Optimal cultivated land operation scale for sustainable agriculture: A global multi-objective optimization framework balancing yield, income and emission

Optimizing the cultivated land operation scale (CLOS) has become a key pathway to resolve the contradiction between yield growth and sustainability in agricultural development. However, global evidence on the trade-offs and synergies among the three objectives of food production, farmers’ income, and environmental sustainability remains insufficient. To address this gap, we propose a multi-objective CLOS regulation framework that integrates the dimensions of global baseline, governance environment, and collaborative optimization. Using panel data from 165 countries over the period 1991–2021, we apply fixed-effects models to examine the relationships between CLOS and the three objectives. We then use the NSGA-III algorithm to identify the optimal scale range. Results show that CLOS exhibits an inverted U-shaped relationship with grain yield per unit area (GYPA), a U-shaped relationship with agricultural carbon emission density (ACED), and a positive correlation with the added value of agricultural workers (AVA). Across governance environments, significant heterogeneity exists among countries due to differences in their stages of development and agricultural policy orientations. Low-income countries show a U-shaped yield response, while high-income countries show an inverted U-shape. While agricultural policy support enhances productivity and income, it fails to reduce marginal carbon costs on large scales. Notably, medium-scale operations represent the only optimal range that simultaneously achieves yield enhancement and income growth. The Pareto frontier analysis reveals scale-specific challenges, as small-scale systems struggle with food production, medium-scale operations face constraints in farmers’ income growth, and large-scale systems are burdened by high carbon emissions. The study further proposes differentiated scale adjustment strategies, providing global empirical evidence and decision support for formulating multi-objective synergistic land scale policies.