Journal of Water Resources Planning and Management

The paper describes the development of a computer model GANET that involves the application of an area of evolutionary computing, better known as genetic algorithms, to the problem of least-cost design of water distribution networks. Genetic algorithms represent an efficient search method for nonlinear optimization problems; this method is gaining acceptance among water resources managers/planners. These algorithms share the favorable attributes of Monte Carlo techniques over local optimization methods in that they do not require linearizing assumptions nor the calculation of partial derivatives, and they avoid numerical instabilities associated with matrix inversion. In addition, their sampling is global, rather than local, thus reducing the tendency to become entrapped in local minima and avoiding dependency on a starting point. Genetic algorithms are introduced in their original form followed by different improvements that were found to be necessary for their effective implementation in the optimization of water distribution networks. An example taken from the literature illustrates the approach used for the formulation of the problem. To illustrate the capability of GANET to efficiently identify good designs, three previously published problems have been solved. This led to the discovery of inconsistencies in predictions of network performance caused by different interpretations of the widely adopted Hazen-Williams pipe flow equation in the past studies. As well as being very efficient for network optimization, GANET is also easy to use, having almost the same input requirements as hydraulic simulation models. The only additional data requirements are a few genetic algorithm parameters that take values recommended in the literature. Two network examples, one of a new network design and one of parallel network expansion, illustrate the potential of GANET as a tool for water distribution network planning and management.

A multiobjective analysis technique is presented to determine the optimum operation of pumps and reservoirs in service-water-transmission systems. Three major objectives were identified as (1) economics in terms of energy cost minimization; (2) stability in pump operation; and (3) reliability in meeting stochastically varying demands. These objectives were evaluated based on the required number of times the pumps were turned on or off, the required total energy cost, and the minimum required storage during the operating horizon. A set of nondominated solutions to show the explicit trade-off relationships between the considered objectives was generated using a combination of the ε-constraint method and the weighting method. A forward dynamic programming algorithm was applied to find the optimal solution to the discretized multiobjective problem. Decision makers can evaluate the developed trade-off relationship to identify potential operational alternatives for more detailed evaluation. The methodology was illustrated by application to the Kumi service-water-transmission system in the Republic of Korea.

In the National Research Council (NRC) report, “Flood Risk Management and the American River Basin—An Evaluation,” the use of expected probability (accounting for sampling uncertainty) in estimating flood frequencies and average annual flood damages, as practiced by the Corps of Engineers, was concluded to be biased. Alternative procedures recommended in the report are based on studies of samples drawn from a Gaussian population with a fixed damage function. There is no extension of the study to diverse populations (many flood locations) with different flow-damage functions, but conclusions drawn are that the recommended procedures provide frequency and damage estimates that are nearly unbiased. Rationale behind the report study is examined, and it is demonstrated herein that expected-probability procedures used by the Corps are indeed appropriate for flood-frequency estimation and for estimation of average annual flood damages.

The U.S. Army Corps of Engineers (USACE) has instituted a new analysis methodology for estimating the expected annual damage (EAD) and resulting economic benefits accruing to proposed flood damage-reduction projects. Although the methodology is new, it still, in effect, uses expected probability to estimate the frequency of flooding and EAD. The National Research Council (NRC) in a review of USACE's study of the American River levees stated that the use of expected probability results in significantly biased estimates of EAD. An alternative damage model to that proposed by NRC is used to show that expected probability leads to an unbiased estimate of EAD. The damage model proposed requires that an unbiased estimate of damage results when applied to many projects. A simulation study demonstrates that EAD estimated with expected probability is unbiased, whereas the NRC's recommended estimator is biased.

A geographic information system (GIS) is interfaced with a geomorphic-based hydrologic and sediment transport model. The modeling strategy makes use of the “grouped response unit” concept whereby land classes are identified within homogeneous regions and used as hydrologic and sediment response units. The computational units are defined on the basis of homogeneity of topography and soil characteristics using frequency histograms of relevant parameters as objective criteria. The model is then applied to each land class within the computation units. The GIS/model interface is accomplished on an interactive basis in order to allow the user to have some decision-making authority. The methodology is demonstrated in detail and six years of runoff and sediment data are simulated for a watershed in western Puerto Rico. GIS functions are used to demonstrate how the data may be analyzed under various options the planner or manager may desire.

A management model for optimal operation and control of a regional water system is developed and evaluated. The system consists of numerous water sources with various qualities and consumers with differing flow rates and quality requirements. Flow at the nodes, supplies and demands, and solute mass balance are defined as mass balance constraints. Binary on/off controls for the hydraulic components are defined by continuous nonlinear functions. A two-time step formulation representing on-peak and off-peak power cost periods is solved on a personal computer using GAMS/MINOS. The method is readily extensible to cover more time periods and larger networks.

This paper presents a simulation model to be used for water supply planning by a metropolitan water utility. Water supply operations for a single, monthly time step are formulated as a mixed integer linear program (or more simply, LP). The LP is then embedded in a month-by-month simulation model. The LP is formulated using a priority-based objective function. The model has been used successfully by the Alameda County Water District (California) staff for its long-range, integrated planning. The model also shows that some of the inherent weaknesses of math programming in general and mixed integer linear programming in particular, can be overcome to build a successful model.

Controversy continues over the relative merits of traditional frequency estimators and the “expected probability” estimator of flood risk that incorporates an adjustment for parameter uncertainty. Both have solid theoretical motivation, but address different concerns. The description of hydrologic risk and uncertainty provided by new risk and uncertainty procedures adopted by the U.S. Army Corps of Engineers, and risk-based design procedures developed by others, are shown to be equivalent to the expected probability model in simple cases. A 1995 National Research Council (NRC) report recommended against use of the expected probability model for evaluating expected annual damages and the probability of flooding; in particular, the NRC analysis and the 1989 Arnell analysis demonstrated that expected probability estimators yield risk and damage estimators that generally have large positive biases. Historical arguments and related issues are reviewed. Resolution of this controversy and success of the new U.S. Army Corps of Engineers (USACE) risk and uncertainty procedures require a clear framework for understanding what is meant by risk, variability, and uncertainty. Such risk analyses can better represent a community's vulnerability to flooding and the large uncertainty in estimates of expected damages and residual flood risk.