Achieving water quality system reliability using genetic algorithms

This paper presents an efficient approach far obtaining wasteload allocation solutions that provide the optimal trade-off between treatment cost and reliability. This approach links a genetic algorithm (GA) with the first-order reliability method (FORM) for estimating the probability of system failure under a given wasteload allocation. The GA-FORM optimization approach is demonstrated for the case study of managing water quality in the Willamette River in Oregon. The objective function minimizes the sum of the treatment cost and the penalty associated with breaching a reliability target for meeting a water quality standard. The random variables used to generate the reliability estimates include streamflow, temperature, and reaeration coefficient values. The results obtained indicate that the GA-FORM approach is nearly as accurate as the approach that links the GA with Monte Carlo simulation and is far more efficient. The trade-off between total treatment cost and reliability becomes more pronounced at higher water quality standards and is most sensitive to the uncertainty in the reaeration coefficient. The sensitivity to the reaeration coefficient also increases at increased reliability levels.