With the growth of online networks, understanding the intricate structure of communities has become vital. Traditional community detection algorithms, while effective to an extent, often fall short in complex systems. This study introduced a meta-heuristic approach for community detection that leveraged a memetic algorithm, combining genetic algorithms (GA) with the stochastic hill climbing (SHC) algorithm as a local optimization method to enhance modularity scores, which was a measure of the strength of community structure within a network. We conducted comprehensive experiments on five social network datasets (Zachary's Karate Club, Dolphin Social Network, Books About U.S. Politics, American College Football, and the Jazz Club Dataset). Also, we executed an ablation study based on modularity and convergence speed to determine the efficiency of local search. Our method outperformed other GA-based community detection methods, delivering higher maximum and average modularity scores, indicative of a superior detection of community structures. The effectiveness of local search was notable in its ability to accelerate convergence toward the global optimum. Our results not only demonstrated the algorithm's robustness across different network complexities but also underscored the significance of local search in achieving consistent and reliable modularity scores in community detection.

A genetic algorithm (GA) evolves the population of candidate solutions to a particular problem through crossover and mutation operators. Since a newly generated solution may not satisfy the constraints of the given problem, it is common to penalize infeasible solutions or to repair them to feasible solutions. For the minimum vertex cover (MVC) problem, we propose an adaptive greedy repair operator. Our repair operator first repairs an infeasible solution into a feasible one using a randomized greedy algorithm, and then removes unnecessary vertices from the feasible vertex cover, making it a minimal vertex cover. During the repair process, when adding or removing vertices, the degree of exploration and exploitation in the randomized greedy algorithm is adaptively adjusted based on the convergence level of the population. When the population lacks high-quality solutions, the operator strives to generate superior solutions greedily. However, when the solution set has enough high-quality solutions, it explores unexplored choices to break through the limitations of the existing solution set. We compared our GA with a deterministic greedy algorithm, a randomized greedy algorithm, and GAs using various repair operators. Experimental results on benchmark graphs from the Benchmarks with Hidden Optimum Solutions Library (BHOSLIB) demonstrated that the proposed repair operator improved the performance of the GA for the MVC problem.