Abstract
Optimization methods have been used in groundwater modeling as well as for the planning and management of groundwater systems. This paper reviews and evaluates the various optimization methods that have been used for solving the inverse problem of parameter identification (estimation), experimental design, and groundwater planning and management. Various model selection criteria are discussed, as well as criteria used for model discrimination. The inverse problem of parameter identification concerns the optimal determination of model parameters using water-level observations. In general, the optimal experimental design seeks to find sampling strategies for the purpose of estimating the unknown model parameters. A typical objective of optimal conjunctive-use planning of surface water and groundwater is to minimize the operational costs of meeting water demand. The optimization methods include mathematical programming techniques such as linear programming, quadratic programming, dynamic programming, stochastic programming, nonlinear programming, and the global search algorithms such as genetic algorithms, simulated annealing, and tabu search. Emphasis is placed on groundwater flow problems as opposed to contaminant transport problems. A typical two-dimensional groundwater flow problem is used to explain the basic formulations and algorithms that have been used to solve the formulated optimization problems.
Résumé
Les méthodes d’optimisation ont été utilisées pour la modélisation des eaux souterraines ainsi que pour la planification et la gestion de ces systèmes. Le présent article passe en revue et évalue les méthodes d’optimisation variées qui ont été utilisées pour apporter une solution au problème inverse d’identification (estimation) des paramètres, de démarche expérimentale et de planification et gestion des eaux souterraines. Le problème inverse d’identification des paramètres concerne la détermination optimale des paramètres du modèle faisant appel aux observations sur le niveau de l’eau. En général, la démarche expérimentale optimale vise à atteindre des stratégies d’échantillonnage qui permette d’estimer les paramètres non connus du modèle. Un objectif classique de la planification d’une utilisation conjuguée optimale des eaux de surface et des eaux souterraines est de minimiser les coûts opérationnels de la réponse à la demande en eau. Les méthodes d’optimisation incluent des techniques de programmation mathématique, telles que la programmation linéaire, la programmation quadratique, la programmation dynamique, la programmation stochastique, la programmation non linéaire et des algorithmes de recherche globale comme les algorithmes génétiques, le recuit simulé et la recherche avec tabou. L’accent est mis sur les problèmes d’écoulement souterrain par opposition aux problèmes de transfert de contaminants. Le problème-type d’écoulement souterrain bi-dimensionnel est utilisé pour expliciter les formulations de base et les algorithmes employés pour résoudre les problèmes d’optimisation formulés.
Resumen
Los métodos de optimización se han utilizado en la modelación, planificación y manejo de los sistemas de agua subterránea. Este trabajo revisa y evalúa los distintos métodos de optimización que han sido usados para resolver el problema inverso de la identificación de parámetros (estimación), diseño experimental y planificación y manejo del agua subterránea. Se discuten varios criterios de selección de modelos, así como los criterios usados para la discriminación del modelo. El problema inverso de la identificación de parámetros se refiere a la determinación óptima de los parámetros del modelo usando observaciones de niveles de agua. En general, el diseño óptimo experimental busca encontrar estrategias de muestreo con el fin de estimar los parámetros desconocidos del modelo. Un objetivo típico de óptima planificación de uso conjuntivo de agua superficial y agua subterránea es minimizar los costos operativos de la demanda de agua. Los métodos de optimización incluyen técnicas de programación matemática, tales como programación lineal, programación cuadrática, programación dinámica, programación estocástica, programación no lineal, y la búsqueda global de algoritmos, tales como algoritmos genéticos, de recocidos simulados y de búsqueda tabú. Se hace hincapié sobre los problemas de flujo de las aguas subterráneas en contraposición a los problemas del transporte de contaminantes. Se utiliza un típico problema de flujo bidimensional de agua subterránea para explicar las formulaciones básicas y los algoritmos que han sido usados para resolver los problemas de optimización formulados.
摘要
最优化方法用于地下水模拟以及用于地下水系统的规划和管理。本文综述和评估了用于解决参数识别(估算)、试验设计和地下水挂会和管理逆问题的各种最优化方法。探讨了各种模型选择标准,以及探讨了用于模型识别标准。参数识别的逆问题采用水文观测数据关注模型参数的最优化确定。总的来说,最优化试验设计寻求找到采样策略,以估算未知的模型参数。地表水和地下水最优化联合利用规划中一个典型的目标就是在满足供水需求的情况下尽量减少运行费用。最优化方法包括数学编程技术,诸如线性编程、二次方编程、动态编程、随机编程、非线性编程及全局搜寻算法,诸如遗传算法、模拟的处理及禁忌算法。重点强调了与污染物运移问题对立的地下水流问题。利用典型的二维地下水流问题解释用于解决所阐述的最优化问题的基本构想和算法。
Resumo
Os métodos de otimização têm sido utilizados tanto para a modelagem de águas subterrâneas quanto para o planejamento e gerenciamento desses sistemas. Esse artigo revisa e avalia diversos métodos de otimização que têm sido utilizados para resolver o problema inverso da identificação (estimação) de parâmetros, delineamento experimental e planejamento e gerenciamento de águas subterrâneas. São discutidos vários critérios de seleção de modelos, assim como critérios usados para o descarte de modelos. O problema inverso de identificação de parâmetros consiste na determinação de parâmetros ótimos do modelo por intermédio de observações de níveis de água. O planejamento ótimo de experimentos, por sua vez, busca estratégias de amostragem necessárias para tal estimação de parâmetros desconhecidos do modelo. No planejamento integrado ótimo entre águas superficiais e subterrâneas, o objetivo típico é minimizar os custos operacionais de atendimento à demanda. Os métodos de otimização incluem técnicas de programação matemática, como programação linear, programação quadrática, programação dinâmica, programação estocástica, programação não-linear e os algoritmos de busca global, como algoritmos genéticos, recozimento simulado (simulated anneling) e busca tabu. É dada ênfase em problemas de escoamento de águas superficiais, diferentemente dos problemas de transporte de contaminantes. As formulações básicas dos métodos e seus algoritmos, que tem sido utilizados para resolver os problemas de otimização formulados, são discutidos a partir de um mesmo problema típico de escoamento bi-dimensional de águas subterrâneas.
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This material is based on work supported by National Science Foundation under award EAR-1314422. Partial support is also provided from an AECOM endowment. The author would like to thank the two reviewers for their constructive reviews and the guest editor for the summary comments.
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Yeh, W.WG. Review: Optimization methods for groundwater modeling and management. Hydrogeol J 23, 1051–1065 (2015). https://doi.org/10.1007/s10040-015-1260-3
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DOI: https://doi.org/10.1007/s10040-015-1260-3