Sensitivity of algorithm parameters and objective function scaling in multi-objective optimisation of water distribution systems

Abstract

This paper presents an extensive analysis of the sensitivity of multi-objective algorithm parameters and objective function scaling tested on a large number of parameter setting combinations for a water distribution system optimisation problem. The optimisation model comprises two operational objectives minimised concurrently, the pump energy costs and deviations of constituent concentrations as a water quality measure. This optimisation model is applied to a regional nondrinking water distribution system, and solved using the optimisation software GANetXL incorporating the NSGA-II linked with the network analysis software EPANet. The sensitivity analysis employs a set of performance metrics, which were designed to capture the overall quality of the computed Pareto fronts. The performance and sensitivity of NSGA-II parameters using those metrics is evaluated. The results demonstrate that NSGA-II is sensitive to different parameter settings, and unlike in the single-objective problems, a range of parameter setting combinations appears to be required to reach a Pareto front of optimal solutions. Additionally, inadequately scaled objective functions cause the NSGA-II bias towards the second objective. Lastly, the methodology for performance and sensitivity analysis may be used for calibration of algorithm parameters.