Hierarchical spanning tree network design with Nash genetic algorithm

In this paper, we will propose a Nash genetic algorithm (Nash GA) for solving a hierarchical spanning tree network design problem, formulated as a bi-level programming problem. The proposed algorithm can be employed in designing the backbone topology in a hierarchical link-state (LS) routing domain. Because the well-designed backbone topology structure has a great impact on the overall routing performance in a hierarchical LS domain, the importance of this research is evident. The proposed algorithm is to find an optimal configuration of backbone network for backbone provider (BP) and distribution network for internet service provider (ISP), properly meeting two-aspect engineering goals: i.e., average message delay and connection costs. Also, it is assumed that there are the decision makers for BP and the decision makers for ISP join in the decision making process in order to non-cooperatively optimize the own objective function. From the experiment results, we can see clearly that our proposed algorithm can be employed in effectively designing the spanning tree network of hierarchical LS routing domain considering not only engineering aspects but also specific benefits from systematical layout of backbone network.