Theoretical comparison of mappings of combinatorial optimization problems to Hopfield networks

In solving combinatorial optimization problems by Hopfield networks, mappings of the problems to the networks are not made so carefully. Though many mappings of, for example, the traveling salesman problems (TSP) have been proposed, their theoretical comparisons are not made yet. In this paper, taking two typical mappings of TSP as examples, their theoretical comparisons are made to prove one´s superiority to the other by the asymptotical stability and unstability conditions of the solutions previously shown by the author (1994). This theoretical comparison could be applicable to mappings of many other combinatorial optimization problems