Wastewater treatment process design involves the optimization of multiple conflicting objectives. The detection of different equivalent solutions in terms of objective values is crucial for designers in order to efficiently switch to the new optimal operation policies if changes in the process conditions or new constraints occur. In this work, the dynamic multi-objective optimization of a municipal wastewater treatment plant model is carried out. The aim is to simultaneously optimize an economic cost term and an effluent quality index. The selected process variables for the optimization are (1) an aeration factor in the aerated tank previous to the clarifier, and (2) an internal recycle flow rate. Their time profiles are approximated using the control vector parameterization technique. To solve the multi-objective problem and find the Pareto front, the NSGA-II algorithm has been used. The simulation of different realistic scenarios which impose operational constraints (e.g., maintenance operations) reveals that, indeed, multiple solutions exist at least in some areas of the Pareto front. It is observed that different control profiles can produce nearly identical results in terms of Pareto solutions. The a priori knowledge of these equivalent solutions for different scenarios provides the decision makers with alternative choices to be adapted to their organizations policies when events altering decision variables bounds or adding new constraints to the process model occur.

废水处理工艺设计涉及多个冲突目标的优化。对于目标值而言，检测不同的等效解决方案对于设计人员至关重要，以便在过程条件发生变化或出现新的约束条件时有效地切换到新的最佳操作策略。在这项工作中，对市政污水处理厂模型进行了动态多目标优化。目的是同时优化经济成本项和废水质量指数。用于优化的所选过程变量是（1）澄清池之前的曝气池中的曝气系数，以及（2）内部循环流量。使用控制矢量参数化技术可以估算其时间轮廓。为了解决多目标问题并找到Pareto前沿，已使用NSGA-II算法。对施加操作约束（例如，维护操作）的不同现实情况的仿真显示，实际上，至少在帕累托前沿的某些区域中存在多种解决方案。据观察，就帕累托解而言，不同的控制曲线可以产生几乎相同的结果。这些针对不同场景的等效解决方案的先验知识为决策者提供了在更改决策变量范围或为流程模型添加新约束的事件发生时，可以适应其组织策略的替代选择。至少在帕累托前沿的某些区域中存在多种解决方案。据观察，就帕累托解而言，不同的控制曲线可以产生几乎相同的结果。这些针对不同场景的等效解决方案的先验知识为决策者提供了在更改决策变量范围或为流程模型添加新约束的事件发生时，可以适应其组织策略的替代选择。至少在帕累托前沿的某些区域中存在多种解决方案。据观察，就帕累托解而言，不同的控制曲线可以产生几乎相同的结果。这些针对不同场景的等效解决方案的先验知识为决策者提供了在更改决策变量范围或为流程模型添加新约束的事件发生时，可以适应其组织策略的替代选择。