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Decomposition has become an increasingly popular technique for evolutionary multiobjective optimization (EMO). A decomposition-based EMO algorithm is usually designed to approximate a whole Pareto-optimal front (PF). However, in practice, a decision maker (DM) might only be concerned in her/his region of interest (ROI), i.e., a part of the PF. Solutions outside that might be useless or even noisy to the decision-making procedure. Furthermore, there is no guarantee that the preferred solutions will be found when many-objective problems. This paper develops an interactive framework for the decomposition-based EMO algorithm to lead a DM to the preferred solutions of her/his choice. It consists of three modules, i.e., consultation, preference elicitation, and optimization. Specifically, after every several generations, the DM is asked to score a few candidate solutions in a consultation session. Thereafter, an approximated value function, which models the DM's preference information, is progressively learned from the DM's behavior. In the preference elicitation session, the preference information learned in the consultation module is translated into the form that can be used in a decomposition-based EMO algorithm, i.e., a set of reference points that are biased toward the ROI. The optimization module, which can be any decomposition-based EMO algorithm in principle, utilizes the biased reference points to guide its search process. Extensive experiments on benchmark problems with three to ten objectives fully demonstrate the effectiveness of our proposed method for finding the DM's preferred solutions. [ABSTRACT FROM AUTHOR]

This paper explores the potential savings that can be realized through the identification of optimal asset management business policies for small-diameter (25-50 mm) water communication pipes, which are installed between the customer's property boundary and the distribution main. The outputs from a geospatial mapping tool are used alongside a set of calibrated Weibull deterioration curves to drive a whole-life cost and performance analysis. Against this improved understanding of whole-life costs, an optimization algorithm is used to evaluate the trade-off between total expenditure (totex) and the prevention of future asset failures (serviceability) to identify the optimized investment policy according to the decision maker's priorities. Despite attracting an estimated yearly expenditure from water utilities operating across the developed world in excess of £4.42 billion per annum, the authors believe this is the first instance of optimizing communication pipe maintenance policies at the asset level in the industry. A case study is used to demonstrate the development and deployment of this methodology for South West Water (U.K.), whereby £8.5 million in savings and the prevention of up to 1,320 failures have been identified over a 25-year planning horizon. [ABSTRACT FROM AUTHOR]

A method for optimizing sensor locations to effectively and efficiently detect contamination in a water distribution network is presented here. The problem is formulated and solved as a twin-objective optimization problem with the objectives being the minimization of the number of sensors and minimization of the risk of contamination. Unlike past approaches, the risk of contamination is explicitly evaluated as the product of the likelihood that a set of sensors fails to detect contaminant intrusion and the consequence of that failure (expressed as volume of polluted water consumed prior to detection). A novel importance-based sampling method is developed and used to effectively determine the relative importance of contamination events, thus reducing the overall computation time. The above problem is solved by using the nondominated sorting genetic algorithm II. The methodology is tested on a case study involving the water distribution system of Almelo (The Netherlands) and the potential intrusion of E. coli bacteria. The results obtained show that the algorithm is capable of efficiently solving the above problem. The estimated Pareto front suggests that a reasonable level of contaminant protection can be achieved using a small number of strategically located sensors. [ABSTRACT FROM AUTHOR]

This paper deals with methods aimed at the effective and efficient detection of accidental and/or intentional contaminant intrusion(s) in water distribution systems. The objective of this paper is to present a methodology entitled sensors local optimal transformation system (SLOTS) to address both single-objective and multiobjective sensor layout problems. SLOTS is tested on two benchmark water distribution networks used for the Battle of the Water Sensors Networks challenge (BWSN), held as part of the Water Distribution Systems Analysis Symposium, in Cincinnati in 2006. The objectives considered are detection likelihood and the expected population affected prior to detection. The results obtained demonstrate that SLOTS sensor placements are often near optimal. For both single-objective and multiobjective cases, SLOTS is shown to be capable of identifying placements which are consistently better performing than one of the best BWSN methodologies, the greedy algorithm. [ABSTRACT FROM AUTHOR]

Following the events of September 11, 2001, in the United States, world public awareness for possible terrorist attacks on water supply systems has increased dramatically. Among the different threats for a water distribution system, the most difficult to address is a deliberate chemical or biological contaminant injection, due to both the uncertainty of the type of injected contaminant and its consequences, and the uncertainty of the time and location of the injection. An online contaminant monitoring system is considered as a major opportunity to protect against the impacts of a deliberate contaminant intrusion. However, although optimization models and solution algorithms have been developed for locating sensors, little is known about how these design algorithms compare to the efforts of human designers, and thus, the advantages they propose for practical design of sensor networks. To explore these issues, the Battle of the Water Sensor Networks (BWSN) was undertaken as part of the 8th Annual Water Distribution Systems Analysis Symposium, Cincinnati, Ohio, August 27–29, 2006. This paper summarizes the outcome of the BWSN effort and suggests future directions for water sensor networks research and implementation. [ABSTRACT FROM AUTHOR]

