In view of the main problems faced by household energy management in the context of the carbon peaking and carbon neutrality goals, such as high electricity costs and load peak-valley differences, a grid demand-side household power dispatching strategy based on multi-objective optimization is proposed. Based on the peak-shifting power consumption mechanism, with the goals of lowest power consumption, optimal comfort, and lowest carbon emissions, an optimal dispatching model for household power consumption on the demand side of the power grid is constructed. Furthermore, combining the improved third-generation non-dominated scheduling genetic algorithm and the multi-objective particle swarm algorithm, a hybrid solution algorithm is proposed for optimal scheduling of household electricity. The example analysis results show that the proposed method can better balance the three aspects of electricity economy, comfort and environmental protection. Compared with conventional methods, the proposed method can effectively reduce the peak-valley differences in electricity consumption while ensuring the comfort of electricity consumption, thereby achieving the purpose of reducing electricity consumption and carbon emissions.