Connectivity-Aware Diversity Index: A graph-based diversity metric for evolutionary optimization

Population diversity is widely used in evolutionary computation and swarm intelligence as both a descriptive indicator and an adaptive control signal. However, many commonly used diversity measures are dispersion-based and rely on deviations from the population centroid, which may overestimate diversity in highly concentrated configurations and fail to reflect the local structural organization that influences evolutionary variation. This paper introduces the Connectivity-Aware Diversity Index (CADI), a graph-based diversity metric that models the population as a delta-neighborhood graph and quantifies diversity through nearest-neighbor separation within connected components. By explicitly incorporating connectivity and local spacing, CADI provides a structure-aware characterization of population diversity that better reflects neighborhood organization in the search space. To avoid manual tuning of the connectivity threshold, we also propose a calibration protocol based on Monte Carlo nearest-neighbor estimation and a quadratic regression surrogate, yielding a scale-consistent mapping from problem dimension, domain size, and population size to delta. CADI is evaluated on controlled population setups with distinct geometric structures and by integration into several diversity-driven evolutionary optimizers. Experiments on the CEC17 benchmark suite for dimensions 10, 30, 50, and 100 show that CADI provides a diversity signal that is more consistent with geometric intuition in controlled settings and can translate into measurable performance gains across several algorithms, supported by nonparametric statistical analyses.