Multiobjective evolutionary optimization of water distribution systems : exploiting diversity with infeasible solutions

This article investigates the computational efficiency of constraint handling in multi-objective evolutionary optimization algorithms for water distribution systems. The methodology investigated here encourages the co-existence and simultaneous development including crossbreeding of subpopulations of cost-effective feasible and infeasible solutions based on Pareto dominance. This yields a boundary search approach that also promotes diversity in the gene pool throughout the progress of the optimization by exploiting the full spectrum of non-dominated infeasible solutions. The relative effectiveness of small and moderate population sizes with respect to the number of decision variables is investigated also. The results reveal the optimization algorithm to be efficient, stable and robust. It found optimal and near-optimal solutions reliably and efficiently. The real-world system based optimisation problem involved multiple variable head supply nodes, 29 fire-fighting flows, extended period simulation and multiple demand categories including water loss. The least cost solutions found satisfied the flow and pressure requirements consistently. The cheapest feasible solutions achieved represent savings of 48.1% and 48.2%, for populations of 200 and 1000, respectively, and the population of 1000 achieved slightly better results overall

Investigation into the pressure-driven extension of the EPANET hydraulic simulation model for water distribution systems

Several hydraulic modelling approaches have been proposed previously to simulate pressure deficient operating conditions in water distribution networks more realistically. EPANET-PDX is an extension of EPANET 2 that has an embedded logistic nodal head-flow function. The EPANET-PDX algorithm was investigated to address the weaknesses uncovered under conditions of extremely low pressure. It was observed that, under certain circumstances, the norm of the system of equations increased from one iteration to the next. A criterion that detects false convergence was included. In general, in the examples considered, the formulation proposed had more consistent computational properties, required fewer iterations of the global gradient algorithm, and application of the line minimization procedure was frequent. The formulation proposed is significantly faster in conditions of extremely low pressure. The hydraulic and water quality modelling functionality of EPANET 2 was preserved. For the operating conditions with satisfactory pressure, where direct comparisons with EPANET 2 were possible, EPANET 2 was consistently faster

Practical Application Of Pressure-Dependent EPANET Extension

Hydraulic models have been widely used in the design and operation of water distribution system (WDSs). The models enable planning for possible changes in the system under a wide range of conditions. Under abnormal operating condition, for instance, WDSs become pressure deficient and unable to satisfy demand fully. In such circumstances, pressure dependent models are suitable to quantify the shortfall in flow and pressure accurately for crucial decision-making. Most recently, a pressure dependent extension of the renowned EPANET hydraulic simulator was developed to enable modelling of pressure deficient networks. The model has an integrated pressure dependent demand (i.e. nodal flow) function coupled with a line search and backtracking procedure to facilitate convergence. Extensive verifications were conducted on the model using benchmark and real life networks and good modelling performances were accomplished. The model was combined with multi-objective genetic algorithm for optimisation of design, rehabilitation and operation of WDSs. It generated superior results for benchmark as well as real life networks in terms of cost, hydraulic performance and computational time in reference to previous solutions. It has also been utilised for water quality modelling of real life networks. Overall, the model has not experienced convergence problems when executing the various simulations. Having demonstrated the robustness and benefits of the model previously including seamless integration in genetic algorithms, it would be greatly beneficial on investigating ways of improving the algorithm further. In this work, the line search and backtracking procedure of the algorithm has been improved. This has improved the robustness further by enhancing greatly the computational properties for low flow conditions and increasing the algorithm’s consistency over a wider range of operating conditions. Extended period simulations were executed on real life network considering source head variations and pipe closure conditions

Integration of hydraulic and water quality modelling in distribution networks : EPANET-PMX

Simulation models for water distribution networks are used routinely for many purposes. Some examples are planning, design, monitoring and control. However, under conditions of low pressure, the conventional models that employ demand-driven analysis often provide misleading results. On the other hand, almost all the models that employ pressure-driven analysis do not perform dynamic and/or water quality simulations seamlessly. Typically, they exclude key elements such as pumps, control devices and tanks. EPANET-PDX is a pressure-driven extension of the EPANET 2 simulation model that preserved the capabilities of EPANET 2 including water quality modelling. However, it cannot simulate multiple chemical substances at once. The single-species approach to water quality modelling is inefficient and somewhat unrealistic. The reason is that different chemical substances may co-exist in water distribution networks. This article proposes a fully integrated network analysis model (EPANET-PMX) (pressure-dependent multi-species extension) that addresses these weaknesses. The model performs both steady state and dynamic simulations. It is applicable to any network with various combinations of chemical reactions and reaction kinetics. Examples that demonstrate its effectiveness are included

