New parallel randomized algorithms for the traveling salesman problem

We recently developed a new randomized optimization framework, the Nested Partitions (NP) method. This approach uses partitioning, random sampling, promising index, and backtracking to create a Markov chain that has global optima as its absorbing states. This new method combines global search and local search (heuristic) procedures in a nature way and it is highly matched to emerging massively parallel processing capabilities. In this paper, we apply the NP method to the Traveling Salesman Problem. Preliminary numerical results show that our method generates high quality solutions compared to well known heuristic methods and it can identify a set of near optimal solutions very rapidly.