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The energy optimization in smart power grids (SPGs) is crucial for ensuring efficient, sustainable, and cost-effective energy management. However, the uncertainty and stochastic nature of distributed generations (DGs) and loads pose significant challenges to optimization models. In this study, we propose a novel optimization model that addresses these challenges by employing a probabilistic method to model the uncertain behavior of DGs and loads. Our model utilizes the multi-objective wind-driven optimization (MOWDO) technique with fuzzy mechanism to simultaneously address economic, environmental, and comfort concerns in SPGs. Unlike existing models, our approach incorporates a hybrid demand response (HDR), combining price-based and incentive-based DR to mitigate rebound peaks and ensure stable and efficient energy usage. The model also introduces battery energy storage systems (BESS) as environmentally friendly backup sources, reducing reliance on fossil fuels and promoting sustainability. We assess the developed model across various distinct configurations: optimizing operational costs and pollution emissions independently with/without DR, optimizing both operational costs and pollution emissions concurrently with/without DR, and optimizing operational costs, user comfort, and pollution emissions simultaneously with/without DR. The experimental findings reveal that the developed model performs better than the multi-objective bird swarm optimization (MOBSO) algorithm across metrics, including operational cost, user comfort, and pollution emissions. • Presenting a multi-objective model for energy management via day-ahead scheduling in smart grids. • Enhancing day-ahead scheduling with renewables and demand response strategies. • Introducing a probabilistic model for solar and wind energy uncertainty prediction. • Proposing a hybrid demand response to lower peak energy demand and prevent rebound peaks. • Utilizing MOWDO algorithm for optimal Pareto fronts exploration to achieve tri-objective optimization: cost, emissions, and user comfort. [ABSTRACT FROM AUTHOR]