Journal of Water Resources Planning and Management

Water supply is energy intensive, resulting in large amounts of greenhouse gas emissions and increased electricity bills for water service providers (WSPs). In recent years, the incorporation of microhydropower (MHP) turbines within water supply networks (WSN) has been shown to be a viable option for pressure reduction and improved water supply sustainability. An option for optimal pressure management of a WSN is presented through the installation of MHP turbines. The optimization objective was to find optimal locations in a WSN to install turbines for maximized power generation. For comparison, a nonlinear programming approach, a mixed integer nonlinear programming (MINLP) approach, and an evolutionary optimization approach, using a genetic algorithm, were employed. The performance and suitability of each method was initially demonstrated on a theoretical five-node WSN. MINLP was found to be the most suitable technique. Further analyses were undertaken of a benchmark 25-node network. It was recommended that WSPs adopt this hydropower optimization approach in the decision-making process to reduce carbon footprint, increase revenue, and reduce the operational costs of water supply.

Stochastic optimization methods have been developed over the last few decades to help water managers who are regularly confronted with making complex decisions about reservoir releases in the context of streamflow uncertainties. However, a comparative evaluation of the performance of the methods in an operational context is not an easy task, which makes it difficult to select the approach that offers the best performance. This paper presents a comparison between four optimization algorithms in a test bed in which ensemble streamflow predictions (ESPs) are updated each time a decision is taken. The comparison was performed on the Rio Tinto Alcan (RTA) hydropower system in Québec, Canada, which consists of six generating stations in series and three major reservoirs. The tested optimization algorithms are the deterministic optimization approach currently used by RTA and three explicit stochastic optimization approaches, i.e., stochastic dynamic programming, sampling stochastic dynamic programming, and a scenario tree approach. The results showed that methods on the basis of scenarios prove superior to methods on the basis of probability distributions. Moreover, using an anticipative deterministic approach to calculate the release decisions for the first period was found to be an inadequate strategy. Artificially introducing underdispersion in ESPs was also found to affect the quality of the results, and the optimization methods were affected differently. Given that hydrological dispersion will likely differ in the future as a consequence of climate change, further evaluation of optimization techniques should be carried out before selecting approaches that best meet managers’ needs in a climate change context.

In the past, pressure-dependent models (PDMs) have suffered from convergence difficulties. In this paper conditions are established for the existence and uniqueness of solutions to the PDM problem posed as two optimization problems, one based on weighted least squares (WLS) and the other based on the co-content function. A damping scheme based on Goldstein’s algorithm is used and has been found to be both reliable and robust. A critical contribution of this paper is that the Goldstein theorem conditions guarantee convergence of the new method. The new methods have been applied to a set of eight challenging case study networks, the largest of which has nearly 20,000 pipes and 18,000 nodes, and are shown to have convergence behavior that mirrors that of the global gradient algorithm on demand-dependent model problems. A line search scheme based on the WLS optimization problem is proposed as the preferred option because of its smaller computational cost. Additionally, various consumption functions, including the regularized Wagner function, are considered and four starting value schemes for the heads are proposed and compared. The wide range of challenging case study problems that the new methods quickly solve suggests that the methods proposed in this paper are likely to be suitable for a wide range of PDM problems.

Hydroelectric power systems are largely characterized by variability and uncertainty in water resource obligations. Market volatility and the growing number of operational obligations for flood control, navigation, environmental obligations, and ancillary services (including load-balancing requirements for renewable resources) further the need to quantify sources of uncertainty. The variations caused by these factors require the hydropower system to have enough upward and downward flexibility for control technologies, such as dynamic optimal control load-following, unit commitment, or automatic generation, to be effective. Therefore, it is increasingly important to identify measures of operational flexibility to better manage uncertainty and operational obligations. The objective of this paper is to present and discuss approaches for assessment of operational flexibility as a function of dynamic states and control input and how the available operational flexibility can be used by hydropower producers in a comprehensive optimization reformulation to accommodate business procedures to drive the system in an efficient, safe, and interpretable way. The authors consider simple metrics such as power capability and its derivatives as indicators for upward flexibility and effective energy storage capability for downward flexibility. Test results based on the Federal Columbia River power system (FCRPS), managed by the Bonneville Power Administration, Army Corps of Engineers, and Bureau of Reclamation, are presented and demonstrate how operational flexibility can be assessed and that role it plays in short-term operations.

