Robust multi-objective optimization and probabilistic analysis methods under multiple uncertainties: the CROPAR algorithm.

Appropriate water resource allocation schemes are essential for the coordinated and stable development of the basin. Identifying the risks existing in a basin and proposing a robust water resource allocation scheme are of great significance for water resource management in a basin. In this study, the Coupled Robust Optimization and Robust Probabilistic Analysis (CROPAR) algorithm is proposed based on the Robust Optimization and Robust Probabilistic Analysis (ROPAR) algorithm, taking into account the multiple uncertainties of water resources allocation in a basin. First, this study calculates the multi-objective optimal allocation of water resources under certainty. In this study, a single Pareto front is obtained by minimizing the water shortage rate and minimizing the typical pollutant emissions as two objective functions. Then, this study analyzes the frequency and uncertainty of inflow based on historical record data. This study assumes that the basin inflows vary within a certain interval, while the basin has multiple inflows. In this study, the joint probability distribution function of the inflows was constructed with the Copula function, and nine scenarios were generated. Then, the ROPAR algorithm was applied to these nine cases. A total of 9,000 Pareto fronts were calculated through 1,000 Monte Carlo samples for each scenario. Finally, a probabilistic analysis is performed for each scenario to reach a robust optimal solution for a specific scenario according to the robustness criterion. The results show that the CROPAR algorithm can adequately tackle the uncertainty of water allocation in the basin. It helps to make a wide range of risk-based decisions.