Parameterization of NSGA-II for the optimal design of water distribution systems

Abstract

The optimal design of Water Distribution Systems (WDSs) using multi-objective evolutionary algorithms (MOEAs) has received substantial attention in the past two decades. Many MOEAs have been proposed and applied successfully to this challenging problem. However, these tools are primarily considered black-boxes by end users, especially when the algorithm parameterization issues are taken into consideration. This paper presents a simple yet effective method for capturing the interrelationships among the five key parameters of the Non-dominated Sorting Genetic Algorithm II (NSGA-II), which is one of the state-of-the-art MOEAs in this field. Two representative boundary values for each parameter are selected from a reasonable range, and all the possible combinations are tested on three benchmark design problems. Those benchmarks are based on two widely used small networks and a larger, real-world irrigation network. Results suggest that there is a hierarchy of impacts imposed by the five parameters of NSGA-II. The population size turns out to be the most important one, which implies that NSGA-II is sensitive to the initial population, especially for complex problems. A relatively large population size increases the diversity of a population; hence some key genes may be identified at the beginning (or early stage) of search. Furthermore, it transpires that the distribution indices of crossover and mutation have a more significant impact than their probabilities, where the former are generally overlooked by previous studies. Some useful guidelines are also provided, which can improve the efficacy of NSGA-II and increase the chance of identifying near-optimal solutions.