In the present work, we contribute to the theoretical understanding of a kind of ACO algorithm by investigating the classic maximum independent set problem. Our theoretical results show that with a new construction graph, the ACO algorithm can obtain an approximation ability on maximum independent set problem, and also show the impact of the parameter settings. We first obtain two general upper bounds on arbitrary maximum independent set instance, then we obtain an approximation ratio by ACO algorithm in polynomial time. Finally, we give an instance on which ACO algorithm can escape from local optimum in polynomial time while the local search algorithm is easy to get stuck in local optimum. In the future, we will extend the running time analysis to pheromone evaporation factor, and make in-depth analysis of the impact of pheromone value on the running time.

在当前的工作中，我们通过研究经典的最大独立集问题，为一种ACO算法的理论理解做出了贡献。我们的理论结果表明，使用新的构造图，ACO算法可以获得最大独立集问题的逼近能力，并且还显示了参数设置的影响。我们首先在任意最大独立集实例上获得两个一般的上限，然后在多项式时间内通过ACO算法获得一个近似比。最后，我们给出了一个实例，在这种情况下，ACO算法可以在多项式时间内脱离局部最优，而局部搜索算法很容易陷入局部最优。将来，我们会将运行时间分析扩展到信息素蒸发因子，