'Near-optimal management to improve water resources decision making'
David Rosenberg (email@example.com), Utah State University
Abstract: State-of-the-art systems analysis techniques unanimously focus on efficiently finding optimal solutions. Yet, water resources managers rather need decision aides that show multiple, promising, near-optimal alternatives. Why near-optimal? Because an optimal solution is optimal only for modelled issues; un-modelled issues persist. Early work mathematically formalized near-optimal as performance within a tolerance of the optimal objective function value but found computational difficulties to describe near-optimal regions for large linear programs. Here, I present simple, interactive algorithms that use parallel coordinates to identify and visualize high-dimension near-optimal regions for integer and continuous variable problems. First, describe the near-optimal region from the original optimization constraints and objective function tolerance. Second, determine the maximal extents of each decision variable within the region and plot the extents in parallel coordinates as the lower and upper bounds on parallel axes where each axis represents a decision variable. Third, choose a value for one decision variable within its maximal extent, reduce the problem dimensionality by one degree, find the allowable range for the next variable, and repeat. This process identifies a sub-region and is visually analogous to a control panel with parallel sliders, one for each decision variable. Adjust and set one slider; then determine the feasible ranges for remaining sliders. Extensions automatically identify the near-optimal region. I demonstrate the fast, new methods for integer and continuous variable problems for (a) supply/demand planning in Amman, Jordan, and (b) reducing phosphorus loads to Echo Reservoir, Utah. Keywords: optimization; near-optimal; water management; integer; continuous; Amman, Jordan.