Maximal Independent Sets (MIS) is one of the core issues in distributed computing and has been extensively researched over the course of the last forty years. This paper examines a subset problem called the Maximum Independent Set (MaxIS) Problem which is computationally intractable by definition or sufficiently vast to prohibit the employment of accurate techniques. In these situations, heuristic techniques are typically used to develop good, but not always optimal solutions for the MaxIS problem. In this paper, we propose a hybrid algorithm based on Ant Colony Optimization (ACO) and Genetic Algorithm (GA) to find the Maximum Independent Sets. The reason to use a hybrid algorithm, ACO_GA, is that the problem takes much time to converge if we use ACO or GA as a single algorithm to solve the problem.