This study contributes a many-objective analysis of water supply in the Tarrant Regional Water District (TRWD) in Texas in the United States, in order to demonstrate how multiobjective evolutionary algorithm (MOEA) decision support can be used with sophisticated water infrastructure models in a highly constrained water-planning environment. A detailed representation of TRWD’s network in the river system modeling tool RiverWare (a model actually used by the utility) is coupled with the Borg MOEA to solve a seven-objective problem formulation. Objectives within the formulation include systemwide performance objectives, as well as reliability objectives to balance multiple reservoirs, calculated using two stochastic hydrology scenarios. The results provide valuable information to TRWD that may inform the utility’s approach to optimization and decision making in the future, as well as illuminate the benefits of optimizing systemwide and component-specific objectives to reveal hidden system dynamics.

Optimal management policies for water reservoir operation are generally designed via stochastic dynamic programming (SDP). Yet, the adoption of SDP in complex real-world problems is challenged by the three curses of dimensionality, modeling, and multiple objectives. These three curses considerably limit SDP’s practical application. Alternatively, this study focuses on the use of evolutionary multiobjective direct policy search (EMODPS), a simulation-based optimization approach that combines direct policy search, nonlinear approximating networks, and multiobjective evolutionary algorithms to design Pareto-approximate closed-loop operating policies for multipurpose water reservoirs. This analysis explores the technical and practical implications of using EMODPS through a careful diagnostic assessment of the effectiveness and reliability of the overall EMODPS solution design as well as of the resulting Pareto-approximate operating policies. The EMODPS approach is evaluated using the multipurpose Hoa Binh water reservoir in Vietnam, where water operators are seeking to balance the conflicting objectives of maximizing hydropower production and minimizing flood risks. A key choice in the EMODPS approach is the selection of alternative formulations for flexibly representing reservoir operating policies. This study distinguishes between the relative performance of two widely-used nonlinear approximating networks, namely artificial neural networks (ANNs) and radial basis functions (RBFs). The results show that RBF solutions are more effective than ANN ones in designing Pareto approximate policies for the Hoa Binh reservoir. Given the approximate nature of EMODPS, the diagnostic benchmarking uses SDP to evaluate the overall quality of the attained Pareto-approximate results. Although the Hoa Binh test case’s relative simplicity should maximize the potential value of SDP, the results demonstrate that EMODPS successfully dominates the solutions derived via SDP.

In response to climate change, vulnerability assessment of water resources systems is typically performed based on quantifying the severity of the failure. This paper introduces an approach to assess vulnerability that incorporates a set of new factors. The method is demonstrated with a case study of a reservoir system in Salt Lake City using an integrated modeling framework composed of a hydrologic model and a systems model driven by temperature and precipitation data for a 30-year historical (1981–2010) period. The climate of the selected future (2036–2065) simulation periods were represented by five combinations of warm or hot, wet or dry, and central tendency projections derived from the World Climate Research Programme’s (WCRP’s) Coupled Model Intercomparison Project Phase 5. The results of the analysis illustrate that basing vulnerability on severity alone may lead to an incorrect quantification of the system vulnerability. In this study, a typical vulnerability metric (severity) incorrectly provides low magnitudes under the projected future warm-wet climate condition. The proposed new metric correctly indicates the vulnerability to be high because it accounts for additional factors. To further explore the new factors, a sensitivity analysis (SA) was performed to show the impact and importance of the factors on the vulnerability of the system under different climate conditions. The new metric provides a comprehensive representation of system vulnerability under climate change scenarios, which can help decision makers and stakeholders evaluate system operation and infrastructure changes for climate adaptation.

