Multiobjective Optimization of Dual-Purpose Power Plants and Water Distribution Networks

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.

Water scarcity has led to an increase in the extraction of fresh water from aquifers, dams and lakes in certain regions where water availability is low. It has created serious problems in overexploitation of ground and surface water resources. This issue has been intensified due to population growth and increases in energy and water demands in the industry, agriculture, and households. In this chapter, a mathematical model for energy and water distribution networks in a macroscopic system is proposed. This model considers that the water and electricity demands can be satisfied by the existing power plants in the region and the installation of new power-desalination plants. Also, the model considers that the water demand can be satisfied by supplying water from dams, rivers, and aquifers. The model considers a macroscopic system that involves several cities in a water-stressed region. It accounts for variations in water demands throughout the year, for domestic, agricultural, and industrial users. The model considers both installation costs and operating costs of the new power-desalination plants, the installation of new storage tanks, pumping, and piping costs. The results show attractive solutions, where interesting economic profits can be obtained as well as the potential recharge of aquifers can be achieved.

Water Distribution Networks (WDNs) are crucial for meeting current and future urban water demands. Knowledge of future water demand at different time scales is fundamental for optimal WDN design and operations. Various predictive models of water demand have been proposed in the literature, ranging from traditional time series analysis to cutting-edge machine learning and deep learning techniques. However, the task of forecasting urban water demand remains mostly decoupled from the design of the optimal control of the related WDN. Current performance assessment of demand predictive models focuses predominantly on forecast accuracy, overlooking their practical implications on WDN operations. Meanwhile, the existing research on WDN management often assumes either perfect knowledge of future water demands or employs empirical approximations and aggregate statistics to estimate future water needs. This study bridges this gap by scrutinizing the actual operational value of water demand forecasts in designing optimal operations of WDNs.Here, we develop a forecast-informed optimal WDN control framework to evaluate the operational value of water demand forecasts for WDN operations. Our framework comprises two main modules. The first module computes water demand forecasts. We comparatively evaluate a suite of different forecasting models —including Seasonal Auto-Regressive Integrated Moving Average with eXogenous factors, Multilayer Perceptron, Convolutional Neural Network, and Long Short-Term Memory (a network augmented with an attention mechanism) —across various forecast horizons (1/6/12 hours and 1/3/7/14 days ahead). The most accurate forecasts are integrated into the second module, an economic nonlinear Model Predictive Control (MPC) algorithm designed to optimize WDN operations. Within this module, an Artificial Neural Network (ANN) – based surrogate model encapsulates the hydraulics of the physical WDN, enhancing the optimization process while reducing complexity.We demonstrate our forecast-informed optimal WDN control framework on a real WDN of a rural town with approximately 10,000 inhabitants. Water demand data collected in the Netherlands for a period of 10 years (2007-2017) at 5-minute resolution and corresponding meteorological data are used to train the water demand forecasting models. The MPC module computes the optimal control sequence for 7 pumps and 1 valve in the WDN to minimize pump energy costs while meeting water demands and ensuring safety storage in 5 tanks. Initial findings reveal that the ANN-based surrogate model can accurately incorporate the WDN characteristics (R2 > 0.85), facilitating its integration into the MPC for an efficient and simplified representation of a real-world WDN. Further, MPC fed by 24-hour ahead water demand forecasts achieves potential energy savings of approximately 18% compared to a benchmark rule-based control strategy. Our framework yields a versatile simulation-based optimization tool for evaluating the impact of demand forecasts on WDN management. Future research efforts will aim at refining and comparing deterministic and stochastic water demand forecasts within the MPC framework, under diverse operational objectives.

