Keywords
optimization, near-optimal, multi-objective, water management, amman, jordan
Start Date
1-7-2012 12:00 AM
Abstract
State-of-the-art systems analysis techniques unanimously focus on finding efficient, single-, and pareto-optimal solutions. Yet, environmental 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 problems. Here, I present a new, simple algorithm that uses parallel coordinates to identify and visualize high-dimension near-optimal regions. First, describe the near-optimal region from the original optimization constraints and objective function tolerance. Second, plot the decision region in parallel coordinates and extrude the outer envelopes of lines between each pair of parallel axes. Third, find the feasible range for one decision, choose a value within the range, 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. The method simultaneously shows linkages between high-dimensional decision and objective spaces—add a parallel axis for each new objective. I demonstrate the new, fast, interactive method for a water management problem in Amman, Jordan that identifies mixes of 18 new supply and conservation actions to reduce (i) expected and (ii) cost-variance objectives.
Near-optimal water management to improve multi-objective decision making
State-of-the-art systems analysis techniques unanimously focus on finding efficient, single-, and pareto-optimal solutions. Yet, environmental 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 problems. Here, I present a new, simple algorithm that uses parallel coordinates to identify and visualize high-dimension near-optimal regions. First, describe the near-optimal region from the original optimization constraints and objective function tolerance. Second, plot the decision region in parallel coordinates and extrude the outer envelopes of lines between each pair of parallel axes. Third, find the feasible range for one decision, choose a value within the range, 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. The method simultaneously shows linkages between high-dimensional decision and objective spaces—add a parallel axis for each new objective. I demonstrate the new, fast, interactive method for a water management problem in Amman, Jordan that identifies mixes of 18 new supply and conservation actions to reduce (i) expected and (ii) cost-variance objectives.
