Multi-directional maximum-entropy approach to the evolutionary design optimization of water distribution systems

A new multi-directional search approach that aims at maximizing the flow entropy of water distribution systems is investigated. The aim is to develop an efficient and practical maximum entropy based approach. The resulting optimization problem has four objectives, and the merits of objective reduction in the computational solution of the problem are investigated also. The relationship between statistical flow entropy and hydraulic reliability/failure tolerance is not monotonic. Consequently, a large number of maximum flow entropy solutions must be investigated to strike a balance between cost and hydraulic reliability. A multi-objective evolutionary optimization model is developed that generates simultaneously a wide range of maximum entropy values along with clusters of maximum and near-maximum entropy solutions. Results for a benchmark network and a real network in the literature are included that demonstrate the effectiveness of the procedure

Coupled topology and pipe size optimization of water distribution systems

This paper describes a new multi-objective evolutionary optimization approach to the simultaneous layout and pipe size design of water distribution systems. Pressure-deficient and topologically infeasible solutions are fully incorporated in the genetic algorithm without recourse to constraint violation penalties or tournaments. The proposed approach is demonstrated by solving three benchmark problems taken from the literature. New optimal layouts and/or new feasible solutions that are cheaper than the best solutions in the literature were found for both branched and looped network configurations. Specifically, a new best solution was generated for each of the above-mentioned benchmark problems. In addition, the case of the looped design of a hitherto branched network in the literature was considered. Detailed results are included that show that the proposed approach achieves good solutions efficiently and consistently

Penalty-free feasibility boundary convergent multi-objective evolutionary algorithm for the 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

Optimal design of water distribution systems based on entropy and topology

A new multi-objective evolutionary optimization approach for joint topology and pipe size design of water distribution systems is presented. The algorithm proposed considers simultaneously the adequacy of flow and pressure at the demand nodes; the initial construction cost; the network topology; and a measure of hydraulic capacity reliability. The optimization procedure is based on a general measure of hydraulic performance that combines statistical entropy, network connectivity and hydraulic feasibility. The topological properties of the solutions are accounted for and arbitrary assumptions regarding the quality of infeasible solutions are not applied. In other words, both feasible and infeasible solutions participate in the evolutionary processes; solutions survive and reproduce or perish strictly according to their Pareto-optimality. Removing artificial barriers in this way frees the algorithm to evolve optimal solutions quickly. Furthermore, any redundant binary codes that result from crossover or mutation are eliminated gradually in a seamless and generic way that avoids the arbitrary loss of potentially useful genetic material and preserves the quality of the information that is transmitted from one generation to the next. The approach proposed is entirely generic: we have not introduced any additional parameters that require calibration on a case-by-case basis. Detailed and extensive results for two test problems are included that suggest the approach is highly effective. In general, the frontier-optimal solutions achieved include topologies that are fully branched, partially- and fully-looped and, for networks with multiple sources, completely separate sub-networks

Novel Hybrid Fuzzy-Intelligent Water Drops Approach for Optimal Feeder Multi Objective Reconfiguration by Considering Multiple-Distributed Generation

This paper presents a new hybrid method for optimal multi-objective reconfiguration in a distribution feeder in addition to determining the optimal size and location of multiple-Distributed Generation (DG). The purposes of this research are mitigation of losses, improving the voltage profile and equalizing the feeder load balancing in distribution systems. To reduce the search space, the improved analytical method has been employed to select the optimum candidate locations for multiple-DGs, and the intelligent water drops approach as a novel swarm intelligence based algorithm is used to simultaneously reconfigure and identify the optimal capacity for installation of DG units in the distribution network. In order to facilitate the algorithm for multi-objective search ability, the optimization problem is formulated for minimizing fuzzy performance indices. The proposed method is validated using the Tai-Power 11.4-kV distribution system as a real distribution network. The obtained results proved that this combined technique is more accurate and has the lowest fitness value as compared with other intelligent search algorithms. Also, the obtained results leadto the conclusion that multi-objective simultaneous placement of DGs along with reconfiguration can be more beneficial than separate single-objective optimization

