Fourier and Taylor series on fitness landscapes

Weinberger, Ed

doi:10.1007/bf00216965

Cited by 78 publications

(57 citation statements)

References 6 publications

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“…Fitness values (randomly assigned) are shown in parentheses. Reproduced from (Hordijk, 1996) Weinberger (1990a1991a) proposed a fitness landscape model in which the landscape is represented as a graph on which the vertices correspond to individuals and have associated fitness values, and traversing the edge of the graph corresponds to the action of a genetic operator (mutation, crossover etc.) and so taking a step on the landscape.…”

Section: Evolving Goal-scoring Behaviour For Robot Soccermentioning

confidence: 99%

Analysing the Difficulty of Learning Goal-Scoring Behaviour for Robot Soccer

Riley¹,

Ciesielski²

2007

Robotic Soccer

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Section: Evolving Goal-scoring Behaviour For Robot Soccermentioning

confidence: 99%

Analysing the Difficulty of Learning Goal-Scoring Behaviour for Robot Soccer

Riley¹,

Ciesielski²

2007

Robotic Soccer

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“…While the standard basis and the Walsh basis ψ are orthonormal, this is not necessarily the case in general. In [16], for instance, the Taylor series of a landscape on the Boolean hypercube is introduced in terms of the polynomials τ I (i) = i∈Ix i , such that f (i) = If (I)τ I (i). Let us write i ⊂ I ifx i = x i = 1 for all elements of I.…”

Section: Coordinate Transformationsmentioning

confidence: 99%

“…Thus, we can write the Taylor series expansion in the form f = Υf , i.e.,f = Υ −1 f . The matrix Υ is invertible [16] but is neither normalized nor orthogonal. i.e.…”

Section: Coordinate Transformationsmentioning

confidence: 99%

EC Theory: A Unified Viewpoint

Stephens

Zamora

2003

Genetic and Evolutionary Computation — GECCO 2003

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Abstract. In this paper we show how recent theoretical developments have led to a more unified framework for understanding different branches of Evolutionary Computation (EC), as well as distinct theoretical formulations, such as the Schema theorem and the Vose model.In particular, we show how transformations of the configuration space of the model -such as coarse-grainings/projections, embeddings and coordinate transformations -link these different, disparate elements and alter the standard taxonomic classification of EC and different EC theories. As an illustration we emphasize one particular coordinate transformation between the standard string basis and the "Building Block" basis.

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“…Nevertheless, also in this case, for fixed-length strings, there exists a preferred basis within which crossover looks simplest -the Building Block basis (BBB) [16,2]. The BBB is dual to the Taylor basis, as studied in [24], and has already been found useful in concrete calculations [6], as well as being interestingly related to geometric quantities in the theory of information [21]. In this basis the natural effective degrees of freedom are schemata, the Building Blocks of a particular string.…”

Section: Introductionmentioning

confidence: 99%