Performance of Quadratic Assignment Problem by Hopfield NN with Periodic Brake Hironori Kumeno, Yoko Uwate and Yoshifumi Nishio Dept. of Electrical and Electronic Eng., Tokushima University, 2-1 Minami-Josanjima, Tokushima, 770-8506 JAPAN Email: {kumeno, uwate, nishio}@ee.tokushima-u.ac.jp Abstract—Solving combinatorial optimization problems is one of the important applications of neural networks. Many re- searchers have proposed noise induced hopfield neural networks in which noises are induced state values of neurons. However, the noise inducing method to state values of neurons cause problems. In this study, we propose hopfield neural networks with periodic brake. In the proposed system, external noises are not induced to state values of neurons. Thus, the proposed system can avoid the problem caused in the noise induced system. We investigate the solving ability of the proposed system for quadratic assignment problems and designing of parameters. I. I NTRODUCTION The hopfield neural networks (HNN) is a form of recurrent artificial neural network invented by Hopfield and have been applied to solve combinatorial optimization problems [1]. When connection weights between neurons are related to given problems, the network gives a good solution. Because, the energy of the network converges to a minimum value with natural operation determined by the connection weights. However, the solutions are often trapped into local minimums and do not reach the global minimum demanded. In order to avoid this problem and solve the global minimum effectively, several methods inducing some kinds of noises are proposed by researchers [2]-[8]. Especially, methods that noises are induced into state values of neurons are well proposed and studied. In these methods, noises are induced to state val- ues of neurons in the HNN, and then firing neurons are forcibly switched by the noises. These methods are effective to avoid local minimums. However these noise inducing methods sometimes causes a problem. When the noise induced HNNs are used to solve quadratic assignment problems (QAP), the neurons of HNNs are arranged on a plane surface in order to adapt to two-dimensional matrices of the solving problems. The HNN without noise is constructed to fire only one neuron on each line. However, in the noise induced HNNs, two or more neurons located on a line sometimes fire. Figure 1 shows a pattern of the firing of two neurons on a line. In the figure, black colored squares show firing neurons, and two neurons enclosed in the red colored circle fire on the same horizontal line. The firing of two or more neurons on a line is a problem of this noise inducing method and causes high dependence on solving problems. By the way, in the real wold, human cannot concentrate on one thing for a long period of time. Human can keep high-concentration for ten minutes at most in professional                         Fig. 1. An example of firing of two neurons on a line. view. So that, a break is important to refresh. It is necessary to have a break for keep his mind clear and concentrate again. If he continues to do his task without a break, the efficiency of his task is down. Such a break is inferred to make neurons rest and refresh and then yields high-efficiency. Although the HNN is not real physical neural networks, we adapt this idea to the HNN for escape local minimums and propose a method to escape local minimums. We call the proposing system HNN with periodic brake (HNN-PB). In the proposed system, random values are periodically given to coupling weights between neurons in the network. The state values of neurons in HNN-PB converge according to the given random values of the coupling weights. Then, the system escapes from local minimums. The advantage of the proposed method is that firing of two or more neurons on a line is not caused because the system does not include noise terms in state values. In this study, we investigate the solving ability of the HNN- PB for QAP. We confirm that the method is effective to solve QAP by computer simulations. Then, we investigate designing of optimal parameters for the HNN-PB. 978-1-4673-1490-9/12/$31.00 ©2012 IEEE WCCI 2012 IEEE World Congress on Computational Intelligence June, 10-15, 2012 - Brisbane, Australia IJCNN 1353