[1] The history of environmental flow analysis shows a shift from an emphasis on a flat line minimum flow requirement to the development of a holistic, regime-based, approach to flow management. The ecological flow regime determines environmental flow by embracing the multitude of species within an ecosystem rather than emphasizing a single species. Moreover, this paradigm recognizes that flow magnitude, duration, frequency, timing, and predictability must be incorporated into any flow management strategy. In this study, the ecological flow regime paradigm is used to establish such comprehensive and complex management targets for operating a reservoir to satisfy a downstream aquatic ecosystem. The new paradigm incorporates the intermediate disturbance hypothesis, which holds that ecosystems are healthier under disturbances that are neither too small nor too large. The nondominated sorting genetic algorithm is used to find the Pareto set of operating rules that provides decision makers with the optimal trade-off between human needs and ecological flow regime maintenance.

This paper builds on the work of Meyer and Brill (1988) and subsequent work by Meyer et al. (1990, 1992) on the optimal location of a network of groundwater monitoring wells under conditions of uncertainty. We investigate a method of optimization using genetic algorithms (GAs) which allows us to consider the two objectives of Meyer et al. (1992), maximizing reliability and minimizing contaminated area at the time of first detection, separately yet simultaneously. The GA‐based solution method has the advantage of being able to generate both convex and nonconvex points of the trade‐off curve, accommodate nonlinearities in the two objective functions, and not be restricted by the peculiarities of a weighted objective function. Furthermore, GAs have the ability to generate large portions of the trade‐off curve in a single iteration and may be more efficient than methods that generate only a single point at a time. Four different codings of genetic algorithms are investigated, and their performance in generating the multiobjective trade‐off curve is evaluated for the groundwater monitoring problem using an example data set. The GA formulations are compared with each other and also with simulated annealing on both performance and computational intensity. Simulated annealing relies on a weighted objective function which can find only a single point along the trade‐off curve for each iteration, while all of the multiple‐objective GA formulations are able to find a larger number of convex and nonconvex points of trade‐off curve in a single iteration. Each iteration of simulated annealing is approximately five times faster than an iteration of the genetic algorithm, but several simulated annealing iterations are required to generate a trade‐off curve. GAs are able to find a larger number of nondominated points on the trade‐off curve, while simulated annealing finds fewer points but with a wider range of objective function values. None of the GA formulations demonstrated the ability to generate the entire trade‐off curve in a single iteration. Through manipulation of GA parameters certain sections of the trade‐off curve can be targeted for better performance, but as performance improves at one section it suffers at another. Run times for all GA formulations were similar in magnitude.

The genetic algorithm (GA), a new search technique, is applied to a multiple objective groundwater pollution containment problem. This problem involves finding the set of optimal solutions on the trade-off curve between the reliability and cost of a hydraulic containment system. The decision variables are how many wells to install, where to install them, and how much to pump from each. The GA is an optimization technique patterned after the biological processes of natural selection and evolution. A GA operates on a population of decision variable sets. Through the application of three specialized genetic operators: selection, crossover, and mutation, a GA population "evolves" toward an optimal solution. In the paper, simple GAs and GAs that can solve multiple objective problems are described. Two variations of a multiple objective GA are formulated: a vector-evaluated GA (VEGA) and a Pareto GA. For the zerofixed cost situation, the Pareto GA is shown to be superior to the VEGA and is shown to produce a trade-off curve similar to that obtained via another optimization technique, mixed integer chance constrained programming (MICCP). The effect on the VEGA and Pareto GA of parameter variation is shown. The Pareto GA is shown to be capable of incorporating the fixed costs associated with installing a system of wells. Results for several levels of fixed cost are presented. A comparison of computer resources required by the GAs and the MICCP method is given. Future research plans are discussed, including the incorporation of the objective of pump-out time into the model and the development of parallelized GAs. 1589 1590 RITZEL ET AL.: USING GENETIC ALGORITHMS FOR GROUNDWATER PROBLEM

