Enhancing Computational Promise of Neural Optimization for Graph-Theoretic Problems in Real-Time Environments

This paper demonstrates enhanced utility of neural static optimization algorithms for graph-theoretic problems in real-time environments under the assumption that fast computation cycles for near-optimal solutions are desirable. It assumes that a hardware realization of the neural optimization algorithm, which is then likely to fully exploit the high-degree of parallelism inherent to such optimization problems, is feasible. Accordingly, the paper discusses the application of an adaptive neural optimization scheme, which is based on a known model and training algorithm, on the shortest path computation for digraphs with unit edge costs, which proved to be “difficult” for neural optimization algorithms that were non-adaptive, i.e. Hopfield network and its stochastic derivatives. A simulation study demonstrates that the presented neural optimization scheme is able to compute near-optimal solutions for large instances of the problem, i.e. 1000-vertex graphs. The study concludes with the finding that a hardware realization of the presented neural optimization algorithm is poised to compute near-optimal solutions for a class of problems entailing graph search and its rich set of variants within a real-time environment.