  This paper explores the enhancement of solution diversity in evolutionary
algorithms (EAs) for the maximum matching problem, concentrating on complete
bipartite graphs and paths. We adopt binary string encoding for matchings and
use Hamming distance to measure diversity, aiming for its maximization. Our
study centers on the $(\mu+1)$-EA and $2P-EA_D$, which are applied to optimize
diversity. We provide a rigorous theoretical and empirical analysis of these
algorithms.
  For complete bipartite graphs, our runtime analysis shows that, with a
reasonably small $\mu$, the $(\mu+1)$-EA achieves maximal diversity with an
expected runtime of $O(\mu^2 m^4 \log(m))$ for the small gap case (where the
population size $\mu$ is less than the difference in the sizes of the bipartite
partitions) and $O(\mu^2 m^2 \log(m))$ otherwise. For paths, we establish an
upper runtime bound of $O(\mu^3 m^3)$. The $2P-EA_D$ displays stronger
performance, with bounds of $O(\mu^2 m^2 \log(m))$ for the small gap case,
$O(\mu^2 n^2 \log(n))$ otherwise, and $O(\mu^3 m^2)$ for paths. Here, $n$
represents the total number of vertices and $m$ the number of edges. Our
empirical studies, which examine the scaling behavior with respect to $m$ and
$\mu$, complement these theoretical insights and suggest potential for further
refinement of the runtime bounds.
