Managing spatio-temporal complexity in Hopfield neural network simulations for large-scale static optimization

A simulation methodology, which trades space complexity with time complexity, to create the Hopfield neural network weight matrix, the costliest data structure for simulation of Hopfield neural network algorithm for large-scale optimization problems, is proposed. Modular composition of a weight term of the Hopfield neural network weight matrix for a generic static optimization problem, which facilitates construction and reconstruction of the weights on demand during a simulation, is exposed. Proposed methodology is demonstrated on a static combinatorial optimization problem, namely the Traveling Salesman Problem (TSP), through the algebraic procedure for temporal (versus spatial) weight matrix construction, pseudo code and C/C++ code implementation, and an associated simulation study. The proposed methodology is successfully tested through simulation on a general purpose Windows™-AMD™ platform for up to 1000 city Traveling Salesman Problem instance, which would require approximately no less than 1TB of memory to be allocated simply to instantiate the weight matrix in the memory space of the simulation process.