A Multi-Objective Evolutionary Algorithm for Promoting the Emergence of Cooperation and Controllable Robustness on Directed Networks

The directedness of links is of significance in complex networks, and much attention has been paid to study the dynamics of directed networks recently.In networked systems, where the emergence of cooperation and robustness are two hot issues in recent decades. Previous studies have indicated that the structures for promoting these two properties are opposite, which also reveals the great impact of structures on the functionalities of networks. Moreover, several realistic problems also reflect the importance of simultaneously promoting the robustness and cooperation maintaining ability on directed networks, however, few studies have focused on solving this urgent problem. Therefore, in this paper, concentrating on optimizing the cooperation maintaining ability together with controllable robustness on directed networks, we first model this issue as a multi-objective optimization problem, and then a multi-objective evolutionary algorithm, labeled as MOEA-Netcc, has been devised to solve this problem. In the experiments, the performance of MOEA-Netcc is validated on both synthetic and real networks, and the results show that MOEA-Netcc can not only achieve balanced optimal results without changing degree distribution of networks; but also create diverse Pareto fronts, which provide various potential candidates for decision makers to deal with social and economic dilemmas.