The importance of reducing greenhouse gas (GHG) emissions, which have been linked to human-induced climate change, is gradually being recognized by water utilities. Although multiobjective optimization has been applied by previous literature to minimize cost and GHG emissions associated with water distribution systems (WDSs), this has primarily been achieved by considering design options of pipe size and pump type. Little consideration has been given to the appropriate sizing of storage tanks. As such, this paper aims to investigate the effect of storage tank size on the minimization of cost and GHG emissions associated with WDSs. Increases in storage tank size are considered by increasing the tank reserve size (TRS), i.e., the portion of the storage tank available for system balancing purposes. Because storage tanks are critical to the operation of a WDS, it is necessary to accurately model the operation of a WDS. Although electricity tariffs (ETs) are used to consider the time dependency of pumping operational cost, no such consideration has been given to pumping operational GHG emissions. As such, time-dependent emissions factors are used to calculate pumping operational GHG emissions. To investigate the effect of TRS on the minimization of cost and GHG emissions associated with a WDS, the multiobjective optimization of two WDS case studies is performed. The results show that using different TRSs can affect the optimal pumping operational management of a WDS, and increasing the TRS can result in GHG emissions reductions. However, using a very large TRS is likely to be associated with prohibitive costs.

This study demonstrates how Arrow’s Impossibility Theorem, a theory of social choice, is of direct concern when formulating water-resources systems planning problems. Traditional strategies for solving multiobjective water resources problems typically aggregate multiple performance measures into single composite objectives (e.g., a priori preference weighting or grouping-like measures by category). Arrow’s Impossibility Theorem, commonly referred to as Arrow’s Paradox, implies that a subset of performance concerns will inadvertently dictate the properties of the optimized design alternative in unpredictable ways when using aggregated objectives. This study shows how many-objective planning can aid in battling Arrow’s Paradox. Many-objective planning explicitly disaggregates measures of performance while supporting the discovery of planning tradeoffs, using tools such as multiobjective evolutionary algorithms (MOEAs). An urban water portfolio planning case study for the Lower Rio Grande Valley, Texas is used to demonstrate how aggregate, lower objective-count formulations can adversely bias risk-based decision support. Additionally, this study employs a comprehensive diagnostic assessment of the Borg MOEA’s ability to address Arrow’s Paradox by enabling users to explore problem formulations with increasing numbers of objectives and decisions. Counter to conventional assumptions, the diagnostic analysis carefully documents that for modern self-adaptive MOEA searches, increasing objective counts can lead to more effective, efficient, reliable, and controllable searches. The increased objective counts are also shown to directly reduce decision biases that can emerge from problem formulation aggregation and simplification, related to Arrow’s Paradox.

Understanding the factors affecting residential water demand is critical to implement and to improve water management policies during the extreme climate conditions such as drought. As few studies relating water demand to uniform volumetric water pricing exist, this study aims to determine the price and income elasticity of residential water demand under uniform water pricing. Second, this study compares the elasticity of both marginal and average pricing for predrought and during-drought periods and seasonal low and high consumption periods. Individual household water consumption, household age, household value, parcel size, water price, and weather variables from July 2009 through December 2012 for the Oklahoma City area, OK were used. A two-stage least-squares estimation with an instrumental variable was used to develop a water demand model. Results indicate that water demand was inelastic to water price except for high-consumption periods. Parcel size, income, and temperature were positively related to water demand while rainfall, household age, and water price negatively influenced water demand. This study provides important insights into the major variables affecting water demand using easily-obtained data.

