Investigation of global optimum seeking methods in water resources problems

A. Efstratiadis, Investigation of global optimum seeking methods in water resources problems, MSc thesis, 139 pages, Department of Water Resources, Hydraulic and Maritime Engineering – National Technical University of Athens, Athens, May 2001.



The methods for determining the global optimum of nonlinear functions without constraints are investigated. Initially, the global optimisation problem is posed, which was first remedied using classical analytical mathematics and subsequently using deterministic numerical techniques. In the next chapter, a detailed literature review of modern approaches for the global optimisation problem is done. Next, an original optimisation scheme, named evolutionary annealing-simplex algorithm, is presented, which was developed within the framework of this thesis. This algorithm incorporates in an efficient manner the principles of simulated annealing into the well-known downhill simplex method, applying some heuristic strategies in order to escape from local optima. The following two chapters are referred to the evaluation of the major global optimisation methodologies on the basis of theoretical as well as real-world problems, taken from the water resources field. Through the analysis it was proved that the shuffled complex evolution, which is a recent and well-established method, as well as the evolutionary annealing-simplex algorithm, had the best performance, both in terms of accuracy in locating the global optimum and convergence speed. The thesis concludes with a summary of most important points and a list of some proposals for further improvement of the evolutionary annealing-simplex algorithm.

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Our works that reference this work:

1. E. Rozos, A. Efstratiadis, I. Nalbantis, and D. Koutsoyiannis, Calibration of a semi-distributed model for conjunctive simulation of surface and groundwater flows, Hydrological Sciences Journal, 49 (5), 819–842, doi:10.1623/hysj.49.5.819.55130, 2004.
2. A. Efstratiadis, Y. Dialynas, S. Kozanis, and D. Koutsoyiannis, A multivariate stochastic model for the generation of synthetic time series at multiple time scales reproducing long-term persistence, Environmental Modelling and Software, 62, 139–152, doi:10.1016/j.envsoft.2014.08.017, 2014.

Other works that reference this work (this list might be obsolete):

1. #Hendershot, Z. V., A differential evolution algorithm for automatically discovering multiple global optima in multidimensional, discontinuous spaces, Proceedings of the 15th Midwest Artificial Intelligence and Cognitive Science Conference, 2004.
2. #Hendershot, Z. V., and F. W. Moore, MultiDE: A simple, powerful differential evolution algorithm for finding multiple global optima, Proceedings of the 7th International Florida Artificial Intelligence Research Society Conference, 2004.
3. Charizopoulos, N., A. Psilovikos, and E. Zagana, A lumped conceptual approach for modeling hydrological processes: the case of Scopia catchment area, Central Greece, Environmental Earth Sciences, 76:18, doi:10.1007/s12665-017-6967-0, 2017.

Tagged under: Optimization