Dynamic interactive robust consensus reaching framework for maximum experts considering uncertain cost and adjustment strategy

Consensus optimization models often struggle to coordinate continuous updates of expert opinions and costs, easily falling into the illusion of temporary consensus. Moreover, accurately estimating the extent of opinion adjustments and unit adjustment costs is challenging, posing obstacles to reaching consensus. Based on the maximum expert consensus model (MECM), this study introduces a dynamic interactive robust consensus-reaching framework that considers uncertain costs and adjustment strategies. First, we construct three uncertainty sets to describe uncertain costs, which are then used to develop the robust consensus models. Simultaneously, we propose a dynamic adjustment strategy that uses the optimal adjustment opinions from the model as reference information, objectively indicating the direction and magnitude of expert opinion adjustments and the cost compensation provided by the moderator. This approach helps objectively indicate the direction and magnitude of expert opinion adjustments. This study combines the complementary strengths of identification and direction rule (IR-DR) along with optimization-based rule (OR), aiming to dynamically facilitate consensus among all experts under uncertain conditions. Finally, we design an improved genetic algorithm (GA) to handle the robust models and validate the performance of the proposed consensus framework through case studies and comparative analyses. Results reveal how experts can accelerate consensus through dynamic strategies.