Booster Optimization for Water Distribution System Based on Trapezoidal Fuzzy Distribution

In this work, an optimization model to deal with uncertainty of boosters in water distribution systems (WDSs) was proposed. The model proposed can cope with the nonlinearities and intervals of the objective function, the intervals of the left-hand sides of the constraints, and trapezoidal fuzzy uncertainty of the right-hand sides of the constraints. The proposed model was applied to two case studies to obtain the optimal intervals of booster costs. The results indicated that the lower bounds and the upper bounds increased with confidence levels, preference parameter lambda values, and the booster numbers. In addition, the boosters located at the end far from the source is beneficial for reducing booster costs. Moreover, the operation costs decreased with increase of booster numbers, and increased with lambda values and the confidence levels. The results obtained can help managers making economical decisions for booster numbers and injection rates under uncertainty.

Automated summary

In this work, an optimization model is proposed to handle the uncertainty of boosters in water distribution systems (WDSs). The model can handle the nonlinear and interval objective function, interval left-hand sides of constraints, and trapezoidal fuzzy uncertainty of the right-hand sides of constraints. The model was applied to two case studies to obtain optimal cost intervals for boosters. The results showed that the lower and upper bounds of costs increased with confidence levels, preference parameter lambda values, and the number of boosters. Additionally, boosters located far from the source were beneficial for reducing costs. Operation costs decreased with an increase in booster numbers and increased with lambda values and confidence levels. The obtained results can assist managers in making economical decisions for booster numbers and injection rates under uncertainty.