Immunization of networks using genetic algorithms and multiobjective metaheuristics

The immunization of complex networks can be formulated as a subset selection problem, where the goal is to select a limited number of nodes to be immunized in order to effectively prevent or decelerate the spread of an epidemic. The drop of the largest eigenvalue (eigen-drop) is a measure for the impact of an immunization strategy. It was recently shown that the problem of selecting k out of n nodes from a network such that eigenvalue drop is maximum belongs to the class of NP hard problems. Heuristic algorithms have been suggested to solve these problems approximately, most importantly the netshield algorithm, a greedy approach that approximates the eigenvalue drop by means of a submodular function, the shield value, and then maximizes the shield value by means of a greedy approximation algorithm. In this paper, we design a problem specific genetic algorithm and compare it to netshield plus - an improved variant of netshield - and show that on six moderate size problems from literature that their performance is competitive and often better. We also formulate the node immunization problem as a multiobjective problem, including the cost of immunization as a second objective. First results are presented on biobjective optimization using multiobjective genetic algorithms as solver. The method is demonstrated on the USA domestic airline network and the global city network of the Pandemic cooperative board game, which are augmented by immunization cost data. First insights into the reliability of solvers and the typical shapes of Pareto fronts are obtained.