Arbitrary elementary landscapes &amp; AR(1) processes

Dimova, B.; Barnes, J. Wesley; Popova, Elmira

doi:10.1016/j.aml.2004.09.006

Cited by 10 publications

(5 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Stadler [6] showed that if T is symmetric-regular, then L is elementary if and only if a univariate time series generated from a random walk on L is consistent with an autoregressive process of order 1, i.e., an AR(1) process. Dimova et al [3] showed that all elementary landscapes are consistent with an AR(1) process.…”

Section: The Characteristic Landscape Equation For Ar(2) Processmentioning

confidence: 92%

See 1 more Smart Citation

The characteristic landscape equation for an AR(2) landscape

Dimova

Barnes

Popova

2006

Applied Mathematics Letters

Self Cite

View full text Add to dashboard Cite

Grover's equation [L.K. Grover, Local search and the local structure of some NP-complete problems, Operations Research Letters 12 (1992)] and, equivalently, the Laplacian equation [J.W. Barnes, S. Dokov, B. Dimova, A. Solomon, A theory of elementary landscapes, Applied Mathematics Letters 16 (2003)] define an elementary landscape which has favorable properties for direct search methods. Dimova et al. [B. Dimova, J.W. Barnes, E. Popova, Arbitrary elementary landscapes & AR(1) processes, Applied Mathematics Letters (in press)] prove that the autocorrelation function associated with an arbitrary elementary landscape is consistent with an AR(1) time series. In this work, we develop the characteristic landscape equation for AR(2) consistent landscapes and show that they also possess favorable properties for direct search methods.

show abstract

Section: The Characteristic Landscape Equation For Ar(2) Processmentioning

confidence: 92%

“…Weinberger [7] defines the sample autocorrelation function of a time series, [ f αi ], of length n generated by a random walk on L. Dimova et al [3] show that the matrix form of the theoretical autocorrelation function for any L is…”

Section: Proposition 1 If the Time Series Based On A Random Walk On mentioning

confidence: 99%

The characteristic landscape equation for an AR(2) landscape

Dimova

Barnes

Popova

2006

Applied Mathematics Letters

Self Cite

View full text Add to dashboard Cite

show abstract

“…Stadler [13] showed that a landscape (with a symmetric neighborhood operator) is elementary if and only the time series generated by a random walk on the landscape using transitions defined by the neighborhood operator is an AR(1) process: an observation that was later generalized by Dimova et al [7]. This observation, along with Grover's results about local extrema lying above or below the mean solution value, imply that elementary landscapes describe a class of relatively smooth and structured problems.…”

Section: Plateaus and Local Optimamentioning

confidence: 99%

Understanding elementary landscapes

Whitley

Sutton

Howe

2008

Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation

View full text Add to dashboard Cite

The landscape formalism unites a finite candidate solution set to a neighborhood topology and an objective function. This construct can be used to model the behavior of local search on combinatorial optimization problems. A landscape is elementary when it possesses a unique property that results in a relative smoothness and decomposability to its structure.In this paper we explain elementary landscapes in terms of the expected value of solution components which are transformed in the process of moving from an incumbent solution to a neighboring solution. We introduce new results about the properties of elementary landscapes and discuss the practical implications for search algorithms.

show abstract

“…Dimova et al [4] proved that fitness autocorrelation for a random walk on an elementary landscapes falls exponentially. Since the autocorrelation of all the components of parity fall monotonically, the correlation of parity itself must also fall monotonically with distance.…”

Section: Walsh Analysis Of Fitness Autocorrelationmentioning

confidence: 99%

“…Therefore, when using Equation 4, we have to use a version of the Laplacian which includes the half of the search space which (starting from the origin) was previously inaccessible. E.g.…”

Section: Construction Of 3-bit Flip Laplacianmentioning

confidence: 99%

Elementary bit string mutation landscapes

Langdon

2011

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

View full text Add to dashboard Cite

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.

show abstract

Arbitrary elementary landscapes & AR(1) processes

Cited by 10 publications

References 5 publications

The characteristic landscape equation for an AR(2) landscape

The characteristic landscape equation for an AR(2) landscape

Understanding elementary landscapes

Elementary bit string mutation landscapes

Contact Info

Product

Resources

About