Blended near‐optimal alternative generation, visualization, and interaction for water resources decision making

Abstract

State-of-the-art systems analysis techniques focus on efficiently finding optimal solutions. Yet an optimal solution is optimal only for the modeled issues and managers often seek near-optimal alternatives that address unmodeled objectives, preferences, limits, uncertainties, and other issues. Early on, Modeling to Generate Alternatives (MGA) formalized near-optimal as performance within a tolerable deviation from the optimal objective function value and identified a few maximally different alternatives that addressed some unmodeled issues. This paper presents new stratified, Monte-Carlo Markov Chain sampling and parallel coordinate plotting tools that generate and communicate the structure and extent of the nearoptimal region to an optimization problem. Interactive plot controls allow users to explore region features of most interest. Controls also streamline the process to elicit unmodeled issues and update the model formulation in response to elicited issues. Use for an example, single-objective, linear water quality management problem at Echo Reservoir, Utah, identifies numerous and flexible practices to reduce the phosphorus load to the reservoir and maintain close-to-optimal performance. Flexibility is upheld by further interactive alternative generation, transforming the formulation into a multiobjective problem, and relaxing the tolerance parameter to expand the near-optimal region. Compared to MGA, the new blended tools generate more numerous alternatives faster, more fully show the near-optimal region, and help elicit a larger set of unmodeled issues.

Engaging stakeholders in research to address water–energy–food (WEF) nexus challenges

“…The technical complexity and computational requirements of MOO reduce the accessibility of these tools to non-academic parties. Further optimisation does not always provide practical solutions, as uncertainties surrounding future conditions can leave optimal solutions vulnerable to failure, and practitioners may seek near-optimal solutions that address objectives beyond the scope of the model (Rosenberg 2015 ). Uncertainty can be partially addressed by coupling MOO with deep uncertainty approaches to assess the performance of potential interventions under different plausible futures (Herman et al 2014 ).…”

Review of Mathematical Programming Applications in Water Resource Management Under Uncertainty

“…Marinoni et al [140] propose a framework for planning major investment decisions and apply this to the case of a water quality enhancement program in a river catchment in Brisbane, Australia. Compromise programming is first used to score the options [42,87,118,121,126,132,139,150,174,176,208,213,224] Storm water [17] Wastewater [1,33,65,80,86,98,106,113,129,139,141,169,187,197,206,219,238] Water allocation [172,230,233] Water trading [224] Water treatment [33,206] Wetlands [39,207,225] for pollution reduction at various sites and the optimal investment problem is then formulated as a multicriteria knapsack problem. In some cases, legislation needs to be considered alongside other management strategies.…”

Interpreting a Pareto set of operating options for water grids: a framework and case study

“…Interactive plotting is particularly useful for parallel coordinates plots, as brushing and reordering of parallel axes can be applied dynamically. Rosenberg (2015) provides an example of this in Matlab code, at https://github.com/dzeke/Blended-Near-Optimal-Tools. Figure 15 shows a screenshot of an interactive 3D scatter plot of the case-study Pareto set, constructed using Plotly.…”