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The study presents a two-level multi-objective approach for energy scheduling in a smart distribution electrical grid. The proposed energy optimization strategy combines hybrid demand management at the upper level and multi-objective functions at the lower level. The multi-objective function in lower level is designed to minimize operational costs and enhance reliability. The upper-level demand management is optimized by taking into account price signals from the upstream grid. The hybrid demand management such as load shifting and load interruption are proposed as effective approaches for consumers. The energy scheduling in both levels by improved sunflower optimization (ISFO) algorithm is solved, and fuzzy approach based on linear programming technique for multidimensional analysis of preference (LINMAP) method is proposed for finding desired solution of the multi-objective function in lower-level. The effectiveness of the electrical grid is examined on the 69-bus distribution network through the utilization of day-ahead scheduling and incorporating findings from mathematical modeling. The results of the proposed problem with demand-side optimization lead to decreasing operation cost by 2.43% and enhancing reliability index by 0.6% compared to lack of demand-side optimization.