Tunably Rugged Landscapes with Known Maximum and Minimum

Manukyan, Narine; Eppstein, Margaret J.; Buzas, Jeffrey S.

doi:10.48550/arxiv.1409.1143

Cited by 2 publications

(7 citation statements)

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“…, N}, where U k is a set of indices of the features in the kth term, and the length |U k | is the order of the interaction. By convention [9], it is assumed that when U k = ∅, j∈U k x j ≡ 1. Also by convention, we assume that the model is defined for binary variables represented as…”

Section: Nm-landscape 21 Definitionmentioning

confidence: 99%

“…The NM models [9] comprise the set of all general interactions models specified by Equation 1, with the following constraints:…”

Section: Nm-landscape 21 Definitionmentioning

confidence: 99%

“…One key element of the model is how the parameters of the interactions are generated. In [9], each β U k is generated from e −abs(N (0,σ)) , where N (0, σ) is a random number drawn from a Gaussian distribution with mean 0 and standard deviation σ. Increasing σ determines smaller range and increasing clumping of fitness values.…”

Section: Nm-landscape 21 Definitionmentioning

confidence: 99%

“…The following transformation [20] maps the desired representation to the one used by the mNM-landscape. Given the analysis presented in [9], it also guarantees that the Pareto set will comprise at least two points, respectively reached at (0, . .…”

Section: Multi-objective Nm-landscapesmentioning

confidence: 99%

“…Another recently introduced landscape model is the NM-landscape [9]. It can be seen as a generalization of the NK-landscape.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Computing factorized approximations of Pareto-fronts using mNM-landscapes and Boltzmann distributions

Santana,

Mendiburu,

Lozano

2015

Preprint

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NM-landscapes have been recently introduced as a class of tunable rugged models. They are a subset of the general interaction models where all the interactions are of order less or equal M . The Boltzmann distribution has been extensively applied in single-objective evolutionary algorithms to implement selection and study the theoretical properties of model-building algorithms. In this paper we propose the combination of the multi-objective NM-landscape model and the Boltzmann distribution to obtain Pareto-front approximations. We investigate the joint effect of the parameters of the NM-landscapes and the probabilistic factorizations in the shape of the Pareto front approximations.

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Section: Nm-landscape 21 Definitionmentioning

confidence: 99%

“…The NM models [9] comprise the set of all general interactions models specified by Equation 1, with the following constraints:…”

Section: Nm-landscape 21 Definitionmentioning

confidence: 99%

Section: Nm-landscape 21 Definitionmentioning

confidence: 99%

Section: Multi-objective Nm-landscapesmentioning

confidence: 99%

“…Another recently introduced landscape model is the NM-landscape [9]. It can be seen as a generalization of the NK-landscape.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Computing factorized approximations of Pareto-fronts using mNM-landscapes and Boltzmann distributions

Santana,

Mendiburu,

Lozano

2015

Preprint

View full text Add to dashboard Cite

show abstract

Analysis of adaptive walks on NK fitness landscapes with different interaction schemes

Nowak¹,

Krug²

2015

J. Stat. Mech.

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Fitness landscapes are genotype to fitness mappings commonly used in evolutionary biology and computer science which are closely related to spin glass models. In this paper, we study the NK model for fitness landscapes where the interaction scheme between genes can be explicitly defined. The focus is on how this scheme influences the overall shape of the landscape. Our main tool for the analysis are adaptive walks, an idealized dynamics by which the population moves uphill in fitness and terminates at a local fitness maximum. We use three different types of walks and investigate how their length (the number of steps required to reach a local peak) and height (the fitness at the endpoint of the walk) depend on the dimensionality and structure of the landscape. We find that the distribution of local maxima over the landscape is particularly sensitive to the choice of interaction pattern. Most quantities that we measure are simply correlated to the rank of the scheme, which is equal to the number of nonzero coefficients in the expansion of the fitness landscape in terms of Walsh functions.

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Tunably Rugged Landscapes with Known Maximum and Minimum

Cited by 2 publications

References 0 publications

Computing factorized approximations of Pareto-fronts using mNM-landscapes and Boltzmann distributions

Computing factorized approximations of Pareto-fronts using mNM-landscapes and Boltzmann distributions

Analysis of adaptive walks on NK fitness landscapes with different interaction schemes

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