The Hopfield neural network model has been proposed as a novel approach to solve NP-complete problems. T h e concept has been widely acknowledged as a major milestone to revive neural computing research and to widen its applications. However, the result of applying the Hopfield model to solve a classical optimization problem (i.e. Traveling Salesman Problem) has been less encouraging or promising as indicated by many published results. Currently, much of the research in this area is focused o n tuning the Hopfield model with little success, instead of analyzing to investigate its suitability for NPcomplete problems. This report presents a rigorous matrix-based analysis of the Hopfield model in order to understand the fundamental characteristics of the model, its strengths, and its weaknesses. The analysis formally shows why the results obtained by applying the Hopfield model to most NP-complete problems are in general unsatisfactory. I t also indicates that promising results are achieved randomly. Possible amendments and future research directions are also discussed.
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