Search Space Representation and Reduction Methods to Enhance Multiobjective Water Supply Monitoring Design

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.

Simulation-Optimization Configurations for Real-Time Decision-Making in Fugitive Interception

“…Following [54], three search space representation measures are implemented to speed up convergence: a linear index representation of the search space and consecutive filtering and sorting of the possible values for the decision variables.…”

“…The standard way to represent the set of possible target vertices for the police units is the binary representation, where each combination of police unit 𝑢 and vertex 𝑣 is a binary variable 𝜋 𝑢,𝑣 . Bode et al [54] signal that evolutionary algorithms have difficulty traversing the search space due to the large set of possible combinations and strong interdependency of decision variables. Therefore, Bode et al [54] propose the linear index representation, where the decision variables are linear indices that point to the target vertex for each of the police units.…”

“…Bode et al [54] signal that evolutionary algorithms have difficulty traversing the search space due to the large set of possible combinations and strong interdependency of decision variables. Therefore, Bode et al [54] propose the linear index representation, where the decision variables are linear indices that point to the target vertex for each of the police units. Therefore, the number of decision variables only depends on the number of police units to be positioned and not also on the number of possible target vertices.…”

“…Secondly, Bode et al [54] suggest sorting the indices of the linear index representation so that proximity in the search space is more related to proximity in the objective space. Therefore, we sort the possible target vertices for the police units on their proximity to the starting vertex of the fugitive.…”

Delineation of a PFOA Plume and Assessment of Data Gaps in its Conceptual Model Using PlumeSeeker™

“…Kumari et al (2019) develop two approaches where spatiotemporal concentration values were considered as fuzzy numbers, and a non-dominated sorting genetic algorithm was used to minimize the total spatiotemporal concentration-variance and the total error of estimated mass over sampling locations and times while maximizing the spatial coverage of the sampling network subject to budgetary constraints. Bode et al (2019) employ an evolutionary multi-objective optimization algorithm to minimize the installation and operation costs of the network while identifying all possible contamination sources and detecting contamination as early as possible. The study builds on Bode et al (2016) by introducing an efficient screening of candidate solutions without sacrificing the quality of attained trade-off or Pareto-optimal solutions.…”