Distribution-Prediction-Based Robust Multiobjective Optimization for Wastewater Treatment Process With Time-Linkage Uncertainty
针对污水处理过程中连续时间点间的不确定性存在关联的问题，提出一种基于分布预测的鲁棒多目标优化算法，通过高斯过程预测不确定性分布并自适应调整进化策略，获得更稳定且兼顾出水质量和运行成本的优化设定点。
Robust optimization (RO) methods have been developed to improve the reliable operation performance of wastewater treatment process (WWTP) under uncertainties. However, the time-linkage uncertainty between uncertainties in the successive process of WWTP leads to a more complex problem. To solve this issue, a distribution-prediction-based robust multiobjective optimization (DP-RMO) algorithm is proposed to obtain robust optimal set points, which can enhance the operation stability of WWTP. First, the robust multiobjective optimization (MOO) objectives are established based on adaptive kernel functions. Then, the effluent quality (EQ) and operation cost (OC) objectives with time-linkage uncertainty in WWTP can be dynamically described. Second, a data-driven predictor is designed based on Gaussian process (GP) to obtain the distribution of time-linkage uncertainty. The predictor takes the variations in the robust solution spaces at adjacent moments as input, which can capture the time-linkage uncertainty between uncertainties at different moments. Third, a self-adjustment evolutionary strategy is proposed to optimize the expectation of robust objective functions through the predicted information. The evolutionary parameters are adaptively adjusted according to the discrepancy in evolutionary states, which can obtain robust optimal set points of WWTP. Finally, the proposed DP-RMO algorithm and other comparison algorithms are tested in the benchmark simulation model No. 1 (BSM1) of WWTP. The experimental results show that DP-RMO can reduce the adverse effects of time-linkage uncertainties. Besides, the optimal set points obtained from DP-RMO exhibit better EQ and OC without sacrificing the robustness performance.