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.

设计井场以有效提取地下水或石油时，设计人员通常依靠计算优化方法来确定井的最佳位置。这些方法的目标是找到一种井场解决方案，该解决方案可以最大程度地提高已定义目标函数的值，并且可以在利用最少计算量的情况下做到这一点。为了实现这一目标，研究人员开发了基于多种启发式算法的算法。在地下水管理中，流行的方法包括粒子群优化（PSO）和遗传算法，例如差分进化（DE）。这项研究旨在研究一种最近开发的称为“井位问题的极值优化”（EO-WPP）的方法，并将其性能与PSO和DE等已建立的方法进行比较。EO-WPP是一种基于极值优化（EO）算法的优化方法。EO通过反复标识和修改解决方案中最不有效的组件来进行优化。通过遵循这种启发式方法，EO算法具有快速找到最佳解决方案的潜力，而所需的计算工作却很少。为了测试这一点，在四个基准问题上比较了DE，PSO和EO-WPP的性能。其中两个是Rastrigin和Rosenbrock基准函数。之所以使用这些功能，是因为它们具有快速的评估能力以及在优化文献中的广泛应用。第三个基准是合成地下水模型，旨在在地下水管理的背景下测试方法。最终基准是使用南达科他州阿伯丁地下水模型的现场问题。结果表明，EO-WPP能够在所有测试基准上胜过DE和PSO。EO-WPP是用于地下水管理中井位设计的有效而高效的优化工具。