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

Assessment of water quality modelling capabilities of EPANET multi-species and pressure dependent extension models

The need for accurately predicting water quality through models has increasingly been crucial in meeting rigorous standards and customer expectations. There are several endeavours on developing robust water quality models for water distribution systems. In this paper, two variants of the EPANET 2 water quality model have been assessed to inform future research. The models are the multiple species extension EPANET-MSX and the pressure-dependent extension EPANET-PDX. Water quality analysis was conducted on a hypothetical network considering various operating pressure conditions. Different kinetic models were employed to simulate water quality. First order, limited first order and zero order models were used for predicting chlorine residual, disinfection by-products (DBPs) and water age respectively. Generally, EPANET-MSX and EPANET-PDX provided identical water quality results for normal operating conditions with adequate pressure but different results for pressure-deficient networks. Also, a parallel first order model with fast and slow reacting components was used for chlorine decay and DBPs using the EPANET-MSX model for a network operating under normal pressure conditions

Practical application of penalty-free evolutionary multi-objective optimisation of water distribution systems

Evolutionary algorithms are a commonly applied optimisation approach in water distribution systems. However, the algorithms are time consuming when applied to large optimisation problems. The aim of this paper is to evaluate the application of a penalty-free multi-objective evolutionary optimisation algorithm to solve a real-world network design problem. The optimization model uses pressure-dependent analysis that accounts for the pressure dependency of the nodal flows and thus avoids the need for penalties to address violations of the nodal pressure constraints. The algorithm has been tested previously using benchmark optimisation problems in the literature. In all cases, the algorithm found improved solutions and/or the best solution reported previously in the literature with considerably fewer function evaluations. In this paper, a real-world network with over 250 pipes was considered. The network comprises multiple sources, multiple demand categories, many fire flows and involves extended period simulation. Due to the size and complexity of the optimization problem, a high performance computer that comprises multiple cores was used for the computational solution. Multiple optimisation runs were performed concurrently. Overall, the algorithm performs well; it consistently provides least cost solutions that satisfy the system requirements quickly. The least-cost design obtained was over 40% cheaper than the existing network in terms of the pipe costs

Optimal Tank Design And Operation Strategy To Enhance Water Quality In Distribution Systems

Water storage tanks are key components of water distribution networks (WDNs) and are primarily designed and operated to meet demand variations and pressure needs. However, the common practice in the design of WDNs is to incorporate large storage tanks that may possibly create long residence time. Long residence time is a major contributing factor for loss of disinfectant, increased formation of disinfection by products and microbial regrowth. Also, poor choice in tank geometry, location and operation can play a role in deterioration of water quality. Most of the previous approaches on optimisation of WDNs design and operation do not take into account tank operation explicitly. In this work, optimal tank design, location and operation strategy has been implemented to assess network performance from water quality perspective. The most recently developed genetic algorithm based optimisation model “Penalty-Free Multi–Objective Evolutionary Algorithm (PF-MOEA)” has been employed. PF-MOEA uses a pressure dependent analysis simulator that handles the node pressure constraints and the conservation of mass and energy inherently. The algorithm considers tank operation strategy as one of the objectives in the optimisation process. The optimisation model incorporates pipe sizing, tank siting, tank sizing and pump operation. PF-MOEA has been applied on the benchmark “Anytown” network that comprises multiple loadings, storage tanks and pumps. The model provided many feasible solutions that are cheaper than the best previous solutions. The solutions satisfy both node pressure and operational constraints for the different loading conditions. A significant improvement in water quality has been achieved in terms of water age, disinfection residual and disinfection by-product concentration in the entire network. Results demonstrated that explicit consideration of the tank operation objective has substantially enhanced the network performance in reference to hydraulic as well as water quality

Design optimization of water distribution networks: real-world case study with penalty-free multi-objective genetic algorithm using pressure-driven simulation

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