Competitive self-organization and combinatorial optimization: applications to traveling salesman problem

The author discusses algorithms of competitive self-organization and their application to a typical combinatorial problem, the traveling salesman problem. The main feature of the proposed algorithm is the sophisticated use of excitatory/inhibitory intralayer connections of neurons combined with a judicious selection of neural network topology. Such properties contribute to obtaining excellent approximate solutions. Five hundred sets of 30-city solutions are compared with those obtained by a pure simulated annealing method. From this comparison, it is found that a considerable number of the solutions obtained by this self-organization method are highly likely to be the optimal tours. Successive training algorithms are mainly used; however, applications of batch training algorithms are also discussed. Implications for multisalesman problems are discussed