Application of modified Kohnen's network to optimization problems
Toshihiro Shimizu · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2007
The traveling salesman problem, which is one of combinatorial optimization problems, is solved by using two different methods: the Hopfield type network and the Kohonen type network. In the Hopfield type network the energy function is defined, whose global minimum must be searched. The energy is shown analytically to decrease monotonically. The time behavior can be discussed analytically, because the input-output function is piecewise linear. The network can always find the optimum solution. In the Kohonen type network the modified version is proposed, in which the mechanism of choice of winner neuron is included automatically in the time evolution equation of the internal state. In usual Hopfield 's network N x N neurons are needed to solve TSP with N cities. It is shown that only N neurons are needed in modified Kohonen's network, which means that the network has a great advantage in the case of the application to TSP with higher number of cities or in the application to more complicated combinatorial optimization problems. The relation between the Hopfield type network and the modified Kohonen type network is discussed.