Penalty-Free Multi-Objective Evolutionary Optimization of Water Distribution Systems

This paper presents a new penalty-free multi-objective evolutionary approach (PFMOEA) for the optimization of water distribution systems (WDSs). The proposed approach utilizes pressure dependent analysis (PDA) to develop a multi-objective evolutionary search. PDA is able to simulate both normal and pressure deficient networks and provides the means to accurately and rapidly identify the feasible region of the solution space, effectively locating global or near global optimal solutions along its active constraint boundary. The significant advantage of this method over previous methods is that it eliminates the need for ad-hoc penalty functions, additional “boundary search” parameters, or special constraint handling procedures. Conceptually, the approach is downright straightforward and probably the simplest hitherto. The PFMOEA has been applied to several WDS benchmarks and its performance examined. It is demonstrated that the approach is highly robust and efficient in locating optimal solutions. Superior results in terms of the initial network construction cost and number of hydraulic simulations required were obtained. The improvements are demonstrated through comparisons with previously published solutions from the literature.

A new approach for reliability-based optimization of water distribution networks is presented. The approach links a genetic algorithm (GA) as the optimization tool with the first-order reliability method (FORM) for estimating network capacity reliability. Network capacity reliability in this case study refers to the probability of meeting minimum allowable pressure constraints across the network under uncertain nodal demands and uncertain pipe roughness conditions. The critical node capacity reliability approximation for network capacity reliability is closely examined and new methods for estimating the critical nodal and overall network capacity reliability using FORM are presented. FORM approximates Monte Carlo simulation reliabilities accurately and efficiently. In addition, FORM can be used to automatically determine the critical node location and corresponding capacity reliability. Network capacity reliability approximations using FORM are improved by considering two failure modes. This research demonstrates the novel combination of a GA with FORM as an effective approach for reliability-based optimization of water distribution networks. Correlations between random variables are shown to significantly increase optimal network costs.

Water distribution systems are an integral part of the economic infrastructure of modern-day societies. However, previous research on the design optimization of water distribution systems generally involved few decision variables and consequently small solution spaces; piecemeal-solution methods based on pre-processing and search space reduction; and/or combinations of techniques working in concert. The present investigation was motivated by the desire to address the above-mentioned issues including those associated with the lack of high-performance computing (HPC) expertise and limited access in developing countries. More specifically, the article’s aims are, firstly, to solve a practical water distribution network design optimization problem and, secondly, to develop and demonstrate a generic multi-objective genetic algorithm capable of achieving optimal and near-optimal solutions on complex real-world design optimization problems reliably and quickly. A multi-objective genetic algorithm was developed that applies sustained and extensive exploration of the active constraint boundaries. The computational efficiency was demonstrated by the small fraction of 10-245 function evaluations relative to the size of the solution space. Highly competitive solutions were achieved consistently, including a new best solution. The water utility’s detailed distribution network model in EPANET 2 was used for the hydraulic simulations. Therefore, with some additional improvements, the optimization algorithm developed could assist practitioners in day-to-day planning and design.

Water stands as the fundamental cornerstone of life, and with the human population growing exponentially, the critical importance of sustainable water management becomes increasingly evident. Water not only serves as the essential working fluid for major chemical processes, including thermal energy generation, but it is also integral to manufacturing and domestic use. Despite its significance, water is a scarce commodity, and the planet continues to lose this precious resource due to theft, pipe bursts, and leakages in water distribution networks (WDNs). The consequences of water loss extend beyond the impact on physical resources, as it is intricately linked to financial challenges. Thus, water loss has the potential to result in substantial financial setbacks for companies, organizations, and government entities, underscoring the interdependence of water management and fiscal sustainability. In response to these challenges, digital technologies have been harnessed to optimize WDNs. A major constraint lies in deciphering the applicable digital technologies due to the multidisciplinary nature of the research area encompassing WDNs and digital technologies; therefore, this study adopts a systematic literature review (SLR) combined with digital tools, to comprehensively extract all aspects of a WDN, ranging from sensors to enterprise resource planning (ERP), including equipment and systems. This literature forms the foundational basis for constructing a framework aimed at creating a content repository for digital WDN sustainability. To further develop the framework, this study reviews international best practices in digital WDN. This is adopted in developing a digital WDN framework based on the literature and classifying a database structure from sensor to ERP for a generic WDN. Furthermore, the study explores tools and systems for optimization as well as updating the theoretical structure with Johannesburg WDN data and provides a comprehensive evaluation for enabling digital WDN in South Africa. The digital WDN framework comprises three distinct components: security, a central management database (CMDB), and best practice architecture. The architecture involves five layers, including the physical layer, communication layer, data storage and analysis layer, benefit layer, and application layer. Utilizing systematic literature review and bibliometric keyword analysis, the study determines the equipment, systems, and their uses, leading to the development of a generic WDN. Validation of the framework using the generic WDN emphasizes the equipment and systems used in each of the five layers. Furthermore, the framework is validated using Johannesburg Water's WDN, leading to the development of a CMDB. The CMDB underscores the possibility of storing physical layer and communication layer configuration items (CIs) and highlights asset management, CI relations, change management, and historian capabilities. Maintaining an accurate and updated CMDB necessitates employing asset discovery solutions, while CMDB relationship mapping plays a crucial role in assessing the ripple effects of CI changes within a complex system. Finally, the measurement of the digital maturity of Johannesburg Water's WDN using the Administração e Gestão de Sistemas de Salubridade (AGS) maturity index reveals a maturity index of 62%. The index emphasizes strong capabilities in GIS integration and data collection through the SCADA system. Despite advancements in planning systems, such as domestic flow metering, there remains an opportunity to enhance asset management capabilities for continuous improvement in WDN operations.

