Multiple-resolution divide and conquer neural networks for large-scale TSP-like energy minimization problems

We describe a multiple-resolution divide-and-conquer ANN approach for large-scale constrained optimization problems like the TSP. The goal of the approach is to divide a problem into sub-problems, solve them with parallel ANNs, then combine the resulting sub-solutions. The divide-and-conquer approach is based on a mathematical principle of orthogonal division errors, which provides the criteria for optimal problem division. The resulting division minimizes the cross-correlation among sub-problems, and hence the necessary communication among them. It therefore provides a minimum-communication allocation of sub-problems to parallel processors. Moreover, the divide and conquer can be done recursively, so that it occurs at all resolutions of the data. We show how wavelets can perform the necessary multiple-resolution data clustering. The divide-and-conquer approach is particularly effective for large-scale fractal data, which exhibits clustering over a large number of resolutions