### Stochastic sampling design using a multi-objective genetic algorithm and adaptive neural networks

Abstract

This paper presents a novel multi-objective genetic algorithm (MOGA) based on the NSGA-II algorithm, which uses metamodels to determine
optimal sampling locations for installing pressure loggers in a water distribution system (WDS) when parameter uncertainty is considered.
The new algorithm combines the multi-objective genetic algorithm with adaptive neural networks (MOGA-ANN) to locate pressure loggers. The
purpose of pressure logger installation is to collect data for hydraulic model calibration. Sampling design is formulated as a two-objective
optimization problem in this study. The objectives are to maximize the calibrated model accuracy and to minimize the number of sampling
devices as a surrogate of sampling design cost. Calibrated model accuracy is defined as the average of normalized traces of model prediction
covariance matrices, each of which is constructed from a randomly generated sampling set of calibration parameter values. This method of
calculating model accuracy is called the 'full' fitness model. Within the genetic algorithm search process, the full fitness model is progressively
replaced with the periodically (re)trained adaptive neural network metamodel where (re)training is done using the data collected by calling
the full model. The methodology was first tested on a hypothetical (benchmark) problem to configure the setting requirement. Then the model
was applied to a real case study. The results show that significant computational savings can be achieved by using the MOGA-ANN when compared
to the approach where MOGA is linked to the full fitness model. When applied to the real case study, optimal solutions identified by MOGA-ANN
are obtained 25 times faster than those identified by the full model without significant decrease in the accuracy of the final solution.