Using Genetic Algorithms to Solve a Multiobjective Groundwater Monitoring Problem

Abstract

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.

Optimal Expansion of Water Quality Monitoring Network by Fuzzy Optimization Approach

“…Earlier studies in the 1990s focused on fundamental principles and applications in siting the water quality monitoring stations (Smith and McBride, 1990;Loftis et al, 1991;Esterby et al, 1992). Later on, in an attempt to assess systematic issues relevant to network design, more studies applied the techniques of integer programming (Hudak et al, 1995), statistical assessment (Hussain et al, 1995), multi-objective programming (Harmancioglu and Alpaslan, 1992;Cieniawski et al, 1995), and Kriging theory (Lo et al, 1996). A broader sense of applications was gained from the discussions of design principles of monitoring network (Dixon and Chiswell, 1996) and the guidelines related to biological impact assessment in the rivers (Timmerman et al, 1997).…”

Using artifical neutral networks and the genetic algorithm to optimize well-field design: Phase I

“…The population size of 100 chosen for the current study is a fairly small value. In water resources applications, values have ranged from 64 [27] to 300 [28] and even up to 1,000 [29]. A larger population helps maintain greater diversity but does so at considerable computational cost when the full model is being used to generate performance predictions.…”

How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration?

“…There is a growing body of water resources literature (Horn and Nafpliotis, 1993;Ritzel et al, 1994;Cieniawski et al, 1995;Halhal et al, 1997;Loughlin et al, 2000;Reed et al, 2001;Erickson et al, 2002;Reed and Minsker, 2004) demonstrating the importance of multiobjective problems (MOPs) and evolutionary multiobjective solution tools. A key characteristic of MOPs is that optimization cannot consider a single objective because performance in other objectives may suffer.…”