Multilevel Evolutionary Algorithm that Optimizes the Structure of Scale-Free Networks for the Promotion of Cooperation in the Prisoner's Dilemma game.

Understanding the emergence of cooperation has long been a challenge across disciplines. Even if network reciprocity reflected the importance of population structure in promoting cooperation, it remains an open question how population structures can be optimized, thereby enhancing cooperation. In this paper, we attempt to apply the evolutionary algorithm (EA) to solve this highly complex problem. However, as it is hard to evaluate the fitness (cooperation level) of population structures, simply employing the canonical evolutionary algorithm (EA) may fail in optimization. Thus, we propose a new EA variant named mlEA-CPD-SFN to promote the cooperation level of scale-free networks (SFNs) in the Prisoner's Dilemma Game (PDG). Meanwhile, to verify the preceding conclusions may not be applied to this problem, we also provide the optimization results of the comparative experiment (EAcluster), which optimizes the clustering coefficient of structures. Even if preceding research concluded that highly clustered scale-free networks enhance cooperation, we find EAcluster does not perform desirably, while mlEA-CPD-SFN performs efficiently in different optimization environments. We hope that mlEA-CPD-SFN may help promote the structure of species in nature and that more general properties that enhance cooperation can be learned from the output structures.