A new seismic reliability evaluation model is proposed that quantifies the impact of earthquakes on hydraulic behavior of water supply networks. Probabilistic seismic events are produced in the target areas, and the depth of earthquake failure is evaluated by seismic reliability indicators. The developed model was applied to several case studies and used for an intensive examination on how a water supply system hydraulically responds to a seismic event and what system characteristics influence the system’s performance in the event of an earthquake. First, the system reliability of a real network in South Korea when subjected to earthquakes of various magnitudes and locations was quantified. Next, the reliabilities of full and simplified network models were evaluated to investigate how system layouts affect the reliability evaluation. Finally, networks with different configurations, pipe sizes, and system densities were compared with respect to the seismic reliability and various seismic damage indicators.

This paper examines the effect of implementing a water transaction program to address potential water quality limitations for returning adult fall-run Chinook salmon in a stream system where the agriculture is the dominant land and water use. Water transactions are becoming an increasingly used approach to provide instream flows during periods when there are competing water uses. Water transactions are often used to achieve ecological objectives, but their water quality or biological effects are rarely quantified. The effects of a water transaction implemented in the Shasta River were evaluated by using a spreadsheet model to quantify changes in dissolved oxygen conditions as they relate to discharge, pool volumes, holding habitat capacity, and potential dissolved oxygen demand by holding fish. The results indicate that water transactions may mitigate potential water quality impairments by decreasing the residence time in holding habitat, and are particularly effective during periods when flows are low, holding habitats are near carrying capacity, and dissolved oxygen demand by fish is elevated.

Success in the application of any model-based methodology (e.g., design, control, supervision) highly depends on the availability of a well-calibrated model. The calibration of water distribution networks needs to be performed online due to the continuous evolution of demands. During the calibration process, background leakages or bursts can be unintentionally incorporated to the demand model and treated as a system evolution (change in demands). This work proposes a leak-detection and localization approach to be coupled with a calibration methodology that identifies geographically distributed parameters. The approach proposed consists in comparing the calibrated parameters with their historical values to assess if changes in these parameters are caused by a system evolution or by the effect of leakage. The geographical distribution allows unexpected behavior of the calibrated parameters (e.g., abrupt changes, trends, etc.) to be associated with a specific zone in the network. The performance of the methodology proposed is tested on a real water distribution network using synthetic data. Tested scenarios include leaks occurring at different locations and ranging from 2.5 to 13% of the total consumption. Leakage is represented as pressure-dependent demand simulated as emitter flows at the network nodes. Results show that even considering a low number of sensors, leaks with an effect on parameters higher than the parameters’ uncertainty can be correctly detected and located within 200 m.

In this study, a joint-probabilistic interval multistage programming (JIMP) method is developed for planning water resources management under uncertainty. The JIMP method can tackle uncertainties presented in terms of interval parameters in objective function and constraints, in addition to random variables in the left and right-hand sides of constraints. It can also reflect the dynamics in terms of decisions for water resources allocation through transactions at discrete points of a complete scenario set over a multistage context. Moreover, the JIMP method can be used for analyzing various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. The JIMP method is applied to a real case of planning water trading for supporting the regional sustainable development of the Kaidu-Qongque River basin, which is one of the most arid regions of China. Monte Carlo simulation is introduced into the JIMP framework for evaluating the probability distributions of the water-trading ratio. Results of water-trading amount, water-allocation pattern, and system benefit under different probabilities have been obtained, which reveals that the water-trading scheme is an effective manner to allocate limited water resources with a maximized system benefit in such an arid region. However, the results disclose that a variety of factors such as trading ratio, recycling ratio, trading cost, and water availability have significant effects on the water-allocation pattern and system benefit. Results also show that the market approach can help mitigate water shortage in such an arid region; however, enormous deficits would still occur (particularly for agriculture) as a result of excessive exploration of human activity and overexpansion of cultivated land, which has had adverse effects on the socio-economic development of such an arid region. These findings can help decision makers to adjust the water-resources allocation policy and trading-market behavior pattern to support sustainability in arid regions.

