Toward improved global multi-objective optimization for solving water resources engineering and decision-making problems
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The first contribution of this research was developing a novel though simple approach to tackle the dominance resistance for solving many-objective water resources problems. The proposed rounded archiving does not need any changes in the structure of the multi-objective (MO) algorithm because it rounds the value of the objectives to the user-specified precision level prior to the dominance check. The results show that the rounded archiving effectively reduces the archive size by up to 87% for algorithms with unbounded archive structure compared to the original archiving strategy in these algorithms. The necessity to tackle the multi-modal characteristic of water resources problems led to developing a novel cluster-based solution archiving strategy to preserve a diverse set of solutions for MO algorithms. Solutions are dynamically clustered in the decision space and solutions that are distant from each other are kept in the archive of good solutions, even if they are globally dominated by solutions from outside their cluster. The proposed method helps the algorithm identify good quality solutions that belong to significantly different parts of the decision space, provides a larger archive size, and detects optimal and near-optimal tradeoffs. The cluster-based optimization developed in this research is also used for approximating parameter uncertainty of hydrologic models in a MO fashion. This algorithm finds distinct parameter sets that satisfy the so-called acceptance thresholds in each optimization trial. The proposed method is either equally effective to or perform better than popular single-objective uncertainty methods for deriving 95% prediction bounds. Furthermore, the acceptance threshold individually specified for each objective in an MO uncertainty approximation method shrinks the behavioral solution space and reduces the size of the behavioral solution set by up to 98% compared to a single-threshold assignment for the aggregated objective formulation. Further research on uncertainty analysis motivated the development of a new multi-modelling framework. The model-wrapper performs better than the individual models, and the weights associated with each model indicate its contribution rate to the model-wrapper in all ranges of streamflow simulation. The proposed framework aids in model selection strategy, especially when a hydrologic model has minimal contribution to the model-wrapper performance.