Nowadays, potable water supply has become a problem, involving different aspects such as water quality, pollution, pipes' quality, supply and demand of drinking water, water leaks, and supply cuts, among other aspects that have complicated the efficient use of potable water in urbanized regions. The objective of this chapter is to define potable water distribution network (PWDN) optimization as a complex problem, from the perspective of an NP-Hard problem, and the complexity as a variant of water distribution network optimization. The main result of the proposal is the definition of a problem that identifies the main variables involved in the supply of quality potable water as a global problem where each researcher can solve the main problem as one or propose solutions for different parts. The proposal simulation is oriented to present a brief solution related to the supply and demand of drinking water as a part of the PWDN.

Nowadays, due to increasing population and water shortage and competition for its consumption, especially in the agricultural that is the largest consumer of water, proper and suitable utilization and optimal use of water resources is essential. One of the important parameters in agriculture field is water distribution network. In this research, differential evolution algorithm (DE) was used to optimize Ismail Abad water supply network. This network that is pressurized network and includes 19 pipes and nodes 18. Optimization of the network has been evaluated by developing an optimization model based on DE algorithm in MATLAB and the dynamic connection with EPANET software for network hydraulic calculation. The developing model was run for the scale factor (F), the crossover constant (Cr), initial population (N) and the number of generations (G) and was identified best adeptness for DE algorithm is 0.6, 0.5, 100 and 200 for F and Cr, N and G, respectively. The optimal solution was compared with the classical empirical method and results showed that Implementation cost of the network by DE algorithm 10.66% lower than the classical empirical method.

Optimization of water distribution network is one of the popular problems faced by hydrologists and water distribution designers. The nonlinear complexity involved in this problem makes it challenging for optimization. To solve this complexity, several researchers have studied various approaches involving numerous optimization techniques. This paper focuses on using one such approach involving a simulation and optimization models. The optimization technique used is Cuckoo Search (CS), and the simulation model is EPANET. This proposed model is tested for two water distribution network benchmark problems, namely two-loop network and Hanoi network. The obtained results when compared with previous studies show significant improvement.

A simulation optimization model, WCANET that combines water cycle optimization algorithm with EPANET hydraulic simulation software to tackle water distribution problem for least cost design is proposed. The developed model is to achieve optimal design outputs within the hydraulic and design constraints of the problem. The model has been put to test against two benchmark water distribution network problems, namely (1) Hanoi water distribution network and (2) Two loop network problem. The study shows promising results for WCANET compared to earlier studies. Analysis of the results suggests WCANET can be considered for planning of water distribution networks which has high economic benefits.

Optimization of water distribution networks has been of central importance for recent decades. Genetic Algorithms (GA) are the most famous metaheuristics widely used for this purpose with great success. However, the fact that GA basically requires a large number of computations, has led to investigate for faster solvers. In this research, a new approach is proposed in which a simple GA is linked with the Integer-Linear Programming (ILP) method resulting in a hybrid optimization scheme. Using the mathematical method of ILP, the search space is significantly reduced thereby a limited number of evaluations are required to achieve a good solution. The approach is applied to two benchmark pipe-networks in order to show its ability in terms of accuracy and speed. The results are then compared with the previous works. The obtained results indicate that the proposed model is computationally efficient, like classic methods, while is still very promising in finding the global optimum like the nature-inspired metaheuristics.

Genetic algorithms (GAs) have become the preferred water system design optimisation technique for many researchers and practitioners. The main reason for using GAs is their ability to deal with nonlinear complex optimisation problems. The optimal decision in terms of designing, expansion / extending, addition or rehabilitation of water supply systems has to review possible options and select a cost-effective and efficient solution. This paper presents a new approach in determining a penalty value depending on the degree of failure, of the set pressure criteria, and the importance of the link supplying a specific node. Further modifications are also made in the cross-over and mutation procedures to ensure an increase in algorithm convergence. EPANET, a widely used water distribution network simulation model, is used in conjunction with the proposed newly developed GA for the optimisation of water distribution systems. The developed GA procedure has been incorporated in a software package called GANEO, which can be used to design new networks, analyse existing networks and prioritise improvements on existing networks. The developed GA has been tested on several international benchmark problems and has proved to be very efficient and robust. The EPANET hydraulic modelling software as well as the developed GANEO software, which performs the optimisation of the water distribution network, is freeware. The software provides a tool for consulting engineers to optimise the design or rehabilitation of a water distribution network.

