Search Space Representation and Reduction Methods to Enhance Multiobjective Water Supply Monitoring Design. Issue 3 (21st March 2019) - Bode, Felix; Reed, Patrick; Reuschen, Sebastian; Nowak, Wolfgang
Abstract: Optimal design of groundwater monitoring networks is challenging due to (1) conflicting objectives for assessing the performance of candidate monitoring networks, (2) uncertainty in system dynamics and hydrogeological context, and (3) the large decision space of possible monitoring‐well positions (also termed the search space). The immensity of the search space poses a significant challenge for modern multiobjective optimization tools. This study introduces two approaches that improve the efficiency and effectiveness of evolutionary multiobjective optimization tools when solving monitoring design problems. We show how a careful mathematical representation of the monitoring design search space and reductions of possible monitoring‐well positions enhance the solution and attainment of decision‐relevant multiobjective trade‐offs in monitoring quality. We demonstrate the value of our improved representation and reduction techniques on a three‐objective monitoring network design problem focused on urban source water protection (termed the U_Protect benchmarking problem). U_Protect abstracts a real‐world case study within an urban drinking‐water well catchment, including inaccessible and restricted areas for monitoring‐well installation, and random heterogeneities in the conductivity field. Our representation and reduction methods significantly enhance the effectiveness, efficiency, and reliability of the optimization. Our proposed framework shifts focus to the most impactful monitoring design decisions while also enhancing decision makers understanding of key performance trade‐offs. In combination, our proposed representation and reduction techniques have significant promise for enhancing the size and the scope of combinatorial monitoring problems that can be explored. Key Points: We present methods to improve optimization of discrete combinatorial problems with precalculated search space We present a search‐space representation that yields robust, and efficient solutions in optimal groundwater monitoring network design We present a rigorous reduction of the search space without losing optimal solutions for an effective optimization