Enhancing Soft Happiness via Evolutionary Algorithms

Mohammad Hadi Shekarriz, Dhananjay R. Thiruvady, Asef Nazari

Abstract: For $0\leq \rho\leq 1$, a $\rho$-happy vertex $v$ in a coloured graph shares a colour with at least $\rho\mathrm{deg}(v)$ of its neighbours. Soft happy colouring of a graph $G$ with $k$ colours extends a partial $k$-colouring to a complete vertex $k$-colouring such that the number of $\rho$-happy vertices is maximum among all such colouring extensions. The problem is known to be NP-hard, and an optimal solution has a direct relation with the community structure of the graph. In addition, some heuristics and local search algorithms, such as Local Maximal Colouring (LMC) and Local Search (LS), have already been introduced in the literature. In this paper, we design Genetic and Memetic Algorithms for soft happy colouring and test them for a large set of randomly generated partially coloured graphs. Memetic algorithms yield a higher number of $\rho$-happy vertices, but Genetic Algorithms can perform well only when their initial populations are generated by LMC or LS. Statistically significant results indicate that both Genetic and Memetic Algorithms achieve high average accuracy in community detection when their initial populations are generated using LMC. Moreover, among the competing methods, the memetic algorithm whose initial population is generated by LMC identified the greatest number of complete solutions.

External IDs:dblp:journals/corr/abs-2508-20934