Effective Tour Searching for TSP by Contraction of Pseudo Backbone Edges

Abstract. We introduce a reduction technique for the well-known TSP. The basic idea of the approach consists of transforming a TSP instance to another one with smaller dimension by contracting pseudo backbone edges computed in a preprocessing step, where pseudo backbone edges are edges which are likely to be in an optimal tour. A tour of the small instance can be retransformed to a tour of the original instance. We experimentally investigated TSP benchmark instances by our reduction technique combined with the currently leading TSP heuristic of Helsgaun. The results strongly demonstrate the effectivity of this reduction technique: for the six VLSI instances xvb13584, pjh17845, fnc19402, ido21215, boa28924, and fht47608 we could set world records, i.e., find better tours than the best tours known so far. The success of this approach is mainly due to the effective reduction of the problem dimension so that we can search the more important tour subspace more intensively.