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Mapping the problem onto the network

We believe that this is probably the most important phase when dealing with computational models such as neural nets. Suppose we are given an optimization problem then we need to consider the following steps:

  1. A representation of the problem is needed in which the feasible solutions lie at hypercubegif vertices.
  2. Each hypercube vertex is regarded as a configuration of the problem, with an associated energy (or cost) function.
  3. The partition function is then formed by summing the Boltzmann factors of the admissible configurations.
  4. A quadratic energy function (to be mapped onto the first term of equation (9)) for which the minima correspond to solutions and the depth of each minimum reflects the solution quality.

Hopfield and Tank mapped the TSP onto their model using a permutation matrix representation of the TSP tours. Other likewise problems can be mapped using a similar representation.



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Mon Nov 18 19:45:42 EST 1996