Some additional properties of elementary landscapes

Dimova, B.; Barnes, J. Wesley; Popova, Elmira; Colletti, Bruce W.

doi:10.1016/j.aml.2008.03.016

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Bound On Maximum Fitness1

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Cited by 4 publications

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“…4] prove a global upper bound f ≤ f + maxd/λ for the whole search space. Where max is the largest change in fitness for any single step in the landscape [5,23]. (Remember d is the number of possible moves and λ is ∆'s eigenvalue.)…”

Section: Bound On Maximum Fitnessmentioning

confidence: 99%

Elementary bit string mutation landscapes

Langdon

2011

Proceedings of the 11th Workshop Proceedings on Foundations of Genetic Algorithms

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Genetic Programming parity with only XOR is not elementary. GP parity can be represented as the sum of k/2 + 1 elementary landscapes. Statistics, including fitness distance correlation (FDC), of Parity's fitness landscape are calculated. Using Walsh analysis the eigen values and eigenvectors of the Laplacian of the two bit, three bit, n-bit and mutation only Genetic Algorithm fitness landscapes are given. Indeed all elementary bit string landscapes are related to the discrete Fourier functions. However most are rough (λ/d ≈ 1). Also in many cases fitness autocorrelation falls rapidly with distance. GA runs support eigenvalue/graph degree (λ/d) as a measure of the ruggedness of elementary landscapes for predicting problem difficulty. The elementary needle in a haystack (NIH) landscape is described.

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Section: Bound On Maximum Fitnessmentioning

confidence: 99%