An interval two-stage robust stochastic programming under a bi-level multi-objective framework towards river basin water resources allocation

The uncertainty stemming from hydrological variables and socio-economic parameters poses new challenges to river basin water resources allocation (RBWRA). Given the pressing need for efficient, environmentally friendly, and equitable solutions in RBWRA, a bi-level multi-objective interval two-stage robust stochastic programming (BLMOITRSP) model is proposed. This model aims to achieve the optimal balance among efficiency, eco-friendliness, and equity, collectively called the "3E". A novel hierarchical mixed water allocation mechanism is introduced within this model. The basin authority pursues the "3E" objectives at the macro- control level through administrative water allocation. Conversely, sub-areas as followers prioritize economic interests, striving for economic benefit maximization through water market allocation. Furthermore, uncertain parameters (e.g., water demand) are treated as interval parameters, employing interval two-stage robust stochastic programming (ITRSP) to address uncertainty issues and control systemic risks in the model. To solve the BLMOITRSP model, we present a bi-level interactive global equilibrium optimization algorithm, fusing with the modified particle swarm optimization (PSO) algorithm. The bi-level algorithm provides solutions tailored to the preferences of different decision-makers. The proposed model and method are also applied to the Hanjiang River Basin in China to demonstrate its feasibility and effectiveness. The results indicate that the proposed model effectively ensures the "3E" balance. The introduction of the hierarchical mixed water allocation mechanism proves conducive to promoting water distribution and enhancing economic benefits. ITRSP effectively controls the systemic risks of the model's impact on the basin's total economic benefit. The economic performance of each sub-area varies in response to different decision preferences under RBWRA schemes. Finally, the conclusions and future research directions are provided.