The scarcity of water resources is the driving force behind modernizing irrigation systems in order to guarantee equal rights to all beneficiaries and to save water. Traditional distribution systems have the common shortcoming that water must be distributed through some rotational criteria. This type of distribution is necessary to spread the benefits of scarce resources. Irrigation systems based on on-demand delivery scheduling offer flexibility to farmers and greater potential profit than other types of irrigation schedules. However, in this type of irrigation system, the network design has to be adequate for delivering the demand during the peak period whilst satisfying minimum pressure constraints along with minimum and maximum velocity constraints at the farm delivery points (hydrants) and in the pipes, respectively. In this paper, optimum design and management of pressurized irrigation systems are considered to be based on rotation and on-demand delivery scheduling using a genetic algorithm. Comparison is made between the two scheduling techniques by application to two real irrigation systems. Performance criteria are formulated for the optimum design of a new irrigation system and better management of an existing irrigation system. The design and management problems are highly constrained optimization problems. Special operators are developed for handling the large number of constraints in the representation and fitness evaluation stages of the genetic algorithm. The performance of the developed genetic algorithm is assessed in comparison to traditional optimization techniques. It is shown that the methodology developed performs better than the linear programming method and that solutions generated by the modified genetic algorithm show an improvement in capital cost. The method is also shown to perform better in satisfying the constraints. Comparison between on-demand and rotation delivery scheduling shows that a greater than 50% saving can be achieved in total cost at the cost of reducing flexibility in the irrigation time. Finally, it is shown that minimizing standard deviation of flow in pipes does not result in the best distribution, and therefore minimum cost, neither for systems with uniform flows or those with large variations in discharge at hydrants. [ABSTRACT FROM AUTHOR]

Estimating model parameters is a difficult, yet critical step in the use of water distribution system models. Most of the optimization-based approaches developed so far concentrate primarily on efficient and effective ways of obtaining optimal calibration parameter values. At the same time, very little effort has been made to determine the uncertainties (i.e., errors) associated with those values (and related model predictions). So far, this has typically been done using the first-order second moment (FOSM) method. Even though reasonably computationally efficient, the FOSM approach relies on several restrictive assumptions and requires computationally demanding calculation of derivatives. To overcome these limitations, the recently developed shuffled complex evolution metropolis (SCEM-UA) global optimization algorithm is linked to the Epanet2 hydraulic model and used to solve a least-squares-type calibration problem. The methodology is tested and verified on the Anytown literature case study. The main advantage of the SCEM-UA algorithm over existing approaches is that both calibration parameter values and associated uncertainties can be determined in a single optimization model run. In addition, no model linearity or parameter normality assumptions have to be made nor any derivatives calculated. The main drawback of the SCEM-UA methodology is that it could, potentially, be computationally demanding, although this is not envisaged as a major problem with current computers. [ABSTRACT FROM AUTHOR]

Two approaches to solving the problem of robust least-cost design of water distribution systems under uncertainty in input parameters are considered. The first approach (redundant design) is based on redundancy in design, where “safety margins” are added to the uncertain parameters and the resulting deterministic optimization problem is then solved. The values of safety margins are determined iteratively. This method requires no changes to the objective function or constraints formulation when used in conjunction with existing deterministic tools. The second approach (integration method) includes within the objective function the influence of uncertainty on system robustness. A fast numerical integration method is used to quantify uncertainties. System robustness is defined here as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in a network. The sources of uncertainty analyzed here are future water consumption (at each node in the network) and hydraulic roughness (for each pipe in the network), which are assumed to be independent random variables with known probability density functions. The objective is to minimize the total design cost subject to a target level of system robustness. A genetic algorithm is used as the optimization tool. The two methodologies considered in this paper are applied to the New York Tunnels case study. The optimal solutions are identified for different levels of robustness. The best solutions obtained are also compared to the previously identified optimal deterministic solution. The results obtained show that both methodologies are capable of identifying robust least-cost designs while achieving significant computational savings when compared to a full sampling methodology. The results obtained also show that, even though slightly more expensive, solutions obtained using the redundant design method can be obtained with significantly less computational effort than the solutions obtained using the integration method. [ABSTRACT FROM AUTHOR]

