Figure 1

Avoidance-driven clustering emerges in non-minimal distance routing. (A) Illustrates design-element connectivity of a shipboard power systems. (B) Illustrates a hypothetical arrangement. (D) Plots radius of gyration (\(R_g\)) versus T that quantifies correlations between elements paired by their degree of connectivity, low-low, high-high, and high-low. Low \(R_g\) at low T, where designs are dominated by minimal routing distance are clustered by attraction. However, low \(R_g\) at high T for functionally disconnected, low-low and high-high connectivity pairs that coincides with high \(R_g\) for functionally connected high-low pairs indicates repulsion driven clustering. The inset network diagram shows example element pairs that \(R_g\) is averaged over. (G) Plots the value of the objective function as internal energy of the system versus temperature. (C, E, F, H) Show element localization in the ship hull. Low T clustering (C and F) is expected since the objective prioritizes routing cost, and the distribution is a single dense region, that is central, and excludes the boundary, all consistent with attraction-driven clustering. High T clustering (H), however, is multi-modal and peripheral. Moderate T (E) corresponds to local peaks in \(R_g\) in (D) and is distributed throughout the hull which indicates de-clustering.