基于蚁群算法的赋权图点覆盖问题 Vertex Covering Problem of Weighted Graphs Based on Ant Colony Algorithm

点覆盖问题是一个在实际生活中具有重要意义的NP完全问题。蚁群算法为近年来新出现的一种仿生类随机寻优算法。文章运用蚁群算法研究了赋权图的最小点覆盖问题。给出了一个基于蚁群算法的近似算法，得出最小点覆盖问题的近似解。通过修改蚂蚁的状态转移概率公式，简化状态转移规则，建立了相应的数学模型，从而得出求解点覆盖的近似算法，最后进行了实例解析。实验结果表明该算法是行之有效的。 Point covering problem is a NP complete problem in real life. Ant colony algorithm is a new bionic stochastic optimization algorithm emerging in recent years. In this paper, the minimum coverage problem of weighting graphs is studied by using the ant colony algorithm. An approximate algo-rithm based on ant colony algorithm is proposed to solve the minimum point covering problem. By modifying the state transition probability formula of ants and simplifying the state transition rules, the corresponding mathematical model is established, and then the approximate algorithm for solving the point coverage is obtained. Finally, an example is analyzed. The experimental results show that the algorithm is effective.