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.