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

Water distribution network optimization using maximum entropy under multiple loading patterns

This paper proposes a maximum entropy-based multi-objective genetic algorithm approach for the design optimization of water distribution networks (WDNs). The novelty is that in contrast to previous research involving statistical entropy the algorithm can handle multiple operating conditions. We used NSGA II and EPANET 2 and wrote a subroutine that calculates the entropy value for any given WDN configuration. The proposed algorithm is demonstrated by designing a six-loop network that is well known from previous entropy studies. We used statistical entropy to include reliability in the design optimization procedure in a computationally efficient way

Reliability assessment of water distribution systems with statistical entropy and other surrogate measures

There is ever increasing commercial and regulatory pressure to minimise the cost of water distribution networks even as the demand for them keeps on growing. But cost minimizing is only one of the demands placed on network design. Satisfactory networks are required to operate above a minimum level even if they experience failure of components. Reliable hydraulic performance can be achieved if sufficient redundancy is built in the network. This has given rise to various water distribution system optimization methods including genetic algorithms and other evolutionary computing methods. Evolutionary computing approaches frequently assess the suitability of enormous numbers of potential solutions for which the calculation of accurate reliability measures could be computationally prohibitive. Therefore, surrogate reliability measures are frequently used to ease the computational burden. The aim of this paper is to assess the correlation of surrogate reliability measures in relation to more accurate measures. The surrogate measures studied are statistical entropy, network resilience, resilience index and modified resilience index. The networks were simulated with the prototype software PRAAWDS that produces more realistic results for pressure-deficient water distribution systems. Statistical entropy outperformed resilience index in this study. The results also demonstrate there is a strong correlation between entropy and failure tolerance

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

Comparison of demand driven and pressure dependent hydraulic approaches for modelling water quality in distribution networks

Water distribution hydraulic models have been used as a basis for water quality modelling in distribution networks. Experts recognized that a realistic hydraulic model is required to accurately simulate water quality. The aim of this paper is to compare Demand Driven Analysis (DDA) and Pressure Dependent Analysis (PDA) based hydraulic models for simulating water quality in networks for future enhancement of water quality models. The well known EPANET 2 and the newly developed EPANET-PDX (pressure dependent extension) have been used as the DDA and PDA models respectively. Water quality analysis was performed for normal and pressure deficient hydraulic conditions on a sample network from literature. The models provide identical results for normal pressure conditions, but different results for pressure deficient conditions. The differences for the case of pressure deficient condition are significant at the farthest nodes from the source during high pressure deficiency situation with low demand satisfaction condition

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

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

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

Evolutionary multi-objective optimal control of combined sewer overflows

This paper presents a novel multi-objective evolutionary optimization approach for the active control of intermittent unsatisfactory discharges from combined sewer systems. The procedure proposed considers the unsteady flows and water quality in the sewers together with the wastewater treatment costs. The distinction between the portion of wastewater that receives full secondary treatment and the overall capacity of the wastewater treatment works (including storm overflow tanks) is addressed. Temporal and spatial variations in the concentrations of the primary contaminants are incorporated also. The formulation is different from previous approaches in the literature in that in addition to the wastewater treatment cost we consider at once the relative polluting effects of the various primary contaminants in wastewater. This is achieved by incorporating a measure of the overall pollution called the effluent quality index. The differences between two diametrically opposed control objectives are illustrated, i.e. the minimization of the pollution of the receiving water or, alternatively, the minimization of the wastewater treatment cost. Results are included for a realistic interceptor sewer system that show that the combination of a multi-objective genetic algorithm and a stormwater management model is effective. The genetic algorithm achieved consistently the frontier optimal control settings that, in turn, revealed the trade-offs between the wastewater treatment cost and pollution of the receiving water