Abstract
This work proposes a multi-start global optimization algorithm that uses dimensional reduction techniques based upon approximations of space-filling curves and simulated annealing, aiming to find global minima of real-valued (possibly multimodal) functions that are not necessarily well behaved, that is, are not required to be differentiable or continuous. Given a real-valued function with a multidimensional and compact domain, the method builds an equivalent, onedimensional problem by composing it with a space-filling curve (SFC), searches for a small group of candidates and returns to the original higher-dimensional domain, this time with a small set of “promising” starting points. Finally, these points serve as seeds to the algorithm known as Fuzzy Adaptive Simulated Annealing, aiming to find the global optima of the original cost functions. New SFCs are built with basis on the well-known Sierpiński SFC, a subtle modification of a theorem by Hugo Steinhaus and several results of ergodic theory.
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Keywords
- Global Optimization
- Global Optimization Algorithm
- Global Optimization Method
- Dimensional Reduction Technique
- Stochastic Global Optimization
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© 2011 Springer-Verlag Berlin Heidelberg
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e Oliveira, H.A., Petraglia, A. (2011). Global Optimization Using Space-Filling Curves and Measure-Preserving Transformations. In: Gaspar-Cunha, A., Takahashi, R., Schaefer, G., Costa, L. (eds) Soft Computing in Industrial Applications. Advances in Intelligent and Soft Computing, vol 96. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20505-7_10
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DOI: https://doi.org/10.1007/978-3-642-20505-7_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20504-0
Online ISBN: 978-3-642-20505-7
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