A Comparison of Extremal Optimization, Differential Evolution and Particle Swarm Optimization Methods for Well Placement Design in Groundwater Management

Abstract

When designing a well field for efficiently extracting groundwater or petroleum, it is common for designers to rely on computational optimization methods to determine the optimal placement of wells. The goal of these methods is to find a well-field solution that maximizes the value of a defined objective function, and to do so while utilizing the least amount of computational effort. To achieve this, researchers have developed algorithms based on a wide range of heuristics. Within groundwater management, popular methods include particle swarm optimization (PSO) and genetic algorithms such as differential evolution (DE). This study seeks to investigate a recently developed method called Extremal Optimization for Well Placement Problems (EO-WPP), and to compare its performance with established methods like PSO and DE. EO-WPP is an optimization method based on the extremal optimization (EO) algorithm. EO optimizes by iteratively identifying and modifying the least effective components of a solution. By following this heuristic, the EO algorithm has the potential to quickly find optimal solutions while requiring minimal computational effort. To test this, the performance of DE, PSO and EO-WPP was compared on four benchmark problems. Two of these are the Rastrigin and the Rosenbrock benchmark functions. These functions were used because of their quick evaluation and their popularity in optimization literature. The third benchmark is a synthetic groundwater model, built to test the methods under the context of groundwater management. The final benchmark is a field problem using the Aberdeen groundwater model in South Dakota. The results reveal that EO-WPP was able to outperform DE and PSO on all tested benchmarks. EO-WPP is an effective and efficient optimization tool for well placement design in groundwater management.