Extended probe method for linkage discovery over high-cardinality alphabets

Abstract

The work addresses the problem of identifying the epistatic linkage of a function from high cardinality alphabets to the real numbers. It is a generalization of Heckendorn and Wright's work that restricts problem representation into the binary-string domain. Discrete Fourier transform is used to analyze underlying structure in high-cardinality alphabets space. Boolean operators are replaced with new operators such as ⊕, , ⊗ and so on in high cardinality alphabets. The "probe" formulation is redesigned to determine epistatic properties of non-binary function. Theoretical analysis shows the close relationship between probe value and problem structure. A deterministic and a stochastic algorithm based on properties of probes are proposed to completely identify the linkage structure and rigourously compute all Fourier coefficients. Some discussion about linkage detection for continuous problems is given.

Research topics in discrete estimation of distribution algorithms based on factorizations

“…Prior information [1,56,91,96] and perturbation methods [63,121,132,133] are other ways of collecting information about the interactions.…”

Matrix interpretation of generalized embedded landscape

“…The notation used is the same as that in [2]. A generalized embedded landscape (GEL) is a function f : M L → R which can be written as…”

Inductive linkage identification on building blocks of different sizes and types

“…In addition to empirical studies Heckendorn and Wright (2004) generalised these methods through Walsh analysis to obtain theoretical resource requirements. Zhou, Sun, and Heckendorn (2007) and Zhou, Heckendorn, and Sun (2008) later extended this study from the binary domain to high-cardinality domains.…”