University of Illinois at Urbana-Champaign. Water Resources Center
Abstract
This research builds on the work of Meyer and Brill [I988] and subsequent work by Meyer et al. [1990], Meyer et al. [1992], and Meyer [I992] on the optimal location of a network of groundwater monitoring wells under conditions of uncertainty. A method of optimization is developed using genetic algorithms (GAS) which allows consideration of the two objectives of Meyer et al. [1992], maximizing reliability and minimizing contaminated area, separately yet simultaneously. The GA-based solution method can generate both convex and non-convex points of the tradeoff curve, can accommodate non-linearities in the two objective functions, and is not restricted to the peculiarities of a weighted objective function. Furthermore, GAS can generate large portions of the tradeoff curve in a single iteration and may be more efficient than methods that generate only a single point at a time.Four multi-objective GAS formulations are investigated and their performance in generating the multi-objective tradeoff curve is evaluated for the groundwater monitoring problem using two example data sets. The GA formulations are compared to each other and to simulated annealing on both performance and computational intensity.The simulated annealing based technique used by Meyer et al. [I992] relies on a weighted objective function which finds only a single point along the tradeoff curve for each iteration, while the multiple-objective GA formulations are able to find many convex and nonconvex points along the tradeoff 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 the tradeoff curve. GAS are able to find a larger number of non-dominated points on the tradeoff curve in a single iteration, and are therefore just as computationally efficient as simulated annealing in terms of generating the tradeoff curves.None of the GA formulations demonstrate the ability to generate the entire tradeoff curve in a single iteration, but they yield either a good estimation of all regions of the tradeoff curve except the very highest and very lowest reliability ends or a good estimation of the high reliability end alone.U.S. Department of the InteriorU.S. Geological Surve
