Mohammad Hadi Shekarriz, Asef Nazari, Dhananjay Thiruvady
The Soft Happy Colouring (SHC) problem serves as a rigorous mathematical framework for identifying homophilic structures in complex networks. The SHC seeks to maximise the number of $Ï$-happy vertices, which are those vertices that the proportion of their neighbours sharing colour with them is at least $Ï$. The problem is NP-hard, making optimal solutions computationally intractable for large-scale networks. Consequently, metaheuristic approaches are useful, yet existing methods often struggle with premature convergence. Based on the problem's solution structure and the characteristics of the feasible region, an effective solution method needs to navigate efficiently among promising solutions while utilising information learned from less favourable ones. The Cross-Entropy method is suitable for this because it has a smoothing mechanism that adaptively balances exploration and exploitation, informed by the knowledge accumulated during the search process. This paper introduces a novel intelligent hybrid algorithm, CE+LS, which synergises the adaptive probabilistic learning of the Cross-Entropy method with a fast, structure-aware local search (LS) mechanism. We conduct a comprehensive experimental evaluation on an extensive dataset of 28,000 randomly generated graphs using the Stochastic Block Model as the ground-truth benchmark. Test results demonstrate that CE+LS consistently outperforms existing heuristic and memetic algorithms in homophily maximisation, exhibiting superior scalability and solution quality. Notably, the proposed algorithm remains efficient even in the tight regime, which is the most challenging category of problem instances where comparative algorithms fail to yield effective solutions.