“Optimal” neural representation of higher order for traveling salesman problems
Satoshi Matsuda · Electronics and Communications in Japan (Part II Electronics) · 2002
Abstract The optimal formulation has been shown based on theoretical measure when the combinatorial optimization problem with linear cost function is solved by a symmetrically connected neural network (Hopfield network) 15 ; however, in this paper, we will present an optimal formulation of higher order for traveling salesman problems defined by a quadratic cost function. The Hopfield neural network constructed by this formulation becomes higher order, and the asymptotic stability and the optimal solution will coincide so far as the vertex of the hypercube which expresses the network state is concerned. Therefore, an optimal solution can always be obtained if the network converges to the vertex. We will confirm by simulations that a good solution of the optimal solutions can be obtained with higher frequency compared to the conventional formulation. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 85(9): 32–42, 2002; Published online in Wiley InterScience ( www. interscience.wiley.com ). DOI 10.1002/ecjb.10070