Optimal Design of Water Treatment Facilities Under Nonlinear Conditions with Uncertainty Based on Flexible Tolerance Concept

Abstract

The nonlinear programming (NLP) model is often encountered when developing an optimal model for design of water treatment. In recent years, researchers have studied numerous NLP solutions. However, some solutions are convergent but nonoptimal whereas others that are convergent and optimal are time consuming and costly to solve, because more than half of the calculations are for satisfying the constraints. Hence, a new concept of flexible tolerance is proposed in this research by allowing a tolerance for each constraint. In the process of calculations, the tolerance is reduced gradually so that it approaches zero when the optimal solution is reached. Therefore, many pull-in operations will become unnecessary, thus leading to more efficient and cost-effective solutions. For practical application, a stochastic optimal water treatment plant design model was developed using the hydrological and water quality data of an existing water treatment plant in Taiwan. A proposed new method for solving NLP problems is applied to solve for the optimal solution; results are then verified by comparing with the field data. Due to the limitation of article length, sensitivity analysis is not included in this article. Research results can be used by policy makers to develop a highly reliable water treatment systems under conditions of uncertain water quality.