Journal of Water Resources Planning and Management

Optimal water distribution system (WDS) design including the layout and pipe sizes is invariably complex, even when hydraulic constraints alone are considered. The addition of water quality (WQ) constraints adds to the computational demands. Using conventional WQ models to evaluate the feasibility of the many networks that must be analyzed can extend the optimization process beyond acceptable limits. Artificial neural networks (ANNs) can approximate disinfectant concentrations in a fraction of the time required by deterministic WQ models, and thus have been used for WDS pipe optimization as fast surrogates of these models. This study seeks to improve the performance of ANNs applied to the optimal design of WDSs by comparing their outcomes on the basis of ANN architecture and data used for ANN training, two factors that affect their speed and accuracy. ANNs were trained to forecast the disinfectant concentration at the relevant nodes of two case studies: A simple WDS (common in the literature of WDS pipe optimization) and a complex WDS that supplies an actual community in the city of Maricopa, Arizona. The results obtained for the first case study showed that ANNs estimated disinfectant concentrations with a satisfactory accuracy, regardless of their architecture or data used for their training. Results obtained for the second case study, however, showed that ANNs with a conventional architecture (wherein multiple ANNs are required to forecast the disinfectant concentration at relevant nodes of the WDS) offered advantages in terms of accuracy over two alternative architectures (that each required a single ANN for the same purpose). However, ANNs trained with a conventional random data set showed a poor performance when compared to ANNs trained with an alternative data set that was obtained with the probabilistic approach described in this paper.

An improved ant colony optimization (ACO) formulation for the allocation of crops and water to different irrigation areas is developed. The formulation enables dynamic decision variable option (DDVO) adjustment and makes use of domain knowledge through visibility factors (VFs) to bias the search towards selecting crops that maximize net returns and water allocations that result in the largest net return for the selected crop, given a fixed total volume of water. The performance of this formulation is compared with that of other ACO algorithm variants (without and with domain knowledge) for two case studies, including one from the literature and one introduced in this paper for different water-availability scenarios within an irrigation district located in Loxton, South Australia near the River Murray. The results for both case studies indicate that the use of VFs (1) increases the ability to identify better solutions at all stages of the search; and (2) reduces the computational time to identify near-optimal solutions. Furthermore, the savings in computational time obtained by using VFs and DDVO adjustment should be considerable for ACO application to problems such as detailed irrigation scheduling that rely on more-complex crop models than those used in the case studies presented in the paper.

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.

Evolutionary algorithms (EAs) have been used extensively for the optimization of water distribution systems (WDSs) over the last two decades. However, computational efficiency can be a problem, especially when EAs are applied to complex problems that have multiple competing objectives. In order to address this issue, there has been a move toward developing EAs that identify near-optimal solutions within acceptable computational budgets, rather than necessarily identifying globally optimal solutions. This paper contributes to this work by developing and testing a method for identifying high-quality initial populations for multiobjective EAs (MOEAs) for WDS design problems aimed at minimizing cost and maximizing network resilience. This is achieved by considering the relationship between pipe size and distance to the source(s) of water, as well as the relationship between flow velocities and network resilience. The benefit of using the proposed approach compared with randomly generating initial populations in relation to finding near-optimal solutions more efficiently is tested on five WDS optimization case studies of varying complexity with two different MOEAs. The results indicate that there are considerable benefits in using the proposed initialization method in terms of being able to identify near-optimal solutions more quickly. These benefits are independent of MOEA type and are more pronounced for larger problems and smaller computational budgets.

This paper evaluates two established decision-making methods and analyzes their performance and suitability within a water resources management (WRM) problem. The methods under assessment are info-gap (IG) decision theory and robust optimization (RO). The methods have been selected primarily to investigate a contrasting local versus global method of assessing water system robustness to deep uncertainty, but also to compare a robustness model approach (IG) with a robustness algorithm approach (RO), whereby the former selects and analyzes a set of prespecified strategies and the latter uses optimization algorithms to automatically generate and evaluate solutions. The study presents a novel area-based method for IG robustness modeling and assesses the applicability of utilizing the future flows climate change projections in scenario generation for water resource adaptation planning. The methods were applied to a case study resembling the Sussex North Water Resource Zone in England, assessing their applicability at improving a risk-based WRM problem and highlighting the strengths and weaknesses of each method at selecting suitable adaptation strategies under climate change and future demand uncertainties. Pareto sets of robustness to cost are produced for both methods and highlight RO as producing the lower cost strategies for the full range of varying target robustness levels. IG produced the more expensive Pareto strategies due to its more selective and stringent robustness analysis, resulting from the more complex scenario ordering process.