Optimization of water distribution networks is a NP-hard problem that researchers have tried to deal with using different formulations and algorithmic approaches. Among these, multi-objective heuristic algorithms are interesting because of their capacity for dealing with separate objectives that allow us to choose a posteriori the best compromise, but one of their main drawbacks is the long time required to obtain good solutions. Parallel processing is the most promising way to reduce the computing time and can make the convergence to adequate solutions faster. This paper intends to investigate the possibility of improving the efficacy and efficiency of an NSGA-II algorithm by parallelization of the optimization process at the same time. Results of different parallel implementations of NSGA-II applied to optimal design of small- and medium-size water distribution networks are presented. Good speed-up can be reached with a global model, hence improving the algorithm efficiency. Unlike the global model, the island model (or the hierarchical parallelization) can also improve its efficacy because it introduces fundamental changes in the algorithm exploration method. Possibilities offered by parallel island models have been investigated showing that some parameter configurations can find better solutions compared with the serial version of the algorithm.

This study was aimed to optimize the designed water distribution system in the Wukro town using WaterGEMS model. The Darwin Designer in WaterGEMS was applied for finding optimal pipe diameter to supply adequate quantity of water at satisfactory pressures to the end users. In the WaterGEMS model, the Darwin Scheduler of daily pumping operations tools also used for optimal control and operation of pump systems. The WaterGEMS model was implemented in water distribution networks which include 117 pipes (40.67km), 99 demand nodes (equivalent to 50480 end users) that are spread across a hilly area over a 1989m to 2046m elevation gradient. The model was calibrated at the selected nodes within very good performance. The results have shown that the maximum pressure before optimization is 31.1m and after optimization increased to 38.1m, the minimum pressure on the former is 7.9m and 16m later during peak hour demand. Comparison of results showed that the optimized networks reduce the cost by 9.6% than those of before optimization networks by traditional hydraulic. In addition to this, the optimal tanks filling/emptying arrangement decreased the daily cost of energy consumptions by 12.5% compare as a currently scheduled pump. The finding of this study indicated that the WaterGEMS model is a promising approach for optimal sizing of pipes in design water distribution networks and pumping operational schedules. Keywords : Water Distribution Network, Genetic Algorithm, Pipe Diameter, Energy consumption, Darwin Designer, Darwin scheduler DOI: 10.7176/CER/12-6-01 Publication date: June 30 th 2020

This paper presents a multiobjective optimization approach for synthesizing water distribution networks involving dual-purpose power plants. The proposed model accounts for environmental, economic, and social objectives by accounting for greenhouse gas emissions, jobs, and net profit. The model considers water and energy demands for domestic, agricultural, and industrial users. Energy is provided through several alternatives including fossil fuels (i.e., natural gas and oil), biofuels (i.e., biomass, biogas, biodiesel, and bioethanol), and solar energy. Water demands are satisfied by fresh water from dams, lakes, rivers, aquifers, and artificial storage tanks. The proposed model is applied to a case study from the Mexican State of Sonora. The results show the viability of the dual-purpose power–water plants, the merits of incorporating solar energy in the system, and the economic, environmental, and social benefits of applying the proposed approach. The optimal solution yields a total annual profit of $MM...

This article provides a comprehensive overview of the most approached heuristic optimization techniques of water distribution networks (WDNs) focusing on their optimal design. A single- and multi-objective optimization problem is generally formulated, and the main optimization objectives, decision variables and constraints for the design, rehabilitation and operation of WDNs are synthesized and discussed. Additionally, the main heuristic methods are briefly described and classified. Finally, literature pertaining to the heuristic optimization models of WDNs is overviewed and in conclusion the advantages and disadvantages of the heuristic techniques used for designing WDNs are discussed along with some recommendations for future research directions.

Due to the conflict between reducing cost and improving water supply performance, how to select the appropriate pipe diameter is a current challenge. In this paper, the problem is transformed into a multi-objective optimization problem, and the evolutionary genetic optimization algorithm is used to solve the problem to determine the optimal selection of pipe diameter in the pipe network. To solve this problem, the evolutionary genetic algorithm was coupled with EPANET hydraulic simulation software in Python environment. The results show that NSGA-II and NSGA-III perform better in two typical case tests. Moreover, the increase of the objective functions will lead to an increase in the amount of data in the optimal solution set, and will affect the optimal value of each objective function. That shows that the balance between the economy and reliability of water supply can be successfully found by coupling the hydraulic model and the multi-objective optimization algorithm, which can provide an auxiliary decision for enterprises.