Water Distribution System Design Problems Research Articles

A Many-Objective Analysis Framework for Large Real-World Water Distribution System Design Problems

This paper presents a many-objective analysis framework to handle large real-world water distribution system design problems (WDSDP), which is a typically difficult infrastructure engineering optimization problem type. Six objectives are formulated, focusing on economic, structural and functional aspects in the operation and management of the water distribution system (WDS), and solved by Borg, which is one state-of-the-art multi-objective evolutionary algorithm (MOEA) in water resources. The framework comprehensively analyzes and reveals the underlying trade-offs among many objectives, thereby facilitating the selection of the most appropriate design solutions for real-world WDSs. A real-world WDSDP with 1278 decision variables is used to demonstrate the effectiveness of the proposed framework, and results show that it can clearly reveal the complex trade-offs among these six different objectives, and it greatly enhances the understanding of the underlying characteristics of Pareto-front solutions. The insights have great practical implications for optimally designing large real-world WDS problems.

A multi-objective adaptive surrogate modelling-based optimization algorithm for constrained hybrid problems

Many multi-objective optimization problems in integrated environmental modelling and management involve not only continuous decision variables but also variables like integers and/or discrete variables. Furthermore, the optimization problems are often subject to various constraints. Solving this kind of constrained hybrid problems usually requires a huge number of model evaluations that can be computationally expensive. This study presents an algorithm known as multi-objective adaptive surrogate modelling-based optimization for constrained hybrid problems (MO-ASMOCH). It incorporates several evolutionary operators to handle different types of decision variables and uses a classification surrogate model to deal with model constraints. MO-ASMOCH was evaluated against the widely used NSGA-II method on three engineering design problems and three water distribution system design problems with up to 30 dimensions. The results showed that MO-ASMOCH is able to obtain nondominated solutions of similar quality as that of NSGA-II using much fewer model evaluations.

How close simple EAs’ optimal solutions can approach global optima: experience from water distribution system design problems

Abstract An issue regarding near-optimal solutions identified by evolutionary algorithms (EAs) is that their absolute deviations from the global optima are often unknown, and hence an EA's performance in handling real-world problems remains unclear. To this end, this paper investigates how close optimal solutions from simple EAs can approach the global optimal for water distribution system (WDS) design problems through an experiment with the number of decision variables ranging from 21 to 3,400. Three simple EAs are considered: the standard differential evolution, the standard genetic algorithm and the creeping genetic algorithm (CGA). The CGA consistently identifies optimal solutions with deviations lower than 50% to the global optimal, even for the WDS with 3,400 decision variables, but the performance of the other two EAs is heavily case study dependent. Results obtained build knowledge regarding these simple EAs’ ability in handling WDS design problems with different sizes. We must acknowledge that these results are conditioned on the WDSs and the parameterization strategies used, and future studies should focus on generalizing the findings obtained in this paper.

An Adaptive Convergence-Trajectory Controlled Ant Colony Optimization Algorithm With Application to Water Distribution System Design Problems

Evolutionary algorithms and other meta-heuristics have been employed widely to solve optimization problems in many different fields over the past few decades. Their performance in finding optimal solutions often depends heavily on the parameterization of the algorithm’s search operators, which affect an algorithm’s balance between search diversification and intensification. While many parameter-adaptive algorithms have been developed to improve the searching ability of meta-heuristics, their performance is often unsatisfactory when applied to real-world problems. This is, at least in part, because available computational budgets are often constrained in such settings due to the long simulation times associated with objective function and/or constraint evaluation, thereby preventing convergence of existing parameter-adaptive algorithms. To this end, this paper proposes an innovative parameter-adaptive strategy for ant colony optimization (ACO) algorithms based on controlling the convergence trajectory in decision space to follow any prespecified path, aimed at finding the best possible solution within a given, and limited, computational budget. The utility of the proposed convergence-trajectory controlled ACO (ACO $_{\mathbf{CTC}}$ ) algorithm is demonstrated using six water distribution system design problems (WDSDPs, a difficult type of combinatorial problem in water resources) with varying complexity. The results show that the proposed ACO $_{\mathbf{CTC}}$ successfully enables the specified convergence trajectories to be followed by automatically adjusting the algorithm’s parameter values. Different convergence trajectories significantly affect the algorithm’s final performance (solution quality). The trajectory with a slight bias toward diversification in the first half and more emphasis on intensification during the second half of the search exhibits substantially improved performance compared to the best available ACO variant with the best parameterization (no convergence control) for all WDSDPs and computational scenarios considered. For the two large-scale WDSDPs, new best-known solutions are found by the proposed ACO $_{\mathbf{CTC}}$ .

