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Water systems planners have long recognized the need for robust solutions capable of withstanding deviations from the conditions for which they were designed. Robustness analyses have shifted from expected utility to exploratory bottom-up approaches which identify vulnerable scenarios prior to assigning likelihoods. Examples include Robust Decision Making (RDM), Decision Scaling, Info-Gap, and Many-Objective Robust Decision Making (MORDM). We propose a taxonomy of robustness frameworks to compare and contrast these approaches based on their methods of (1) alternative generation, (2) sampling of states of the world, (3) quantification of robustness measures, and (4) sensitivity analysis to identify important uncertainties. Building from the proposed taxonomy, we use a regional urban water supply case study in the Research Triangle region of North Carolina to illustrate the decision-relevant consequences that emerge from each of these choices. Results indicate that the methodological choices in the taxonomy lead to the selection of substantially different planning alternatives, underscoring the importance of an informed definition of robustness. Moreover, the results show that some commonly employed methodological choices and definitions of robustness can have undesired consequences when ranking decision alternatives. For the demonstrated test case, recommendations for overcoming these issues include: (1) decision alternatives should be searched rather than prespecified, (2) dominant uncertainties should be discovered through sensitivity analysis rather than assumed, and (3) a carefully elicited multivariate satisficing measure of robustness allows stakeholders to achieve their problem-specific performance requirements. This work emphasizes the importance of an informed problem formulation for systems facing challenging performance tradeoffs and provides a common vocabulary to link the robustness frameworks widely used in the field of water systems planning. [ABSTRACT FROM AUTHOR]

This study demonstrates the use of high-order Pareto optimization (i.e., optimizing a system for more than two objectives) on a long-term monitoring (LTM) application. The LTM application combines quantile kriging and the nondominated sorted genetic algorithm-II (NSGA-II) to successfully balance four objectives: (1) minimizing sampling costs, (2) maximizing the accuracy of interpolated plume maps, (3) maximizing the relative accuracy of contaminant mass estimates, and (4) minimizing estimation uncertainty. Optimizing the LTM application with respect to these objectives reduced the decision space of the problem from a total of 500 million designs to a set of 1,156 designs identified on the Pareto surface. Visualization of a total of eight designs aided in understanding and balancing the objectives of the application en route to a single compromise solution. This study shows that high-order Pareto optimization holds significant potential as a tool that can be used in the balanced design of water resources systems. [ABSTRACT FROM AUTHOR]

The authors explains various issues concerning water resources management. They highlight a historical criticism of water resources planning and management. They discuss the use of optimization in water systems management and water supply engineering. They argue that the future of water resources management calls for constructive modeling.

Optimal management policies for water reservoir operation are generally designed via stochastic dynamic programming (SDP). Yet, the adoption of SDP in complex real-world problems is challenged by the three curses of dimensionality, modeling, and multiple objectives. These three curses considerably limit SDP's practical application. Alternatively, this study focuses on the use of evolutionary multiobjective direct policy search (EMODPS), a simulation-based optimization approach that combines direct policy search, nonlinear approximating networks, and multiobjective evolutionary algorithms to design Pareto-approximate closed-loop operating policies for multipurpose water reservoirs. This analysis explores the technical and practical implications of using EMODPS through a careful diagnostic assessment of the effectiveness and reliability of the overall EMODPS solution design as well as of the resulting Pareto-approximate operating policies. The EMODPS approach is evaluated using the multipurpose Hoa Binh water reservoir in Vietnam, where water operators are seeking to balance the conflicting objectives of maximizing hydropower production and minimizing flood risks. A key choice in the EMODPS approach is the selection of alternative formulations for flexibly representing reservoir operating policies. This study distinguishes between the relative performance of two widely-used nonlinear approximating networks, namely artificial neural networks (ANNs) and radial basis functions (RBFs). The results show that RBF solutions are more effective than ANN ones in designing Pareto approximate policies for the Hoa Binh reservoir. Given the approximate nature of EMODPS, the diagnostic benchmarking uses SDP to evaluate the overall quality of the attained Pareto-approximate results. Although the Hoa Binh test case's relative simplicity should maximize the potential value of SDP, the results demonstrate that EMODPS successfully dominates the solutions derived via SDP. [ABSTRACT FROM AUTHOR]