How to stop undesired propagations by using bi-level genetic algorithms

In this work we introduce a general model to analyse any type of propagation system, whether it represents the spread of a fire, fake news, a virus, etc. We study the computational complexity of the problem of minimising the impact of a propagation by cutting some of the connections it can spread through. Even limiting the scope of our cutting strategy to be short-term, we show that the problem is Σ2P-complete, that is, it is one level above NP-complete in the complexity hierarchy. Intuitively, in Σ2P-complete problems a hard search for the value fulfilling some property is tackled, but just evaluating that property for each candidate value requires performing another hard, independent search. This complexity suggests that a good method to deal with the problem under consideration is a two-level genetic algorithm, that is, a genetic algorithm that uses another genetic algorithm as fitness function: the former algorithm searches for good candidates for solving the target optimisation, and for each candidate within its population, its fitness is calculated by running the latter algorithm. We apply this implementation to two case studies, compare its results with those of greedy and minimax algorithms, and report experimental results. Our results indicate that bi-level genetic algorithms are good candidates to deal with Σ2P-complete problems.