Development of a stochastic multi-objective optimization model for managing the water, food, and energy nexus in agriculture.

Water and energy shortages, as well as environmental degradation, threaten agricultural sustainability in the Sefidroud River basin. This study addresses these challenges by developing a novel multi-objective optimization model based on the water-food-energy nexus, incorporating stochastic uncertainty through chance-constrained programming. The model applies a multi-objective evolutionary algorithm to simultaneously minimize agricultural water shortages and maximize hydropower production in the Sefidroud irrigation network, offering a quantifiable framework for decision-making under uncertainty (tested at 80%, 90%, 95%, and 99% confidence levels). To explicitly determine the trade-offs between competing objectives, a Pareto front is analyzed. For instance, at a 90% confidence level, a 14.8% reduction in water scarcity requires a 3.15% decline in energy production, providing actionable insights for policymakers. The model results indicate that in May, peak hydropower generation (60,000 MWh) is achieved, whereas in June, severe water shortages (127.4 million m³) occur, causing energy production to decline to 13,127 MWh. This study advances nexus-based optimization by integrating stochastic methods and multi-objective trade-offs, addressing gaps in the existing literature. The proposed framework is transferable to other basins and demonstrates how optimized strategies can balance sustainability and resource constraints in water-scarce regions.