A study of genetic algorithms for approximating the longest path in generic graphs

Finding the longest simple path in a generic undirected graph is a challenging issue that belongs to the NP-Complete class of problems. Four approaches based on genetic algorithms to solve this problem are presented in this article. The first three algorithms proposed use crossover mechanisms between pairs of solutions based on their intersecting regions and the fourth one uses a mutation mechanism on individual solutions, in which the perturbation applied depends on the state of the system. Simulation experiments have been carried out to validate the distinct approaches, which reveal their good performance and provide hints for their application in robotics, packet networks and other fields.