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, global random sampling, and local search heuristics to create a Markov chain that has global optima as its absorbing states. This new method combines global and local search in a natural way and it is highly matched to emerging massively parallel processing capabilities. In this paper, we apply the NP method to the Travelling Salesman Problem. Preliminary numerical results show that the NP method generates high-quality solutions compared to well-known heuristic methods, and that it can be a very promising alternative for finding a solution to the TSP. Scope and purpose The traveling salesman problem involves finding the shortest route between a number of cities. This route must visit each of the cities exactly once and begin and finish in the same city. As easy as it is to describe, this problem is notoriously difficult to solve. It is widely believed that there is no efficient algorithm that can solve it accurately. On the other hand, this problem is very important since it has many applications in such areas as routing robots through automatic warehouses and drilling holes in printed circuit boards. We present a new method, the Nested Partitions method, for solving the traveling salesman problem. The method is very flexible in that it is capable of finding good solutions rapidly and given enough time will identify the optimal solution. This new method is also highly matched with parallel processing capabilities.