Water quality sensor placement: a multi-objective and multi-criteria approach

[EN] To satisfy their main goal, namely providing quality water to consumers, water distribution networks (WDNs) need to be suitably monitored. Only well designed and reliable monitoring data enables WDN managers to make sound decisions on their systems. In this belief, water utilities worldwide have invested in monitoring and data acquisition systems. However, good monitoring needs optimal sensor placement and presents a multi-objective problem where cost and quality are conflicting objectives (among others). In this paper, we address the solution to this multi-objective problem by integrating quality simulations using EPANET-MSX, with two optimization techniques. First, multi-objective optimization is used to build a Pareto front of non-dominated solutions relating contamination detection time and detection probability with cost. To assist decision makers with the selection of an optimal solution that provides the best trade-off for their utility, a multi-criteria decision-making technique is then used with a twofold objective: 1) to cluster Pareto solutions according to network sensitivity and entropy as evaluation parameters; and 2) to rank the solutions within each cluster to provide deeper insight into the problem when considering the utility perspectives.The clustering process, which considers features related to water utility needs and available information, helps decision makers select reliable and useful solutions from the Pareto front. Thus, while several works on sensor placement stop at multi-objective optimization, this work goes a step further and provides a reduced and simplified Pareto front where optimal solutions are highlighted. The proposed methodology uses the NSGA-II algorithm to solve the optimization problem, and clustering is performed through ELECTRE TRI. The developed methodology is applied to a very well-known benchmarking WDN, for which the usefulness of the approach is shown. The final results, which correspond to four optimal solution clusters, are useful for decision makers during the planning and development of projects on networks of quality sensors. The obtained clusters exhibit distinctive features, opening ways for a final project to prioritize the most convenient solution, with the assurance of implementing a Pareto-optimal solution.Brentan, B.; Carpitella, S.; Barros, D.; Meirelles, G.; Certa, A.; Izquierdo Sebastián, J. (2021). Water quality sensor placement: a multi-objective and multi-criteria approach. Water Resources Management. 35(1):225-241. https://doi.org/10.1007/s11269-020-02720-3S225241351Barak S, Mokfi T (2019) Evaluation and selection of clustering methods using a hybrid group mcdm. 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Penalty-free multi-objective evolutionary approach to optimization of anytown water distribution network

This paper describes the development and application of a new multi-objective evolutionary optimization approach for the design and upgrading of water distribution systems with multiple pumps and service reservoirs. The optimization model employs a pressure-driven analysis simulator that accounts for the minimum node pressure constraints and conservation of mass and energy. Pump scheduling, tank siting and tank design are integrated seamlessly in the optimization without introducing additional heuristic procedures. The computational solution of the optimization problem is entirely penalty-free, thanks to pressure-driven analysis and the inclusion of explicit criteria for tank depletion and replenishment. The model was applied to the Anytown network that is a benchmark optimization problem. Many new solutions were achieved that are cheaper and offer superior performance compared to previous solutions in the literature. Detailed and extensive simulations of the solutions achieved were carried out. Spatial and temporal variations in water quality were investigated by simulating the chlorine residual and disinfection by-products in addition to water age. The hydraulic requirements were satisfied; efficiency of pumps was consistently high; effective operation of the new and existing tanks was achieved; water quality was improved; and overall computational efficiency was high. The formulation is entirely generic

A hybrid, auto-adaptive, and rule-based multi-agent approach using evolutionary algorithms for improved searching

Selecting the most appropriate heuristic for solving a specific problem is not easy, for many reasons. This article focuses on one of these reasons: traditionally, the solution search process has operated in a given manner regardless of the specific problem being solved, and the process has been the same regardless of the size, complexity and domain of the problem. To cope with this situation, search processes should mould the search into areas of the search space that are meaningful for the problem. This article builds on previous work in the development of a multi-agent paradigm using techniques derived from knowledge discovery (data-mining techniques) on databases of so-far visited solutions. The aim is to improve the search mechanisms, increase computational efficiency and use rules to enrich the formulation of optimization problems, while reducing the search space and catering to realistic problems.Izquierdo Sebastián, J.; Montalvo Arango, I.; Campbell, E.; Pérez García, R. 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Water Distribution System Computer-Aided Design by Agent Swarm Optimization

Optimal design of water distribution systems (WDS), including the sizing of components, quality control, reliability, renewal and rehabilitation strategies, etc., is a complex problem in water engineering that requires robust methods of optimization. Classical methods of optimization are not well suited for analyzing highly-dimensional, multimodal, non-linear problems, especially given inaccurate, noisy, discrete and complex data. Agent Swarm Optimization (ASO) is a novel paradigm that exploits swarm intelligence and borrows some ideas from multiagent based systems. It is aimed at supporting decisionmaking processes by solving multi-objective optimization problems. ASO offers robustness through a framework where various population-based algorithms co-exist. The ASO framework is described and used to solve the optimal design of WDS. 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