Copyright © 2015 American Society of Civil EngineersVarious multiobjective evolutionary algorithms (MOEAs) have been applied to solve the optimal design problems of a water distribution system (WDS). Such methods are able to find the near-optimal trade-off between cost and performance benefit in a single run. Previously published work used a number of small benchmark networks and/or a few large, real-world networks to test MOEAs on design problems of WDS. A few studies also focused on the comparison of different MOEAs given a limited computational budget. However, no consistent attempt has been made before to investigate and report the best-known approximation of the true Pareto front (PF) for a set of benchmark problems, and thus there is not a single point of reference. This paper applied 5 state-of-the-art MOEAs, with minimum time invested in parameterization (i.e., using the recommended settings), to 12 design problems collected from the literature. Three different population sizes were implemented for each MOEA with respect to the scale of each problem. The true PFs for small problems and the best-known PFs for the other problems were obtained. Five MOEAs were complementary to each other on various problems, which implies that no one method was completely superior to the others. The nondominated sorting genetic algorithm-II (NSGA-II), with minimum parameters tuning, remains a good choice as it showed generally the best achievements across all the problems. In addition, a small population size can be used for small and medium problems (in terms of the number of decision variables). However, for intermediate and large problems, different sizes and random seeds are recommended to ensure a wider PF. The publicly available best-known PFs obtained from this work are a good starting point for researchers to test new algorithms and methodologies for WDS analysis

The Battle of the Water Networks II (BWN-II) is the latest of a series of competitions related to the design and operation of water distribution systems (WDSs) undertaken within the Water Distribution Systems Analysis (WDSA) Symposium series. The BWN-II problem specification involved a broadly defined design and operation problem for an existing network that has to be upgraded for increased future demands, and the addition of a new development area. The design decisions involved addition of new and parallel pipes, storage, operational controls for pumps and valves, and sizing of backup power supply. Design criteria involved hydraulic, water quality, reliability, and environmental performance measures. Fourteen teams participated in the Battle and presented their results at the 14th Water Distribution Systems Analysis (WDSA 2012) conference in Adelaide, Australia, September 2012. This paper summarizes the approaches used by the participants and the results they obtained. Given the complexity of the BWN-II problem and the innovative methods required to deal with the multi-objective, high dimensional and computationally demanding nature of the problem, this paper represents a snap-shot of state of the art methods for the design and operation of water distribution systems. A general finding of this paper is that there is benefit in using a combination of heuristic engineering experience and sophisticated optimization algorithms when tackling complex real-world water distribution system design problems.Angela Marchi...Angus R. Simpson, Aaron C. Zecchin, Holger R. Maier...Christopher Stokes, Wenyan Wu, Graeme C. Dandy...et al

The optimization of water networks supports the decision‐making process by identifying the optimal trade‐off between costs and performance (e.g., resilience and leakage). A major challenge in the domain of water distribution systems (WDSs) is the network (re)design. While the complex nature of WDS has already been explored with complex network analysis (CNA), literature is still lacking a CNA of optimal water networks. Based on a systematic CNA of Pareto‐optimal solutions of different WDSs, several graph characteristics are identified, and a newly developed CNA design approach for WDSs is proposed. The results show that obtained designs are comparable with results found by evolutionary optimization, but the CNA approach is applicable for large networks (e.g., 150,000 pipes) with a substantially reduced computational effort (runtime reduction up to 5 orders of magnitude).

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.