The stochastic decision making framework for long-term multi-objective energy-water supply-ecology operation in parallel reservoirs system under uncertainties

The long-term multi-objective reservoir operation (LTMORO) involving multiple competitive goals such as energy, water supply and ecology protection is usually implemented under uncertain and changeable environment. Conventional methods usually obtain trade-off solutions and select most preferred one by multi-criteria decision making (MCDM) under deterministic environment. However, these methods are difficult to handle real-world reservoir system where multiple uncertainties exist in criteria performance values (PVs) and weights (CWs). In this paper, framework for solving reservoir operation and MCDM problem under various uncertainties is developed. A novel multi-objective method based on shuffled frog leaping algorithm (SFLA) is proposed to obtain high-quality trade-off solutions. Besides, hybrid utility forms based on TOPSIS, grey correlation analysis (GCA) or other models are impacted by subjectivity of combination coefficient, resulting in extra uncertainties for MCDM. To this end, the stochastic multi-criteria acceptability analysis (SMAA) model is developed by constructing new utility function based on SMAA-2 and modified GCA. The modified GCA helps to offset the uneven distribution problem in conventional version and enhance differentiation of utility function in SMAA-2. Moreover, deterministic CWs are obtained based on minimum deviation principle and two types of stochastic CWs following probability distributions are used to estimate CWs uncertainty. The risk caused by uncertain information propagating from PVs and CWs to decision results is also quantified. Finally, efficiency of established framework is tested by conducting three numerical experiments compared with deterministic GCA and SMAA-2. Results indicate that, compared with deterministic models, the novel framework provides decision maker with more reliable decision support and quantified risk information. The novel SMAA-GCA model produces relatively high probabilities for solutions to obtain their respective ranks compared with that of SMAA-2. It is effective to reduce impact of complex uncertainties on MCDM for LTMORO under stochastic environment.