A solution to the benchmark ATT48 Traveling Salesman Problem (from the TSPLIB95 library) results from isolating the set of vertices into ten open-ended zones with nine lengthwise boundaries. In each zone, a minimum-length Hamiltonian Path (HP) is found for each combination of boundary vertices, leading to an approximation for the minimum-length Hamiltonian Cycle (HC). Determination of the optimal HPs for subsequent zones has the effect of automatically filtering out non-optimal HPs from earlier zones. Although the optimal HC for ATT48 involves only two crossing edges between all zones (with one exception), adding inter-zone edges can accommodate more complex problems.
@article{arxiv.0710.0539,
title = {A Novel Solution to the ATT48 Benchmark Problem},
author = {Anthony A. Ruffa},
journal= {arXiv preprint arXiv:0710.0539},
year = {2007}
}