  In this study, the Rank Genetic Algorithm (Rank GA) was adapted to address a
problem in the field of Chromatic Graph Theory: the connected
pseudo-pseudoachromatic index. We successfully improved several previously
known lower bounds of that index. To validate the effectiveness of these new
bounds, we performed an analytical approximation, confirming their validity.
The findings highlight the interdisciplinary impact of the use of genetic
algorithms in theoretical mathematical research, particularly in the solution
of complex combinatorial problems. Our work demonstrates that computational
methods can solve problems that are intractable to humans, leading to
scientific advances in many areas. Moreover, the problem we addressed showcases
the robustness of the Rank GA in finding optimal solutions within a reasonable
time frame, as it consistently avoids getting stuck in local optima.
