—It is not possible to ensure that a network is absolutely secure. Therefore, network operators must continually change their defense strategies to counter attackers who constantly seek new ways to compromise networks. However, as defense resources are limited, it is essential that network operators devise effective resource allocation strategies to maximize the survival time of critical/core nodes under attack. In this paper, the problem of effective resource allocation is analyzed as a mixed, nonlinear, integer programming optimization problem. To solve this complex problem, we propose an effective solution approach based on Lagrangean relaxation and the subgradient method. The efficiency and effectiveness of the proposed heuristic are evaluated by computational experiments.