Virtual Magnetic Diminuendo Method: A Search Method for Combinatorial Optimization Problems with a Magnetic Parameter and Its Effectiveness

Recently, a novel method for solving combinatorial optimization problems is proposed. Called a virtual magnetic diminuendo (VMD) method, it is originally inspired by an analogy between the Hopfield network and the spin glass, and provided just controlling a threshold corresponding to a magnetic parameter. According to the preliminary study, it is confirmed that the rate of reaching an optimal solution is improved through introducing the virtual magnetic parameter. But, at the same time, another comment that changing its polarity from negative to positive is essential part of the VMD method is also pointed out. As described above, a detailed mechanism of the VMD method has not been clear yet. Then, in order to solve this severe problem, two kinds of tasks such as an N queens problem and a number place problem are adopted, and we examine their performance under the some different scheduling functions of the virtual magnetic parameter. As a result, it is found experimentally that all trials with changing polarity show better performance than that without changing polarity.