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.
This study develops a new method to calculate the water distribution system's mechanical reliability and locates crucial pipes by using the minimum cutsets method, exhaustive enumeration method and an optimal allocation model. First, a full domain optimization model was established to analyze the water distribution system. Next, the minimum cut-sets method and exhaustive enumeration method were used to discover the water distribution system's key pipes. At last, water distribution system's mechanical reliability can be calculated. The major contributions are that we can use optimal allocation model to locate crucial pipelines in the water distribution whose failure will severely impair the source-demand connectivity. Besides, we can calculate water distribution system's mechanical reliability. Thus we can offer these results for hydraulic construction funds consulting. The developed methodology is applied to a water distribution system in Hsin-Chu, Taiwan.
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