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AN EFFICIENT HYBRID LP‐LP METHOD FOR THE OPTIMAL UTILIZATION OF CONFINED AQUIFERS

This paper presents an efficient hybrid methodology for solution of the groundwater management problem. The problem to be addressed is the minimization of the pumping cost of a predefined number of wells of fixed position in a two‐dimensional (2D) confined aquifer. The solution of the problem is defined by the pumping rate of the wells which satisfy downstream demand, the lower/upper bound on the pumping rates, and the upper bound on the water level drawdown in the wells. This problem is one of non‐linear optimization which can be solved using conventional non‐linear programming (NLP) and modern heuristic algorithms with their corresponding advantages and shortcomings. In the proposed method, the problem is formulated as one of optimization in terms of pumping rates and water level drawdown in the wells by embedding the discretized version of the differential equation governing the aquifer in the problem formulation. The resulting constrained non‐linear optimization problem is then decomposed into two linear optimization problems with different sets of decision variables, namely pumping rates and water level drawdown. The newly formed linear problems are solved iteratively using a simplex method leading to a highly efficient hybrid method. The ability and efficiency of the proposed method are tested against three test examples and the results presented and compared to other methods. The results indicate the superiority of the proposed method over others available in the literature such as NLP and GA in both accuracy and computational effort. While the performance of the available methods is shown to deteriorate with the size of the problem, when the number of wells to be operated are increased, the proposed method is shown to be insensitive to problem size, offering a robust method for solving real‐life groundwater management problems. Copyright © 2012 John Wiley & Sons, Ltd.