The design of a monitoring network to provide initial detection of groundwater contamination at a waste disposal facility is complicated by uncertainty in both the characterization of the subsurface and the nature of the contaminant source. In addition, monitoring network design requires the resolution of multiple conflicting objectives. A method is presented that incorporates system uncertainty in monitoring network design and provides network alternatives that are noninferior with respect to several objectives. Monte Carlo simulation of groundwater contaminant transport is the method of uncertainty analysis. The random inputs to the simulation are the hydraulic conductivity field and the contaminant source location. The design objectives considered are (1) minimize the number of monitoring wells, (2) maximize the probability of detecting a contaminant leak, and (3) minimize the expected area of contamination at the time of detection. The network design problem is formulated as a multiobjective, integer programming problem and is solved using simulated annealing. An application of the method illustrates the configurations of noninferior network solutions and the trade‐offs between objectives. The probability of detection can be increased either by using more monitoring wells or by locating the wells farther from the source. The latter case results in an increase in the average area of the detected contaminant plumes at the time of initial detection. If monitoring is carried out very close to the contaminant source to reduce the expected area of a detected plume, a large number of wells are required to provide a high probability of detection. A sensitivity analysis showed that the predicted performance of a given number of wells decreases significantly as the heterogeneity of the porous medium increases. In addition, a poor estimate of hydraulic conductivity was shown to result in optimistic estimates of network performance. In general, the trade‐offs between monitoring objectives are an important factor in network design unless the cost (as expressed by the number of monitoring wells) is of limited concern.

A new technique, called the mixed-integer-chance-constrained programming (MICCP) method is developed in this research. This technique considers uncertainty in all linear programming constraint coefficients and does not require a priori knowledge of the distribution. A groundwater remediation problem serves as an example. The method is developed to find the globally optimal trade-off curve for maximum reliability versus a minimum pumping objective. As the fields became more heterogeneous, the pumping rate of a reliable solution increases. Four simple "rule of thumb" methods are compared to the MICCP technique. In general, the performance of such methods decreases as the heterogeneity of the hydraulic conductivity field increases. by constructing engineered impervious barriers, (2) physical removal of the contaminated water and soil, (3) in situ treatment of contaminants in the aquifer, or (4) removal of the polluted water by hydraulic means.While the potential of the first three approaches is recognized, only the latter approach is considered in the research reported here. Such techniques consist of selectively pumped extraction and injection wells that flush the polluted water from the aquifer and bring it to the surface for treatment to a quality acceptable for surface discharge or reinjection.Designing such a flushing and extraction system, which consists of determining the least cost well locations and extraction or withdrawal rates, is especially challenging due to the great deal of hydrogeological uncertainty. Certain basic information about the aquifer must be known, for example, aquifer thickness, hydraulic conductivity, storativity, permeability of overlying and underlying strata, the hydraulic head, effects of evapotranspiration and infiltration, and porosity. Quite often, however, these parameters are not adequately known throughout the region of interest to predict the aquifer respon.se to pumping with a degree of accuracy sufficient for the design of the remediation system. Because of the heterogeneous and uncertain nature of most aquifers, the errors involved in predictions of solute transport can be considerable.The degree to which the hydraulic gradient is changed by injection or withdrawal of water into the aquifer is dependent upon the hydraulic conductivity of the aquifer. The hydraulic conductivity (K) of the aquifer can vary spatially by orders of magnitude. This spatial variability implies that K at any point is uncertain and ideally this uncertainty should be incorporated into the optimal design. The main goal of this paper is the development of a new chance constrained programming technique to perform that optimal design. This technique is used to develop a tradeoff curve between cost and reliability in the containment of a contaminant in a groundwater aquifer. The effect of different degrees of heterogeneity of the parameters in the aquifer will be studied. PREVIOUS WORK In a series of early papers, Charnes et al. [1958] and Charnes and Cooper [1963] studied chance constrained programming....