An Optimization-Based Truthfulness Framework with an Inertial Influence Algorithm for Consensus Decision-Making in Smart Grid Planning

Group decision-making is important in many real-world applications, particularly in smart grid planning, where different stakeholders need to work together to identify appropriate strategies for energy infrastructure deployment. In this study, we develop an optimization-based truthfulness framework combined with an inertial influence algorithm to facilitate consensus among decision-makers in smart grid planning. Unlike classical heuristic approaches, the truthfulness of each expert is derived through a constrained optimization problem that identifies the closest additive reciprocal preference relation. Based on this optimization model, a diagonal truthfulness matrix is constructed and incorporated into a modified Friedkin–Johnsen influence model to better represent the reliability of expert opinions during the consensus process. To accelerate convergence, an inertial iterative scheme is introduced, and fixed-point analysis is employed to establish the existence and uniqueness of the equilibrium solution under standard contraction assumptions. As an application, the proposed framework is employed to support consensus decision making for selecting suitable locations for Battery Energy Storage Systems (BESS) and Electric Vehicle Charging Station (EVCS) infrastructure in a smart grid environment. The numerical results show that the proposed inertial method converges faster than the classical influence model and keeps the opinion changes more stable. It also combines the preferences of different experts effectively and helps to reach a reliable consensus. These results show that combining optimization techniques, inertial fixed-point methods, and social influence models can provide a simple and effective framework for decision-making in smart grid planning.