Set‐theoretic comparison of mappings of combinatorial optimization problems to hopfield neural networks
Satoshi Matsuda · Systems and Computers in Japan · 1996
Abstract In solving combinatorial optimization problems by Hopfield neural networks, mappings of the problems to the networks are not made so carefully. Although many mappings of, for example, the traveling salesman problems (TSP) have been proposed, their theoretical comparisons are not yet made. In this paper, taking two typical mappings of TSP as examples, their theoretical comparisons are made to prove the superiority of one over the other by the asymptotical stability and unstability theory of the solutions shown by Matsuda [8, 9]. This theoretical comparison method could be applicable to mappings of many other combinatorial optimization problems.