Abstract
This paper looks at proofs concerning Gray codes and the locality of local search; it is shown that in some cases such proofs can be generalized to Binary and real valued encodings, while in other cases such proofs do not hold for Binary encodings. The paper also looks at a modified form of Quad Search that is proven to converge in under 2L evaluations to a global optimum on unimodal 1-D bijective functions and to a local optimum on multimodal 1-D bijective functions. Quad Search directly exploits the locality of the Gray code representation.
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Whitley, D., Rowe, J.E. (2005). Gray, Binary and Real Valued Encodings: Quad Search and Locality Proofs. In: Wright, A.H., Vose, M.D., De Jong, K.A., Schmitt, L.M. (eds) Foundations of Genetic Algorithms. FOGA 2005. Lecture Notes in Computer Science, vol 3469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11513575_2
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DOI: https://doi.org/10.1007/11513575_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27237-3
Online ISBN: 978-3-540-32035-7
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