Detecting the epistatic structure of generalized embedded landscape

Zhou, Shude; Heckendorn, Robert B.; Sun, Zengqi

doi:10.1007/s10710-007-9045-7

Cited by 4 publications

(5 citation statements)

References 24 publications

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“…The behavior of these algorithms for other decomposable problems has been also studied from the perspective of ADFs [46,148]. Linkage identification methods have been analyzed using ADFs [19,24,128,165,190].…”

Section: Class Of Problemsmentioning

confidence: 99%

“…First and foremost, by model-building EAs, which create a representation of the relationships among the variables of the problem and use this representation to conduct a more efficient sampling of the search space. These algorithms have undergone rapid development in recent years [8,45,70,151,190,191]. Significant research has been conducted in the field of estimation of distribution algorithms (EDAs) [70,106] to better exploit information about the problem structure while solving the optimization problem.…”

Section: Introductionmentioning

confidence: 99%

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Gray-box optimization and factorized distribution algorithms: where two worlds collide

Santana

2017

Preprint

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The concept of gray-box optimization, in juxtaposition to black-box optimization, revolves about the idea of exploiting the problem structure to implement more efficient evolutionary algorithms (EAs). Work on factorized distribution algorithms (FDAs), whose factorizations are directly derived from the problem structure, has also contributed to show how exploiting the problem structure produces important gains in the efficiency of EAs. In this paper we analyze the general question of using problem structure in EAs focusing on confronting work done in gray-box optimization with related research accomplished in FDAs. This contrasted analysis helps us to identify, in current studies on the use problem structure in EAs, two distinct analytical characterizations of how these algorithms work. Moreover, we claim that these two characterizations collide and compete at the time of providing a coherent framework to investigate this type of algorithms. To illustrate this claim, we present a contrasted analysis of formalisms, questions, and results produced in FDAs and gray-box optimization. Common underlying principles in the two approaches, which are usually overlooked, are identified and discussed. Besides, an extensive review of previous research related to different uses of the problem structure in EAs is presented. The paper also elaborates on some of the questions that arise when extending the use of problem structure in EAs, such as the question of evolvability, high cardinality of the variables and large definition sets, constrained and multi-objective problems, etc. Finally, emergent approaches that exploit neural models to capture the problem structure are covered.

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Section: Class Of Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gray-box optimization and factorized distribution algorithms: where two worlds collide

Santana

2017

Preprint

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

Section: Learning the Structurementioning

confidence: 99%

Research topics in discrete estimation of distribution algorithms based on factorizations

2008

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In this paper, we identify a number of topics relevant for the improvement and development of discrete estimation of distribution algorithms. Focusing on the role of probability distributions and factorizations in estimation of distribution algorithms, we present a survey of current challenges where further research must provide answers that extend the potential and applicability of these algorithms. In each case we state the research topic and elaborate on the reasons that make it relevant for estimation of distribution algorithms. In some cases current work or possible alternatives for the solution of the problem are discussed.

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“…A GEL is k-bounded epistatic if it can be written as the sum of subfunction each of whose number of variables is at most k. It has recently shown the close relationship between Fourier coefficients and the structure of k-bounded GEL [17,18]. …”

Section: Theorem 1 (Sum Of Power Of Roots Of One)mentioning

confidence: 99%

Extended probe method for linkage discovery over high-cardinality alphabets

Zhou

Sun

Heckendorn

2007

Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation

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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.

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Detecting the epistatic structure of generalized embedded landscape

Cited by 4 publications

References 24 publications

Gray-box optimization and factorized distribution algorithms: where two worlds collide

Gray-box optimization and factorized distribution algorithms: where two worlds collide

Research topics in discrete estimation of distribution algorithms based on factorizations

Extended probe method for linkage discovery over high-cardinality alphabets

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