An Analysis of the Performance of Traveling SalesmanHeuristics on In nite - Size Fractal Instances in

We show how, by a constructive process we can generate arbitrarily large instances of the Traveling Salesman Problem (TSP) using standard fractals such as those of Peano, Koch or Sierpinski. We show that optimal solutions for these TSPs can be known a priori and thus they provide us with new non-trivial TSP instances ooering the possibility of testing heuristics well beyond the scope of testbed instances which have been solved by exact numerical methods. Furthermore , instances may be constructed with diierent features, for example with diierent fractal dimensions. To four of these fractal TSPs we apply three standard constructive heuristics namely Multiple Fragment, Nearest Neighbour, and Farthest Insertion from Convex-Hull, which have eecient general-purpose implementations. The ability of diierent algorithms to solve these diierent fractal TSPs gives us signiicant insight into the nature of TSP heuristics, in a way which is complementary to approaches such as worst-case or average-case analysis.