%0 Journal Article %1 Zhou:2008:GPEM %A Zhou, Shude %A Heckendorn, Robert B. %A Sun, Zengqi %D 2008 %J Genetic Programming and Evolvable Machines %K Epistasis, Fourier Generalised Linkage Problem algorithms, detection, embedded genetic landscape, structure transform, %N 2 %P 125--155 %R doi:10.1007/s10710-007-9045-7 %T Detecting the epistatic structure of generalized embedded landscape %V 9 %X Working under the premise that most optimisable functions are of bounded epistasis, this paper addresses the problem of discovering the linkage structure of a black-box function with a domain of arbitrary-cardinality under the assumption of bounded epistasis. To model functions of bounded epistasis, we develop a generalisation of the mathematical model of embedded landscapes over domains of cardinality M. We then generalise the Walsh transform as a discrete Fourier transform, and develop algorithms for linkage learning of epistatically bounded GELs. We propose Generalised Embedding Theorem that models the relationship between the underlying decomposable structure of GEL and its Fourier coefficients. We give a deterministic algorithm to exactly calculate the Fourier coefficients of GEL with bounded epistasis. Complexity analysis shows that the epistatic structure of epistatically bounded GEL can be obtained after a polynomial number of function evaluations. Finally, an example experiment of the algorithm is presented.

@article{Zhou:2008:GPEM, abstract = {Working under the premise that most optimisable functions are of bounded epistasis, this paper addresses the problem of discovering the linkage structure of a black-box function with a domain of arbitrary-cardinality under the assumption of bounded epistasis. To model functions of bounded epistasis, we develop a generalisation of the mathematical model of embedded landscapes over domains of cardinality M. We then generalise the Walsh transform as a discrete Fourier transform, and develop algorithms for linkage learning of epistatically bounded GELs. We propose Generalised Embedding Theorem that models the relationship between the underlying decomposable structure of GEL and its Fourier coefficients. We give a deterministic algorithm to exactly calculate the Fourier coefficients of GEL with bounded epistasis. Complexity analysis shows that the epistatic structure of epistatically bounded GEL can be obtained after a polynomial number of function evaluations. Finally, an example experiment of the algorithm is presented.}, added-at = {2008-06-19T17:46:40.000+0200}, author = {Zhou, Shude and Heckendorn, Robert B. and Sun, Zengqi}, biburl = {https://www.bibsonomy.org/bibtex/2f1a8d5fd7ebbed44ad2a370c7aa443b3/brazovayeye}, doi = {doi:10.1007/s10710-007-9045-7}, interhash = {cf74e6dfe07e7d98486473ffacf93b12}, intrahash = {f1a8d5fd7ebbed44ad2a370c7aa443b3}, issn = {1389-2576}, journal = {Genetic Programming and Evolvable Machines}, keywords = {Epistasis, Fourier Generalised Linkage Problem algorithms, detection, embedded genetic landscape, structure transform,}, month = {June}, note = {Special Issue on Theoretical foundations of evolutionary computation}, number = 2, pages = {125--155}, size = {31 pages}, timestamp = {2008-06-19T17:55:52.000+0200}, title = {Detecting the epistatic structure of generalized embedded landscape}, volume = 9, year = 2008 }