A major limitation of the widely used evolutionary optimization (EO) methods is their inability to handle constraints directly. To address this issue, penalty function methods have been used in most EO applications involving constrained problems such as those of the water distributions networks (WDNs). However, the disadvantage of penalty function methods is that the parameters involved require great expertise in calibration with numerous time consuming trial runs. In addition, penalty parameters are case sensitive and do not necessarily steer the EO search toward the best solutions in every situation. This paper presents a penalty-free multi-objective evolutionary approach (PFMOEA) for the optimization of water distribution networks. The basis behind this approach is to involve the pressure dependent analysis (PDA) in developing a multi-objective evolutionary search. PDA is capable of simulating both normal and pressure deficient networks and provides a quick and precise means to identify the feasible region of the solution space. The proposed PFMOEA couples the renowned NSGA II with an enhanced seamless version of EPANET 2 which is capable of PDA. The PFMOEA has been applied to several WDN benchmarks. Excellent results in terms of the initial network cost and number of hydraulic simulations required were obtained. Comprehensive discussions along with comparisons of solutions from previous studies are presented herein.

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.

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.

Water distribution networks require huge investment for construction. Involved people, especially researchers, are always seeking to find a way for decreasing costs and achieving an efficient design. One of the main factors of the network design is the selection of proper diameters based on costs and deficit of flow pressure and velocity in the network. The reduction in construction costs is accomplished by minimizing the diameter of network pipes which leads to the pressure drop in the network. Supplying proper pressure in nodes is one of the important design principles, and low pressure will not provide a complete water supply at the consumption site. Therefore, in this research, the problem of optimization in several sample networks was defined with the objectives of cost minimization and minimization of pressure deficit in the whole network. The EPANET software was used for hydraulic analysis of sample networks, and the multi-objective optimization process was performed by coding NSGA-II and MOPSO algorithms in the MATLAB software environment and linking them to EPANET. The cost function was initially defined only by considering the relationship between cost and diameter and the length of pipes, and in the next definition, the cost resulted by violation of the allowable pressure range was added to this function In both cases, the schedule for achieving the optimal answer was executed. The results showed that these algorithms have a high ability to find optimal solutions and are able to optimize the network in terms of cost and pressure by finding the appropriate pipe diameter. The time for reaching convergence was reduced by considering the cost of violation of the allowable pressure limits significantly and the optimal answer is obtained in a small number of repetitions. In NSGA-II and MOPSO algorithms in two-looped network with 20 and 30 iterations and run time of 0.66 and 0.8 s, respectively, and in Lansey network with 150 and 250 iterations and run time of 5.7 and 9.5 s, the optimal solutions were obtained.

Drinking water distribution networks are important because they provide water to meet basic human needs, and to protect humans in the event of fires and other public emergencies. With aging infrastructure, there is an urgent need to design water distribution networks to ensure safety and reliability of service in the future. The uncertainty that surrounds future scenarios of climate-induced drought, population levels, and urbanization patterns – all factors that influence water demand – means that a system design chosen today may be inadequate to meet future demands in a water distribution network. Water utilities often have to plan the design of their water distribution network with only limited information on future water demand levels. For example, if water demand in the future is higher than the level predicted at the time of design, then a municipality will eventually have to retrofit the system, perhaps at great expense, to meet the unanticipated water demand. Thus, there is a need for methods to design networks to minimize the need for future system retrofit under uncertain demands, and to make networks economically robust. In this paper a new framework is presented to design water distribution networks for economic robustness. Economic robustness supplements the least-cost optimality criterion by providing a measure of the variability involved in retrofit costs of a system under uncertain future conditions. In the new framework, water demand projected at the end of a 20-year planning period is treated as an uncertain quantity and modeled as a random variable with an error probability density function (PDF). In the proposed framework, new criteria such as the expected value and standard deviation of retrofit cost are developed to evaluate the economic robustness of water distribution networks. The framework is applied to a simple network, with comparison of design alternatives done on the basis of pipe cost and expected retrofit cost. The results obtained indicate that surplus hydraulic capacity lowers the uncertainty of future retrofit costs and increases confidence of retrofit cost estimates. Consequently, the results substantiate the intuitive understanding of the benefits of surplus hydraulic capacity in a system.

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.

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.

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.

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.