University of Illinois at Urbana-Champaign. Water Resources Center
Abstract
A method for sensitivity analysis in nonlinear programming is described and then illustrated using a least-cost model of a secondary wastewater treatment system. A sensitivity equation approach is used to calculate normalized sensitivity coefficients, which approximate the percent changes in model variables and objective function due to a small parameter variation. Design changes predicted by the sensitivity coefficients are confirmed by a perturbation analysis of the optimal solution. Sensitivity concepts are used to develop a robustness measure which is incorporated into the constraint set of the nonlinear model. Robustness is narrowly defined as the ability of a model solution to maintain a level of performance that meets the system design criteria even if the actual values of model parameters are not exactly the same as the values assumed for design. A gradient optimization procedure is used to examine the tradeoff between total cost and the robustness measure. A preliminary analysis shows that the trends in robust wastewater treatment plant design are in direct conflict with the optimal decisions obtained when minimizing cost without a constraint on robustness but are in agreement with those designs observed to work in practice. The robustness constraint method presented should be applicable to other optimization models of water resources systems.U.S. Department of the InteriorU.S. Geological SurveyOpe
