In this paper we present a hybrid neural method that uses a neural network to generate initial search points for a discrete heuristic. We demonstrate the method for the subset-sum problem (SSP). The method hinges on using the continuous valued activations of the neural system to select a corner of the n-cube that can be used to initialize a discrete search. This can be done at each neural iteration, resulting in many discrete searches over the coarse of a single neural run. Without the discrete heuristic, the selected corners can be interpreted as instantaneous neural solutions and the best-so-far tabulated as the neural system runs. This allows the neural system to be terminated without losing the full effort of the run, and should the network be run until convergence, the best-so-far result is at least as good as the convergent corner, and usually better. With the discrete heuristic, a search is launched from the instantaneous neural solutions, greatly improving the overall results (again keeping the best-so-far). The results are presented for an n equals 25 SSP, with comparisons to simulated annealing and genetic approaches.
William J. Wolfe,
"Hybrid Hopfield networks", Proc. SPIE 2353, Intelligent Robots and Computer Vision XIII: Algorithms and Computer Vision, (10 October 1994); doi: 10.1117/12.188908; https://doi.org/10.1117/12.188908