Solving the Multi-tasking Robust Optimization on Networks via Structural Reconstructions using a Multi-factor Evolutionary Algorithm

Networks tend to be operated in complicated environments, where attacks and errors threaten their functionality. Previous studies indicated that structural damages may impair the performance of networks, and the information propagation process is at risk. The corresponding optimization tasks are modeled as the network robustness optimization problem and the robust influence maximization problem, respectively. These two problems are of great significance in theory and practice and have attracted increasing attention in recent studies. However, existing approaches are far from comprehensive. The impact of structural perturbances on the information propagation process has not been thoroughly investigated. The determination of robust seeds against topological failures remains an open question. Meanwhile, the possible parallelism between the two robust optimization problems has been completely ignored in the current research. Therefore, the multi-tasking optimization theory is employed in this work to tackle the above challenges. The correlative relationship between the two problems is analyzed, and a positive correlation is detected. Further, a multi-factor evolutionary algorithm with multiple problem-oriented operators, named MFEA-Net, is developed to solve both network robustness optimization problems and robust influence maximization problems simultaneously. Experimental results demonstrate that the algorithm is competitive compared with other methods, which contributes to the solution of diffusion problems on networks.