Improved Understanding on the Searching Behavior of NSGA-II Operators Using Run-Time Measure Metrics with Application to Water Distribution System Design Problems

In recent years, multi-objective evolutionary algorithms (MOEAs) have been widely used to handle various water resources problems. One challenge within MOEAs’ applications is a lack of understanding on how various operators alter a MOEA’s behavior to achieve its final performance (i.e., MOEAs are black-boxes to practitioners), and hence it is difficult to select the most appropriate operators to ensure the MOEA’s best performance for a given real-world problem. To address this issue, this study proposes the use of the run-time measure metrics to reveal the underlying searching behavior of the MOEA’s operators. The proposed methodology is demonstrated by the non-dominated sorting genetic algorithm II (NSGA-II, a widely used MOEA in water resources) with five commonly used crossover operators applied to six water distribution system design problems. Results show that the simulated binary crossover (SBX) and the simplex crossover (SPX) operators possess great ability in extending the front and finding Pareto-front solutions, respectively, while the naive crossover (NVX) strategy exhibits the overall worst performance in identifying optimal fronts. The obtained understanding on the operators’ searching behavior not only offers guidance for selecting appropriate operators for real-world water resources problems, but also builds fundamental knowledge for developing more advanced MOEAs in future.

Impact of Starting Position and Searching Mechanism on the Evolutionary Algorithm Convergence Rate

AbstractEvolutionary algorithms (EAs) have been used extensively to find globally optimal solutions for water distribution system (WDS) optimization problems. However, as these algorithms are being applied to increasingly complex systems, computational efficiency is becoming an issue, and hence approaches that enable near-optimal solutions to be identified within reasonable computational budgets have received increasing attention. One of these approaches is the initialization of EAs in a manner that accounts for domain knowledge of WDS design problems. Although the effectiveness of these initialization approaches has been studied previously, the impact of algorithm searching behavior on the speed with which near-optimal solutions can be found has not yet been examined. To this end, this study aims to investigate the relative impact of different algorithm initialization methods and searching mechanisms on the speed with which near-optimal solutions can be identified for large WDS optimization problems. Fit...

Comparison of the Searching Behavior of NSGA-II, SAMODE, and Borg MOEAs Applied to Water Distribution System Design Problems

AbstractA number of multiobjective evolutionary algorithms (MOEAs) have been developed and applied to water resource optimization problems over the past decade. The comparative performance of these MOEAs has been investigated often according to their overall end-of-run results (quality of optimal fronts) within prespecified computational budgets. Despite the importance of such comparative analyses, these studies have provided little knowledge of how different MOEAs navigate through the decision space toward the Pareto front. To address this issue, this paper uses a range of metrics to quantitively characterize MOEAs’ run-time searching behavior, with a focus on the statistics of search quality and convergence progress. The metrics are applied to three state-of-the-art MOEAs, including the nondominated sorting genetic algorithm-II (NSGA-II), self-adaptive multiobjective differential evolution (SAMODE), and Borg, for six water distribution system (WDS) design problems with the objectives of minimizing netwo...

