the edges which induces a planar graph, and solve either the TSP or its graphical relaxation on that graph. In this paper, we give several motivations for considering this heuristic, along with extensive computational results. It turns out that the Delaunay and greedy triangulations make effective choices for the induced planar graph. Indeed, our experiments show that the
more » ... esulting tours are on average within 0.1% of optimality. Scope and purpose The traveling salesman problem (TSP) is a fundamental and well-known problem in combinatorial optimisation. It has many applications, for example in vehicle routing and machine scheduling. This paper proposes several heuristics methods for the Euclidean TSP, based on the use of triangulations, and gives extensive computational results. ᭧
doi:10.1016/j.cor.2006.03.025 fatcat:q7zovspt75clvjhq7wazcsoekq