The problem of stochastic ( i.e . robust) water distribution system (WDS) design is formulated and solved here as an optimization problem under uncertainty. The objective is to minimize total design costs subject to a target level of system robustness. System robustness is defined as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in the network. The sources of uncertainty analysed here are future water consumption and pipe roughnesses. All uncertain model input variables are assumed to be independent random variables following some pre-specified probability density function (PDF). Two new methods are developed to solve the aforementioned problem. In the Integration method, the stochastic problem formulation is replaced by a deterministic one. After some simplifications, a fast numerical integration method is used to quantify the uncertainties. The optimization problem is solved using a standard genetic algorithm (GA). The Sampling method solves the stochastic optimization problem directly by using the newly developed robust chance constrained GA. In this approach, a small number of Latin Hypercube (LH) samples are used to evaluate each solution’s fitness. The fitness values obtained this way are then averaged over the chromosome age. Both robust design methods are applied to a New York Tunnels rehabilitation case study. The results obtained lead to the following main conclusions: (i) neglecting demand uncertainty in WDS design may lead to serious under-design of such systems; (ii) both methods shown here are capable of identifying (near) optimal robust least cost designs achieving significant computational savings. [ABSTRACT FROM AUTHOR]

In design of water distribution networks, there are several constraints that need to be satisfied; supplying water at an adequate pressure being the main one. In this paper, a self-adaptive fitness formulation is presented for solving constrained optimization of water distribution networks. The method has been formulated to ensure that slightly infeasible solutions with a low objective function value remain fit. This is seen as a benefit in solving highly constrained problems that have solutions on one or more of the constraint bounds. In contrast, solutions well outside the constraint bounds are seen as containing little genetic information that is of use and are therefore penalized. In this method, the dimensionality of the problem is reduced by representing the constraint violations by a single infeasibility measure. The infeasibility measure is used to form a two-stage penalty that is applied to infeasible solutions. The performance of the method has been examined by its application to two water distribution networks from literature. The results have been compared with previously published results. It is shown that the method is able to find optimum solutions with less computational effort. The proposed method is easy to implement, requires no parameter tuning, and can be used as a fitness evaluator with any evolutionary algorithm. The approach is also robust in its handling of both linear and nonlinear equality and inequality constraint functions. Furthermore, the method does not require an initial feasible solution, this being an advantage in real-world applications having many optimization variables. [ABSTRACT FROM AUTHOR]

Genetic algorithm (GA) optimization is well suited for optimizing the operation of water distribution systems, especially large and complex systems. GAs have good initial convergence characteristics, but slow down considerably once the region of optimal solution has been identified. In this study the efficiency of GA operational optimization was improved through a hybrid method which combines the GA method with a hillclimber search strategy. Hillclimber strategies complement GAs by being efficient in finding a local optimum. Two hillclimber strategies, the Hooke and Jeeves and Fibonacci methods, were investigated. The hybrid method proved to be superior to the pure GA in finding a good solution quickly, both when applied to a test problem and to a large existing water distribution system. [ABSTRACT FROM AUTHOR]

The Battle of Water Networks District Metered Areas (BWNDMA) was the latest of the Battle of Water Networks competition series held at the 18th Water Distribution Systems Analysis Conference (WDSA 2016) as part of ASCE's Environmental and Water Resources Institute (EWRI) stand-alone conferences in Cartagena, Colombia in July 2016. In these competitions, the main objective was to address a specific problem related to water distribution systems (WDS) regarding how to optimize the design and operation of the system's main components. This time, the competition was focused on the challenge of WDS network sectorization, that is, determination of the new district metered areas (DMAs) for an existing network. Design requirements involved constraints related to costs, pressure uniformity, and water quality. Changes in valve and pump operations were needed to supply demands at adequate pressures and acceptable water quality for the given supply scenarios: a wet season and a dry season with water shortages. Seven teams from different parts of the world participated in the BWNDMA and presented their solutions at a special session during the 18th WDSA. This article summarizes the BWNDMA teams' approaches, outcomes, and learned lessons for solving the challenging stated problem. An analysis of some of the decisions that were taken is presented; for instance, some teams ignored the demand similarity criterion, the water age criterion, the pressure restrictions, or the constraints in the water rate that could be extracted from sources. The approaches developed in the BWNDMA represent the state-of-the-art with respect to the analysis of hydraulic conditions in DMAs of real-world water distribution networks for which it is mandatory to make efficient use of available water resources. [ABSTRACT FROM AUTHOR]