A hybrid cuckoo–harmony search algorithm for optimal design of water distribution systems

Meta-heuristic algorithms have been broadly used to deal with a range of water resources optimization problems over the past decades. One issue that exists in the use of these algorithms is the requirement of large computational resources, especially when handling real-world problems. To overcome this challenge, this paper develops a hybrid optimization method, the so-called CSHS, in which a cuckoo search (CS) algorithm is combined with a harmony search (HS) scheme. Within this hybrid framework, the CS is employed to find the promising regions of the search space within the initial explorative stages of the search, followed by a thorough exploitation phase using the combined CS and HS algorithms. The utility of the proposed CSHS is demonstrated using four water distribution system design problems with increased scales and complexity. The obtained results reveal that the CSHS method outperforms the standard CS, as well as the majority of other meta-heuristics that have previously been applied to the case studies investigated, in terms of efficiently seeking optimal solutions. Furthermore, the CSHS has two control parameters that need to be fine-tuned compared to many other algorithms, which is appealing for its practical application as an extensive parameter-calibration process is typically computationally very demanding.

Investigating the run-time searching behavior of the differential evolution algorithm applied to water distribution system optimization

In recent years, the differential evolution algorithm (DEA) has frequently been used to tackle various water resource problems due to its powerful search ability. However, one challenge of using the DEA is the tedious effort required to fine-tune parameter values due to a lack of theoretical understanding of what governs its searching behavior. This study investigates DEA's search behavior as a function of its parameter values. A range of behavioral metrics are developed to measure run-time statistics about DEA's performance, with primary focus on the search quality, convergence properties and solution generation statistics. Water distribution system design problems are utilized to enable investigation of the behavioral analysis using the developed metrics. Results obtained offer an improved knowledge on how the control parameter values affect DEA's search behavior, thereby providing guidance for parameter-tuning and hence hopefully increasing appropriate take-up of the DEA within the industry in tackling water resource optimization problems.

Battle of the Water Networks II

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 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 multiobjective, 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.

Hybrid particle swarm optimization and differential evolution for optimal design of water distribution systems

Water distribution system design belongs to a class of large combinatorial non-linear optimization problems, involving complex implicit constraints, such as conservation of mass and energy equations, which are commonly satisfied through the use of hydraulic simulation solvers. Recently, many researchers have shifted the focus from traditional optimization methods to the use of meta-heuristic approaches for handling this complexity. This paper proposes a hybrid particle swarm optimization (PSO) and differential evolution (DE) method, linked to the hydraulic simulator, EPANET, for minimizing the cost design of water distribution systems. The performance of the proposed PSO-DE algorithm is demonstrated using three well-known benchmark water distribution system problems, the two-loop network, the Hanoi network and the New York Tunnels network. The results are compared to that of standard PSO and previously applied optimization methods. It is found that PSO-DE is a promising method for solving water distribution system design problems as it outperforms standard PSO and other algorithms previously presented in the literature for the three case studies considered.

Hybrid Genetic Algorithm and Linear Programming Method for Least-Cost Design of Water Distribution Systems

The problems involved in the optimal design of water distribution networks belong to a class of large combinatorial optimization problems. Various heuristic and deterministic algorithms have been developed in the past two decades for solving optimization problems and applied to the design of water distribution systems. Nevertheless, there is still some uncertainty about finding a generally trustworthy method that can consistently find solutions which are really close to the global optimum of this problem. The paper proposes a combined genetic algorithm (GA) and linear programming (LP) method, named GALP for solving water distribution system design problems. It was investigated that the proposed method provides results that are more stable in terms of closeness to a global minimum. The main idea is that linear programming is more dependable than heuristic methods in finding the global optimum, but because it is suitable only for solving branched networks, the GA method is used in the proposed algorithm for decomposing a complex looped network into a group of branched networks. Linear programming is then applied for optimizing every branch network produced by GA from the original looped network. The proposed method was tested on three benchmark least-cost design problems and compared with other methods; the results suggest that the GALP consistently provides better solutions. The method is intended for use in the design and rehabilitation of drinking water systems and pressurized irrigation systems as well.