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This paper presents a new valve positioning algorithm (VPA) for water network pressure reduction. The proposed algorithm is a graph theory-based algorithm combined with EPANET2.2 to position pressure-reducing valves (PRVs) at the most effective locations, having the most effect on downstream pressure reduction, and then calculates the setpoint for locally controlled valves. Each algorithm solution positions one valve on the edge with the highest-pressure reduction indicator calculated using the depth-first search algorithm. The setpoint is then calculated according to downstream pressure differences to the minimum service pressure to be supplied. The PRV location and setpoint found by the algorithm may be used to install and set locally controlled PRVs or serve as a guide for positioning remote-controlled PRVs. The algorithm is demonstrated on a simple example network using demand-driven analysis (DDA), pressure-driven analysis (PDA), and genetic algorithms (GA) and on a medium and a large example application (DDA). Any number of PRVs may be installed using the algorithm, which returns stable results and very short solution times while maintaining minimum service pressure requirements to the critical consumers. [ABSTRACT FROM AUTHOR]

This paper shows how pipe replacements and control valve installations can be optimized in water distribution networks to reduce leakage, under minimum nodal pressure constraints. To this end, a hybrid multiobjective algorithm, which has pipe diameters and valve positions and settings as decisional variables, was set up. The algorithm also enables identification of the isolation valves that have to be closed in order to improve effectiveness of the control valves installed. The algorithm is initially applied to the optimal valve location problem, where it explores the trade-off between the number of installed control valves and the daily leakage volume. In this context, the analysis of the results proves the new algorithm more effective than a multiobjective genetic algorithm widely adopted in the scientific literature. Furthermore, it shows that if some isolation valves identified ad hoc are closed in the network, the installation of control valves determines larger leakage volume reductions. In a second application of the algorithm, pipe replacements and control valve installations are simultaneously performed. In this case, a Pareto front of trade-off solutions between installation costs and daily leakage volume is obtained. For the choice of the final solution within the front, an economic criterion based on the long-term convenience analysis is also illustrated. [ABSTRACT FROM AUTHOR]

Evolutionary 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. Fitness function and run-time behavioral statistics are used for this purpose. The results show that both the starting population and algorithm searching mechanism have an impact on the speed with which near-optimal solutions are identified. The fitness function and run-time behavioral statistics indicate that EA parameterizations that favor exploitation over exploration enable near-optimal solutions to be identified earlier in the search, which is due to the "big bowl" shape of the fitness function for all of the WDS problems considered. Using initial populations that are informed by domain knowledge further increases the speed with which near-optimal solutions can be identified. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) algorithms have been successfully used to handle a wide range of water resource optimization problems in recent years. The relative performance of various DE variants has been typically assessed based on the quality of the final solutions for the selected problems within the given computational budget. Such a comparative analysis, however, provides limited under- standing on how various operational mechanisms alter the DE algorithms' searching behavior and what searching properties lead to improved performance. To improve research in this area, this study aims to characterize and compare the searching behavior of four DE variants using a range of measure metrics, mainly focusing on real-time statistics of the algorithm's search quality, search progress, and convergence manner. The utility of the metrics is demonstrated using the four DE variants (SDE, dDE, MdDE, and SADE) applied to three water distribution network (WDN) design problems with significantly increased complexity (scales). The behavioral results offer an appreciably improved understanding of the searching characteristics associated with each DE variant, thereby providing guidance for choosing the most suitable DE algorithm to solve a particular WDN optimization problem as well as offering knowledge to develop new advanced algorithms. For real- world problems, the SDE algorithm is more suitable if a limited computational budget is allowed, whereas the SADE and MdDE variants are respectively more appealing when moderate and large computational budgets are available. A new solution with a cost of $12.62 million for the large-scale problem (1,278 decision variables) is presented. [ABSTRACT FROM AUTHOR]

In order to address the issue of water demand uncertainty due to the effect of climate change and urbanization in the design and management of water distribution systems (WDSs), a flexible methodology that combines sampling techniques (Monte Carlo-MC or Latin Hypercube-LH simulations), decision tree analysis, and genetic algorithm optimization is presented. The methodology gives flexible and optimal decisions as future water demand unfolds. The problem of optimal WDS design under uncertain future water demand is formulated here as a multiobjective optimization problem. The two objectives are as follows: (1) minimisation of total intervention cost; and (2) maximization of WDS end resilience. The decision variables are the conventional design interventions (e.g., pipe duplication and/or replacement of existing pipes with new ones, addition of tanks and pumps, etc.) and the water demand threshold values. The output from the nondominated sorting genetic algorithm (NSGA2) optimisation process is the Pareto front containing staged (developmental) design solutions represented in a decision tree form with an optimal water demand threshold value that results due to the trade-off in terms of the two objectives analyzed over the planning horizon. This methodology was applied on the New York Tunnels and the Anytown network problems. The results show that there is value achieved by building flexibility in design when compared to the deterministic approach in the long-term planning of WDSs under uncertainty. [ABSTRACT FROM AUTHOR]

The multiobjective optimization model described in this study is aimed at exploring the tradeoff between cost and resiliency for water distribution systems optimal design. Many have dealt previously with minimizing cost where reliability was quantified as a constraint. Fewer considered both cost and reliability as objectives. This work suggests a methodology for least cost versus reliability (quantified as resiliency) optimal design, introducing the following contributions: (1) a genetic algorithm multiobjective formulation integrating a previous theoretical result of a possible maximum of two adjacent discrete pipe diameters for a single pipe; (2) comparable results to previous best least-cost design solutions for the two-looped and Hanoi networks; (3) a real life-sized example application analysis for pipes reinforcement; and (4) an interpretation of resiliency through its comparison to two explicit reliability measures involving demands increase and pipes failure, reconfirming that resiliency improvement does not necessarily imply a reliability increase. Three example applications are explored through base runs and sensitivity analyses for demonstrating the study findings. [ABSTRACT FROM AUTHOR]