Generalized Embedded Landscape and Its Decomposed Representation
In this paper, embedded landscapes are extended to a non-binary discrete domain. Generalized embedded landscapes (GEL) are a class of additive decomposable problems where the representation can be expressed as a simple sum of subfunctions over subsets of the representation domain. The paper proposes a Generalized Embedding Theorem that reveals the close relationship between the underlying structure and the Walsh coefficients. Theoretical inductions show that the Walsh coefficients of any GEL with bounded difficulty can be calculated with a polynomial number of function evaluations. A deterministic algorithm is proposed to construct the decomposed representation of GEL. It offers an efficient way to detect the decomposable structure of the search space.
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