## 1. Introduction

[2] The analysis of capture zones is a prominent topic in hydrogeology. For instance, it is important to guarantee reliable pump-and-treat systems as well as to delineate wellhead protection zones. Analytical and semianalytical algorithms for capture zone delineation have been developed by *Javandel and Tsang* [1986], *Shan* [1999], and *Christ and Goltz* [2002]. These techniques are essential aids but require certain simplifications of the prevailing conditions or are limited to specific situations, respectively. More generally applicable methods are based on numerical flow and transport modeling, either within a deterministic framework [e.g., *Mulligan and Ahlfeld*, 1999], where no uncertainty on the spatial parameter distribution is assumed, or by stochastic modeling. For the latter the classical method is the Monte Carlo analysis, where instead of one, several equally probable realizations of the transmissivity distribution are simultaneously considered [e.g., *van Leeuwen et al.*, 2000]. In the case of boundary conditions changing over time, transient simulations have been used to investigate time-related capture zones [*Bair et al.*, 1990; *Varljen and Shafer*, 1991].

[3] The major objective when planning hydraulic containment measures is to find pumping well configurations that accomplish the targeted effects most efficiently. With this, design optimization methods are essential. They ought to be fast and should concurrently exhibit the necessary robustness to be reliably successful independent of the respective characteristics of the problem given. The applicability and the meaningfulness of the results of such methods strongly depend on how capture, i.e., control of a given contaminated area, is formulated. A variety of formulations have been presented so far. According to *Mulligan and Ahlfeld* [1999], they can be subdivided into three groups: (1) concentration control, (2) hydraulic control, and (3) advective control. Concentration control means that feasible well configurations are found by complying with maximum concentration levels at control points [e.g., *Rogers and Dowla*, 1994; *Guan and Aral*, 1999]. Its application requires flow as well as concentration-based transport simulation and is therefore believed to be restricted to well-investigated sites where a comprehensive knowledge about the spatial distribution of the contaminants and transport relevant aquifer properties is available. Hydraulic control formulations are based on predefined head difference, gradient, or velocity constraints at selected points [e.g., *Colarullo et al.*, 1984; *Lefkoff and Gorelick*, 1986; *Gorelick*, 1987]. Hydraulic control is considered a fast method as it is exclusively based on flow modeling and allows utilization of the response matrix technique. However, a major disadvantage arises from the predefinition of constraints which requires anticipation of the flow regime, i.e., the shape of the capture zone of the optimal well configuration [*Mulligan and Ahlfeld*, 1999]. The advective control approach that has been used in this study makes use of particle tracking to delineate the capture zone [*Massmann et al.*, 1991; *Varljen and Shafer*, 1993; *Mulligan and Ahlfeld*, 1999; *Bayer et al.*, 2002]. In contrast to the two other approaches, advective control does not bias the results of optimization because no prejudgment concerning the capture zone must be made. However, since hydrodynamic dispersion is neglected, advective control should be applied only to cases dominated by macroscale heterogeneity sufficiently described in the flow model used. Several authors presented extensions to the advective control approach introducing travel time as an additional constraint [*Shafer and Vail*, 1987; *Massmann and Freeze*, 1987; *Greenwald and Gorelick*, 1989; *Varljen and Shafer*, 1993; *Ophori et al.*, 1998; *Maskey et al.*, 2002].

[4] Many sites allow considerable freedom in selecting the location of pumping wells and their extraction rates in order to reach hydraulic containment of contaminated aquifer zones. A typical task of optimization is to find the well configuration that guarantees complete capture at a minimum total pumping rate, which is of main concern economically due to its direct correlation to the operation costs. Since the objective function of the optimization is supposed to be highly nonlinear and nonconvex and have several local minima, conventional gradient-based nonlinear techniques are believed to be unsuitable. As a result, heuristic optimization techniques such as evolutionary algorithms (EAs) have gained considerable interest in the last decade to solve complex problems of groundwater flow control and remediation. [e.g., *Rogers and Dowla*, 1994; *Huang and Mayer*, 1997; *Zheng and Wang*, 1999; *Yoon and Shoemaker*, 1999; *Aly and Peralta*, 1999]. *Maskey et al.* [2002] successfully managed a time constraint plume remediation problem by advective control and the use of genetic algorithms. *Bayer et al.* [2001] used evolution strategies for the optimization of advective control by one-well pump-and-treat systems and the ideal adaptation of a funnel-and-gate system.

[5] The study presented here compares two forms of evolutionary algorithms which are based on different encodings of the decision variables and which realize a separate algorithm specific evolutionary search. Simple genetic algorithms (SGAs) [*Reed et al.*, 2000] work on binary parameter representations. (Completely) derandomized evolution strategies (DESs) [*Hansen and Ostermeier*, 2001] use real-valued parameter encodings. The performance of both algorithms in solving a hypothetical design optimization problem is analyzed under various settings of algorithm specific parameters. Hydraulic capture of a given area shall be achieved by a number of wells at a minimum total pumping rate. Candidate well configurations are represented by individual well positions and pumping rates leading to a mixed discrete-continuous problem. Since repeated runs of the simulation model during the optimization procedure may imply a remarkable computational burden, optimization algorithms are not only evaluated with respect to their suitability to detect a solution but also to the number of model runs needed.