Scaling up the self-optimization model by means of on-the-fly computation of weights

The Self-Optimization (SO) model is a useful computational model for investigating self-organization in "soft" Artificial life (ALife) as it has been shown to be general enough to model various complex adaptive systems. So far, existing work has been done on relatively small network sizes, precluding the investigation of novel phenomena that might emerge from the complexity arising from large numbers of nodes interacting in interconnected networks. This work introduces a novel implementation of the SO model that scales as $\mathcal{O}\left(N^{2}\right)$ with respect to the number of nodes $N$, and demonstrates the applicability of the SO model to networks with system sizes several orders of magnitude higher than previously was investigated. Removing the prohibitive computational cost of the naive $\mathcal{O}\left(N^{3}\right)$ algorithm, our on-the-fly computation paves the way for investigating substantially larger system sizes, allowing for more variety and complexity in future studies.