Decarbonizing livestock villages: Synergistic electricity-heat-fertilizer systems with demand response

With the advancement of modernization, biogas plants with advanced chemical processing capabilities are gradually being established in biomass-rich livestock villages. Energy aggregators equipped with renewable energy systems are assuming a greater role supplying biogas-based electricity, heat, and fertilizer to meet both production and household needs, while villages with livestock product processing facilities actively participate in electricity market demand response. In the context of global carbon reduction, it is critical to address the multi-objective challenge of minimizing operating costs for both energy aggregators and villages while reducing carbon emissions. This study proposes a large-scale constrained mixed-integer nonlinear three-objective optimization model to capture this problem, together with a model simplification strategy to enhance solution efficiency. A novel Reference Vector Guided Differential Evolutionary Algorithm (RVGDE) is developed, which, with a population size of 300 and 3,000,000 evaluations, successfully identifies 44 Pareto-optimal fronts, of which five representative scenarios are analyzed in depth. Compared with 24 classical or state-of-the-art multi-objective optimization algorithms of the same population size, RVGDE achieves a decisive advantage in finding feasible solutions and demonstrates superior computational efficiency. Furthermore, a non-subjective decision-making method is introduced to select a single optimal scheme from the Pareto set, enabling win-win collaboration between energy aggregators and villages while lowering carbon emissions. Integrating modeling, algorithm design, and decision-making, the proposed framework offers an innovative methodology and practical reference for advancing the decarbonization of livestock villages.