Water supply networks are designed to effectively and efficiently supply water to some originally targeted agglomerations. However, the dynamics over time of water-demand patterns and electricity cost schemes may render these designs inefficient and expensive to operate. This paper considers the challenging problem of optimizing water production and distribution operations in one of the largest water supply networks operating in Flanders (Belgium) while accounting for the water-demand and electricity cost dynamics. Optimizing operations in a real water supply network is a difficult task as it involves many constraints. In addition to the complex hydraulic nonlinear equality constraints stemming from friction losses and pump curves, specific constraints for accurate modeling of storage buffers must be taken into account. These constraints require additional binary variables to model free inflow or possible reinjection of water to the network. The resulting optimization problem is thus a nonconvex mixed-integer and nonlinear mathematical problem that is computationally expensive to solve. A particularly appealing method for solving such optimization problems is Generalized Benders Decomposition (GBD). This paper extends this method to the water supply network optimization problem mentioned previously. It is experimentally shown that the approach is successful through careful selection of the complicating variables and values for the penalty term. Results of the experiments carried out on two network instances show that the carefully fine-tuned model allows convergence to near-optimal solutions. Compared to state-of-the-art solvers, the proposed approach proved to be competitive on the tested networks in terms of solution quality and computational time.

Rigorous calculations of leakage in water distribution networks (WDNs) requires the adoption of a leakage-pressure relationship and the numerical solution of a set of differential (flow continuity and head loss) equations for each pipe of the network. In order to limit the computational effort necessary to solve differential equations, existing hydraulic solvers commonly make use of simplified methods to estimate pipe leakage and convert it into lumped demands at pipe end nodes. In this paper, three well consolidated literature methods for water leakage calculation and allocation to pipe end nodes are compared against the numerical solution of the differential equation, used as a benchmark. A novel method, based on a two-step estimation of pipe nodal piezometric levels was also proposed in this study. Methods were compared considering a single pipe system and using a dimensionless approach for generalisation of results. An application to a water distribution network case study was carried out to show differences in the results obtained with the various methods for a complex system under extended period simulation (EPS) approach. Calculations carried out using the methods described in prior literature had significant prediction errors basically depending on the chosen value for the leakage exponent of the leakage-pressure relationship. In contrast, the proposed two-step method was determined to provide more accurate predictions of pipe leakage and leakage distribution between ending nodes with evident increased potential for implementation in hydraulic solvers.

Pressure management (PM) is commonly used in water distribution systems (WDSs). In the last decade, a strategic objective in the field has been the development of new scientific and technical methods for its implementation. However, due to a lack of systematic analysis of the results obtained in practical cases, progress has not always been reflected in practical actions. To address this problem, this paper provides a comprehensive analysis of the most innovative issues related to PM. The methodology proposed is based on a case-study comparison of qualitative concepts that involves published work from 140 sources. The results include a qualitative analysis covering four aspects: (1) the objectives yielded by PM; (2) types of regulation, including advanced control systems through electronic controllers; (3) new methods for designing districts; and (4) development of optimization models associated with PM. The evolution of the aforementioned four aspects is examined and discussed. Conclusions regarding the current status of each factor are drawn and proposals for future research outlined.

Different river management strategies have different impacts on the water system. Depending on how the future unfolds (e.g., in terms of climate change) impacts on navigation, flood damage, and nature are shaped. Impacts will be evaluated differently by people with different perspectives on river management, and what is considered acceptable now may become unacceptable in the future. The challenge is thus to identify a river management strategy that remains acceptable in different climate change scenarios and under different societal perspectives. Such a strategy is what the authors define as a socially robust river management strategy. This article presents a method—based on cultural theory and an integrated assessment metamodel (IAMM)—to explore the (changing) acceptability of river management measures while taking uncertain developments in climate into account. The result is an overview of different gradations of robustness per measure, indicating the prospected tenability of a measure and its vulnerability for changes in climate and perspective.

