The bi-level consensus model with dual social networks for group decision making

The pursuit of consensus within social networks is a burgeoning area of research, pivotal for harmonizing decision-making amidst diverse opinions. However, existing studies often neglect the crucial balance between costs and benefits in optimizing consensus outcomes. Addressing this gap, this paper introduces a novel bi-level consensus optimization model within the framework of the dual social network. This model aims to achieve an equilibrium between minimizing costs and maximizing benefits, crucial for sustainable decision-making processes. The dual social network framework incorporates positive and negative interactions stemming from trust and opinion similarities, delineating nodes into close, distant, and mixed types based on their relational dynamics. Central to the model is a heterogeneous cost function that integrates individual influence and opinion adjustment, accounting comprehensively for moderator tolerance and incentivization mechanisms. To solve this multi-faceted optimization challenge, the paper proposes a solution leveraging a multi-objective particle swarm algorithm. Through simulation experiments conducted across four distinct social network decision-making scenarios, including a case study on capital investment in an epidemic response center, the paper validates the efficacy and practical applicability of the algorithm. The results underscore the model’s capability to achieve balanced consensus outcomes, offering insights into optimizing decision processes within complex social environments.