A Bi-Level Programming Model for Protecting an Important Node in a Network

Protecting important nodes in a network against natural disasters, security threats, attacks and so on is one of the main goals of network planners. In this paper, a new model is presented for protecting an important node (NMPN) in a typical network based on defensive location problem where the threatening agent (t-agent) has the ability to reinforce its power at some nodes. The NMPN is a bi-level programming problem. At the upper level, the planner agent (p-agent) try to find the best locations for protecting resources in order to protect the important node. The lower level problem is represented as the shortest path problem in the network in which the edges are weighted with positive values and sometimes negative values. Thus, Bellman-Ford algorithm is applied to solve the lower level problem. The NMPN is an NP-hard problem. In this work, the genetic, ant colony optimization, binary artificial bee colony with differential evolution, artificial bee colony algorithms and a modified tabu search (MTS) algorithm are used to solve the problem. A test problem is randomly generated to investigate the performance of the used metaheuristic algorithms in this paper. Parameters of the metaheuristic algorithms are tuned by the Taguchi method for solving the test problem. Also, the ANOVA and Tukey tests are used to compare the performance of metaheuristic algorithms. The best results are obtained by the MTS algorithm