Comparison of quadratic and non-linear programming (QP and NLP) optimization models in groundwater management

Abstract

This project is concerned with the comparison of two algorithms used in groundwater management models, based on Quadratic Programming (QP) and Non-linear Programming (NLP) models. A quadratic objective function is used and solved in two different ways. The first one is the application of the Karush–Kuhn–Tücker (KKT) conditions and Wolfe's algorithm, which are used in solving QP models. The second one is the Conjugate Gradient Method (CGM), which is used in solving NLP models. Two additional ‘shell programs’ are created to formulate the results of the management model. These results are organized in a Mathematical Programming System (MPS) file. This is the management model output and contains the response matrix coefficients and all the management model details in a coded format. The MPS data file is formatted via the two shell programs, constituting the import data file for the optimization procedure that takes place with the GINO model and spreadsheets. An application took place in an aquifer in Northern Greece, just on the border with the Former Yugoslavian Republic of Macedonia (FYROM). The phreatic aquifer was divided into 271 small square areas, 200 m wide. The total area of the aquifer was 10.84 km2. The time increment was equal to 1 month. Finally, the comparison of the two different optimization algorithms took place, concerning the pumping rates, the managed head distribution and the optimum pumping cost.