A water-energy-food-land nexus framework for multi-objective optimization and risk assessment integrating deep...

Climate change has intensified the interdependence within the water-energy-food-land nexus (WEFLN), and the resulting risk mechanism presents significant challenges to traditional resource management approaches. Current research faces challenges in quantifying the dependence structure of multi-resource shortage risks and lacks the capacity to perform synergistic optimization in high-dimensional decision spaces. This study proposes a Trinity framework for the WEFLN nexus, integrating R-vine Copula, Copula-based chance-constrained fuzzy multi-objective programming (CCFMOP), deep reinforcement learning, multi-objective evolutionary algorithm, and a coupling coordinated-gravity model (CCGM) to achieve a systematic process of risk identification-optimization decision-coordinated evaluation. First, a multi-dimensional joint probability model was constructed using the R-vine Copula to assess the risk interactions among water resource availability, electricity supply, and land use. Second, a CCFMOP method was developed to enable collaborative optimization and management of the WEFLN system under joint risks, balancing water supply-demand index (SDI), energy productivity (EP), and food economic benefits (EB). Third, a chaotic multi-objective evolutionary algorithm based on a deep Q-network and decomposition was proposed to solve the WEFLN multi-objective optimization model and obtain the best trade-off schemes (BTS) under different risk scenarios. Finally, the intra-system coupling relationships and inter-system spatial linkages were evaluated using a CCGM model. The proposed framework was applied to Shaanxi Province, China. The study demonstrates that the hierarchical dependency structure composed of Frank, Clayton, and FGM Copulas effectively constructs an R-vine Copula model to characterize the joint distribution of water, electricity, and land resource availability. Based on this model, six risk scenarios (S1-S6) were simulated. Taking S1 as an example, the BTS led to improvements of 22.1 %, 8.7 %, and 6.2 % in SDI, EP, and EB, respectively, compared to the current baseline in Shaanxi Province. This integrated framework effectively identifies joint resource shortage risks, supports the multi-objective coordinated optimization of WEFLN systems, and provides a scientific foundation for enhancing regional coordinated development capacity.