Cost-effective and preventive maintenance for water distribution networks (WDN) is essential for the sustainable and reliable use of water resources. In this work, mathematical models were developed and optimization procedures were used for optimal WDN maintenance planning under random failures. A conditional probabilistic measure known as conditional expected supply impact (CESI) was derived, which took into account both WDN infrastructure conditions and dynamic customer demands. To seek an optimal WDN maintenance plan, an integer programming problem was formulated to minimize the CESI measure with binary decision variables and budget constraints. The mathematical models and optimization approach were demonstrated using a regional WDN in a large United States city. Genetics algorithms (GA) were applied to solve the optimization problem and find the optimum maintenance plan for the WDN. The optimum plan averaged a reduction of CESI by 60%.

A warming climate and land management intensification have altered water supply characteristics in many regions of the world. Incorporation of water supply uncertainties into long-term water resources planning and management is, therefore, significant from both a scientific and societal perspective. This study proposes a set of analyses for integrated water resources management under changing water supply and demand expansion based on a newly developed methodology for vulnerability assessment. The basin of interest for the proposed analysis is the interprovincial Saskatchewan River Basin (SaskRB) in Canada, which supports a wide range of water demands, from municipal and industrial use to irrigated agriculture and hydropower. Proposals for an increase in irrigated area are used as a context for exploring the joint effects of current and future water supply uncertainty and increasing irrigation demand conditions on the water resources system. Changing water supply conditions are represented by perturbing annual volumes and the seasonal timing of the hydrograph peak as input to an integrated water resources model. The analysis enables evaluation of the effects of economic development plans as well as variations in volume and peak timing of flows on water availability and economic productivity, including possibilities for failure to meet demands. Results for the SaskRB show that a large increase in irrigated agriculture raises average net revenues, but these are highly dependent on water supply conditions and loss of revenue may arise under drought conditions. Hydropower production is more sensitive to changes in annual inflow volume than to changes in either annual timing of the peak flow or the magnitude of irrigation expansion. Irrigation expansion can considerably affect the peak flows in the Saskatchewan River Delta, the largest inland delta in North America, during low-flow conditions. For example, a 400% increase in irrigated area under a 25% decrease in inflow volume and 4-week-earlier annual peak timing can reduce the frequency of peak flows in the delta by more than 50%, though potential effects on the riparian and aquatic ecosystems remain uncertain. This case study illustrates the practical utility of stochastic analysis of system vulnerability to feasible futures in such a way that socioeconomic trade-offs can be readily visualized and understood. Such performance assessments are useful for long-term water resources planning and management under water supply uncertainty.

This article presents a simulation-optimization approach for evaluating the feasibility of managed aquifer recharge (MAR) in the Samail Lower Catchment, Oman. The objective is to provide a maximum recharge and extraction rate through MAR in an annual cycle of two successive injection and recovery periods, while meeting operational and system constraints such as water level, gradient, and travel time. Three groundwater management problems were solved by coupling a simulation model with successive linear programming (SLP) and the nondominated sorting genetic algorithm (NSGA-II) multiobjective genetic algorithm. Sensitivity analysis was also completed to examine the overall response of the simulation-optimization results to changes in hydraulic conductivities and maximum injection rates. Results using the SLP algorithm showed that the total volume of injected water for 4 months of injection without recovery is as high as $8\times {10}^6{\mathrm{m}}^3$, and the total recovered volume of water for 4 months injection and 8 months recovery is approximately $5.3\times {10}^6{\mathrm{m}}^3$, giving a total recovery efficiency of approximately 66%. For the same setup the NSGA-II algorithm derived the entire nondominated front of solutions for two conflicting objectives: maximizing recovery rate and maximizing minimum groundwater head close to the sea (for preventing seawater intrusion). This algorithm includes travel time constraints directly in the optimization process. In conclusion, the proposed approach provides a cost-effective means to evaluate MAR in a coastal aquifer.