Reservoir systems are essential for water resources management. The application and development of optimization techniques for optimal reservoir operation is therefore a valuable undertaking. This paper presents a modified firefly algorithm (MFA) and applies it to optimally solve reservoir operation problems. Three well-known benchmark multireservoir operation problems are optimized for energy production. The results of the MFA are compared with results obtained with other mathematical programming approaches, such as linear programming (LP), differential dynamic programming (DDP), and discrete DDP (DDDP), the genetic algorithm (GA), the multicolony ant algorithm (MCAA), the honey-bee mating optimization (HBMO) algorithm, the water cycle algorithm (WCA), the bat algorithm (BA), and the biogeography-based optimization (BBO) algorithm. The MFA was found to be more effective than alternative optimization methods in solving the test problems demonstrating its strong potential to tackle multireservoir operation problems. This paper’s results indicate that the MFA differed by 0.01 and 0.79% with the LP global optimal solutions of a continuous four-reservoir problem (CFP) and a continuous 10-reservoir problem (CTP), respectively. The objective function of a discrete four-reservoir problem (DFP) obtained with the MFA is equal to the LP’s objective function. This paper demonstrates that the MFA is a competitive optimization method with which to solve a variety of reservoir operation problems.

Implementing best management practices (BMP) on watersheds could help mitigate the effects of urbanization and climate change on the hydrological cycle. Techniques such as retention ponds, rain gardens, infiltration trenches, and green roofs vary in technical performance, space requirements, and cost. The trade-offs between these present a challenge toward BMP selection and placement, therefore requiring optimization. Three optimization methods were applied for BMP implementation on a combined sewer: linear programming (LP); genetic algorithm (GA); and simulated annealing (SA). LP served as a reference point. The SA solution was only marginally better, 4.7% cheaper, whereas GA’s solution was 17.9% more expensive after computations froze at a local minimum; both methods required approximately 18 h of computational time. A second round of optimization used the solution from LP as a starting point. This modification significantly increased the performance of GA, providing a new solution that was 14% cheaper than LP, with reduced computational times for both GA and SA. SA’s solution, though still cheaper than that of LP, was 3.9% more expensive than the one previously obtained with SA.

Least-cost design of water distribution system is a well-known problem in the literature. The formulation of the least-cost design problem started by deterministic modeling and later by more sophisticated stochastic models that incorporate uncertainties related to the problem’s parameters. Recently, a new nonprobabilistic modeling, titled the robust counterpart (RC) approach, has been developed for the least-cost design problem to incorporate the uncertainty without the need for full stochastic information. These nonprobabilistic methods, developed in the field of robust optimization, were shown to be advantageous over classical stochastic methods in the following aspects: tractability and computation time, nonnecessity of full probabilistic information, and the ability to integrate correlation of uncertain parameters aspects without adding complexity. Former studies have considered the RC approach for a special case of the least-cost problem with a single load demand uncertainty, and single gravitational source to simplify the problem formulation and facilitate the use of the method. This special case does not handle the joint temporal and spatial correlations between the problem uncertainties and does not include components such as pumping stations and storage facilities. These new components require trading off capital and operation (i.e., energy) costs in the objective function, as the design cost is explicitly influenced by the demand uncertainty, unlike the situation where only capital cost is considered. In this study, the RC approach is expanded to cover the general least-cost design problem, including (1) multiload patterns, (2) pumping stations, and (3) storage facilities. The unknowns are the pipe diameters, pump and tank capacities, and the heads added by the pumping stations. The problem is solved using the cross-entropy method for several possible protection levels, which are defined by the size of the uncertainty set. The results are demonstrated on two examples to show the trade-off between cost and reliability and test the network’s ability to cope with unexpected scenarios.

The main aim of this study was to develop an index to determine groundwater drought. Then, as a case study, for the sustainable use of groundwater, the optimum cropping pattern was determined in full compliance with the drought conditions in a plain. The newly presented index, known as the groundwater recharge drought index (GRDI), was determined based on the values of recharge in different zones in the plain. The GRDI for different zones within the region was calculated using the data covering 30 years (1980–2010). Based on this index, groundwater drought was found to occur frequently in these regions since 1981. According to the obtained results, the developed index, as compared with other indices, had several basic features including the ability to predict drought in groundwater, consideration of the possible effects of basin characteristics on groundwater drought, the capability of using different methods and models to calculate the GRDI, and separation of the human effects on the hydrological system from natural drought. Therefore, the index could be used in the forecasting and warning systems for management and planning purposes. According to the optimization results, the selected cropping patterns for three scenarios, including normal, dry, and wet years, were in such a way that the exploitation of groundwater resources remained in safe yield range and groundwater-level decline was reduced, contributing to sustainable groundwater management.

Ecosystem services valuation has become a popular approach to weighing trade-offs in environmental management, particularly where natural resources such as freshwater are limited. The authors assessed multiple stakeholders’ social perception regarding a suite of ecosystem services in a south-central U.S. watershed that is water stressed and experiencing intense sociopolitical conflict. First, the ecosystem service beneficiaries were identified and characterized according to how they use and value ecosystem services. Second, the factors underlying social importance and economic support for maintaining these ecosystem services were analyzed. Finally, a willingness to pay approach was used to identify the economic value of services and explored potential biases in water management based on social and cultural attributes. Results (1) identified habitat for species and water quality as the most important and economically valuable ecosystem services, respectively, and (2) uncovered potential conflicts between water user groups based on whether or not they resided in the watershed. The authors suggest managers can use results (1) for dealing with water conflicts by examining stakeholder group attitudes toward specific services, and (2) to quantify the economic value of ecosystem services currently invisible in decision-making domains.