An improved ant-based heuristic approach for solving the longest cycle problem in large-scale complex networks

The longest cycle problem (LCP) has a crucial significance in graph theory and has a wide range of applications in the real-world. Although some excellent LCP solvers have been proposed in recent years, there is still a need for more efficient algorithms to solve the LCP of large-scale real-world complex networks. This paper proposed a fast algorithm ANTH-PDLS (ant heuristic with path disturbance local search) for the LCP. In ANTH-PDLS, two reduction strategies are proposed to reduce the scale of the networks, and a path disturbance strategy is proposed to expand the search ability. Experiments with randomly generated instances and real-world instances show that these strategies are effective. The average solution time of ANTH-PDLS on 21 real-world instances is only 15.5% of the existing excellent algorithms.