Approximately 50% of Sweden’s electricity is produced by hydropower. This makes energy production in the country vulnerable to factors affecting water availability. Research has shown a positive correlation between the North Atlantic Oscillation (NAO) and hydropower production in Norway and northern Sweden during winter months. The correlation is, however, weaker in southern Sweden, which indicates that there might be other low-frequency atmospheric drivers (teleconnections) affecting this area. The aim of this paper is to analyze the natural climate forcing that affects hydropower production in southern Sweden on a seasonal basis. This knowledge may be of key importance in improving long-term (seasonal to yearly) water management and planning for electricity production in southern Sweden. The Spearman correlation coefficient was calculated between the principal component time series of electricity production (1999–2010) from 17 hydropower stations in 5 different rivers located in southern Sweden and 5 different teleconnection indices: the NAO, East Atlantic (EA), East Atlantic/Western Russia (EA/WR), Scandinavia (SCA), and Polar/Eurasia (POL). Results show that the impact of teleconnections on hydropower electricity production varies with season. In winter, the NAO shows the strongest positive relation with hydropower electricity production, explaining 24% of the variability in production, while the SCA has an almost as strong (15%) opposite effect. During spring and summer, the EA/WR alone shows a significant negative relation, explaining respectively 9 and 13% of the variance in production. No significant correlation appeared during the fall season.

The essential problem for reservoir operation is how to deal with variability of inflow. The impacts of both climate change and human interferences on streamflow further complicate the issue of reservoir inflow variability. This paper presents a case study of a reservoir that has both natural inflow (NI) and controlled inflow (CI), and analyzes how CI, which can be a deterministic item, mitigates the effect of NI variability on reservoir operation. Through a case study of the Biliu River Reservoir in northeastern China, the following questions are addressed: (1) how will the combined NI and CI improve water supply reliability, and (2) can—and if so, how much—of the reservoir’s storage can be reduced without lowering water supply reliability with a certain level of CI? It is found that CI complements NI in terms of water supply reliability through a nonlinear relationship, as shown by an inverse S curve; the two turning points in the curve specify a range of CI with respect to the stochastic nature of NI and the reservoir operation objectives. For the case study reservoir, if the amount of annual CI increases to about 54% of the NI, the primary reservoir storage capacity can be reduced by 40% while providing the same level of water supply reliability.

This paper introduces an improved bat algorithm (IBA) with a hybrid mutation strategy to improve its global search ability. In an effort to guide the evolution and reinforce the convergence efficiently, the spatial characteristics of the social and cognitive experience of each bat in the population with the differential evolution (DE) algorithm were developed. More specifically, it has been employed in original bat algorithm (BA) six DE mutation mechanisms, namely the explorative and the exploitative mutation operators. The mutation plays an important role to avoid trapping in a local optimal solution, to ensure the search efficiency of a near global optimal solution, and to increase diversity of population. Also, five unimodal and multimodal benchmark functions were used to test the performance of IBA. The results show that the new bat algorithm performs better than the original bat algorithms for each of the test functions. In addition, IBA could keep the diversity of bats and have a better global search performance. It has been demonstrated that the proposed BA can achieve very low standard deviation for 15 runs of the results. Finally, the proposed method is used to solve two benchmark problems of hydropower operations of multireservoir systems, namely four-reservoir and 10- reservoir systems. The obtained results show that the performance of the proposed method is quite comparable with the results of well-developed traditional linear programming (LP) solvers such as LINGO 8.0, in which for the 15 runs, the best results are as close as 99.9 percent of the global solutions of 308.4 and 1,194.44 for the four-reservoir and 10-reservoir systems, respectively.

This paper proposes the application of three different methods for preserving the correlation between duration and intensity of synthetically generated water-demand pulses. The first two methods, that is, the Iman and Conover method and the Gaussian copula, respectively, are derived from known statistical approaches, although they had never been applied to the context of demand-pulse generation. The third is a novel methodology developed in this work and is a variation in the Gaussian copula approach. Poisson models fitted with the methods are applied to reproduce the measured pulses in one household, with parameters being obtained with the method of moments. Comparisons are made with another method previously proposed in the scientific literature, showing that the three methods have similar effectiveness and are applicable under more general conditions.