Effectiveness of the Ring 1-way network for optimizer based on spiking-neural oscillator networks

In our previous study, we proposed Optimizer based on Spiking Neural-oscillator Networks (OSNNs) which are one of the deterministic particle swarm optimization methods. OSNNs are based on dynamics of a spiking neural-oscillator (spiking oscillator) network which consists of plural integrate-and-fire type neurons. In OSNNs, each particle consists of plural spiking oscillators which are coupled with other spiking oscillators by a network topology. The Ring 1-way network topology, which is one of the simple ring-type networks, is introduced into the network topology for OSNNs. The Ring 1-way network can affect search performances of OSNNs, and OSNNs with the Ring 1-way network (Ring OSNNs) have better search performances than Optimizer with Uncoupled Spiking Neurons (OUSNs) in which each spiking oscillator does not connect to the others. In particular, search performances of Ring OSNNs are clearly superior to those of OUSNs in solving separable and multimodal problems. However, the reasons why the Ring 1-way network can improve search performances of OSNNs have not been clarified. In this study, we theoretically analyzed the search dynamics of the Ring 1-way network. In addition, in order to demonstrate analytical results, we conduct numerical simulations by comparing Ring OSNNs with OUSNs. We further discuss the simulation results and clarify effectiveness of the Ring 1-way network.