Dynamic Optimal Groundwater Management with Inclusion of Fixed Costs

Abstract

Obtaining optimal solutions for groundwater resources planning problems, while simultaneously considering both fixed costs and time-varying pumping rates, is a challenging task. Application of conventional optimization algorithms such as linear and nonlinear programming is difficult due to the discontinuity of the fixed cost function in the objective function and the combinatorial nature of assigning discrete well locations. Use of conventional discrete algorithms such as integer programming or discrete dynamic programming is hampered by the large computational burden caused by varying pumping rates over time. A novel procedure that integrates a genetic algorithm ͑GA͒ with constrained differential dynamic programming ͑CDDP͒ calculates optimal solutions for a groundwater resources planning problem while simultaneously considering fixed costs and time-varying pumping rates. The GA determines the number and locations of pumping wells with operating costs then evaluated using CDDP. This study demonstrates that fixed costs associated with installing wells significantly impact the optimal number and locations of wells.

Integration of Optimal Dynamic Control and Neural Network for Groundwater Quality Management

“…In the backward sweep, an update control policy is evaluated through solving a series of sub-problems that require the variable derivative values (Chang et al 1992;Hsiao and Chang 2002). The derivatives of the transition equation (Eq.…”

“…Several studies have investigated the feasibility of coupling optimization technique with groundwater flow and transporting simulation to design P&T systems (Chang et al 1992;McKinney and Lin 1994;Wang and Zheng 1998;Chang and Hsiao 2002;Chu et al 2005;Chang et al 2007). Significant advances over the past two decades apply optimized ground water management (Gorelick et al 1984;Jones et al 1987;Yeh 1992;Ahlfeld et al 1988;McKinney and Lin 1994;Chang and Hsiao 2002;Hsiao and Chang 2002;Hsiao and Chang 2005;Chu and Chang 2010). However, the solution of the optimal groundwater contamination problem is computationally difficult because the nonconvexities inherent in the contaminant transport equation (Ahlfeld and Sprong 1998).…”

Multi-objective optimization for free-phase LNAPL recovery using evolutionary computation algorithms

“…In recent years, most researchers have focused on optimizing the removal of LNAPLs dissolved in groundwater using the pump-and-treat method, which has been the most commonly-used remediation strategy (Gorelick et al 1984, Ahlfeld et al 1988, Chang et al 1992, Culver and Shoemaker 1992, Karatzas and Pinder 1993, Rizzo and Dougherty 1996, Papadopoulou et al 2003 Several studies have also been devoted to optimizing bioremediation designs using a variety of methods, such as: analytical derivatives Shoemaker 1996, 1998); evolutionary algorithms (binary-coded genetic algorithm, real-coded genetic algorithm and derandomized evolution strategy); direct search methods and derivative-based optimization methods (Yoon and Shoemaker 1999); multiscale derivatives Minisker 2002, 2004); a genetic algorithm integrated with constrained differential dynamic programming (Hsiao and Chang 2002); and a combination of stepwise cluster analysis, nonlinear optimization and artificial neural networks (Huang et al 2006).…”

Performance Evaluation and Population Reduction for a Self Adaptive Hybrid Genetic Algorithm (SAHGA)

“…These algorithms have been used in a number of different fields, including transportation engineering [8], water resources modeling [4], operations research [12], and groundwater management [11] to name a few. For example in the so-called "Bicriteria Transportation Problem" presented in [8], the GA was combined with the traditional simplex method to solve linear problems to create the HGA.…”

“…Another example is the groundwater management problem. The HGA presented in [11] was created by combining the GA with constrained differential dynamic programming. In these applications and others, the HGA and the GA solved the problem using the same population size, and the local search step is applied in most of the cases to a small number of individuals in the population generation after generation.…”