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

Abstract

AbstractState‐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 near‐optimal 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.