OPTIMIZATION BY GHOST IMAGE PROCESSES IN NEURAL NETWORKS

We identify processes for structuring neural networks by reference to two classes of interacting mappings, one generating provisional outcom es (''trial solutions'') and the other generating idealized representa tions, which we call ghost images. These mappings create an evolution both of the provisional outcomes and ghost images, which in turn influ ence a parallel evolution of the mappings themselves. The ghost image models may be conceived as a generalization of the self-organizing neu ral network models of Kohonen. Alternatively, they may be viewed as a generalization of certain relaxation/restriction procedures of mathema tical optimization. Hence indirectly they also generalize aspects of p enalty based neural models, such as those proposed by Hopfield and Tan k. Both avenues of generalization are ''context free'', without relian ce on specialized theory, such as models of perception or mathematical duality. From a neural network standpoint, the ghost image framework makes it possible to extend previous Kohonen-based optimization approa ches to incorporate components beyond a visually oriented frame of ref erence. This added level of abstraction yields a basis for solving opt imization problems expressed entirely in symbolic (''non-visual'') mat hematical formulations. At the same time it allows penalty function id eas in neural networks to be extended to encompass other concepts spri nging from a mathematical optimization perspective, including parametr ic deformation and surrogate contractions. This paper demonstrates the efficacy of ghost image processes as a foundation for creating new op timization approaches by providing specific examples of such methods f or covering, packing, generalized covering, fixed charge and multidime nsional knapsack problems. Preliminary computational results for multi dimensional knapsack problems are also presented.