Abstract
In general, classical iterative algorithms for optimization, such as Newton-type methods, perform only local search around a given starting point. Such feature is an impediment to the direct use of these methods to global optimization problems, when good starting points are not available. To overcome this problem, in this work we equipped a Newton-type method with the topographical global initialization strategy, which was employed together with a new formula for its key parameter. The used local search algorithm is a quasi-Newton method with backtracking. In this approach, users provide initial sets, instead of starting points. Then, using points sampled in such initial sets (merely boxes in \({\mathbb {R}}^{n}\)), the topographical method selects appropriate initial guesses for global optimization tasks. Computational experiments were performed using 33 test problems available in literature. Comparisons against three specialized methods (DIRECT, MCS and GLODS) have shown that the present methodology is a powerful tool for unconstrained global optimization.
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Acknowledgements
N.H. and W.F.S. gratefully acknowledge the financial support provided by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, Ministry of Science & Technology, Brazil). M.deS.R. and J.I. were supported by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brazil). The research by N.H. has been carried out in the framework of project PROCIENCIA-UERJ financed by FAPERJ.
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Henderson, N., de Sá Rêgo, M., Imbiriba, J. et al. Testing the topographical global initialization strategy in the framework of an unconstrained optimization method. Optim Lett 12, 727–741 (2018). https://doi.org/10.1007/s11590-017-1137-6
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DOI: https://doi.org/10.1007/s11590-017-1137-6