A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies

Igel, Christian; Suttorp, Thorsten; Hansen, Nikolaus

doi:10.1145/1143997.1144082

Cited by 147 publications

(116 citation statements)

References 16 publications

(21 reference statements)

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“…The restart variant of CMA-ES with iteratively increasing population size (IPOP-CMA-ES) [7] can be considered a parameter-free CMA-ES. The (1+1)-variant of CMA-ES establishes a direct link to GaA by combining the classical (1+1)-ES with a rank-one update of the covariance matrix [8]. In the next subsection, we show that Gaussian Adaptation has been designed in a similar spirit, yet grounding its theoretical justification on a different foundation.…”

Section: Evolution Strategies With Covariance Matrix Adaptationmentioning

confidence: 97%

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Gaussian Adaptation Revisited – An Entropic View on Covariance Matrix Adaptation

Müller

Sbalzarini

2010

Applications of Evolutionary Computation

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We revisit Gaussian Adaptation (GaA), a black-box optimizer for discrete and continuous problems that has been developed in the late 1960's. This largely neglected search heuristic shares several interesting features with the well-known Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and with Simulated Annealing (SA). GaA samples single candidate solutions from a multivariate normal distribution and continuously adapts its first and second moments (mean and covariance) such as to maximize the entropy of the search distribution. Sample-point selection is controlled by a monotonically decreasing acceptance threshold, reminiscent of the cooling schedule in SA. We describe the theoret-

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Section: Evolution Strategies With Covariance Matrix Adaptationmentioning

confidence: 97%

“…For N C → ∞, the covariance stays completely isotropic and GaA becomes equivalent to the (1+1)-ES with a P th -success rule. Keeping N C finite results in an algorithm that is almost equivalent to the (1+1)-CMA-ES [8]. Slight differences, however, remain in deciding when to update the covariance and how to adapt the step size.…”

Section: Gaussian Adaptationmentioning

confidence: 99%

Gaussian Adaptation Revisited – An Entropic View on Covariance Matrix Adaptation

Müller

Sbalzarini

2010

Applications of Evolutionary Computation

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“…The last 3SOME variant we propose in this paper replaces the middle distance exploration with the (1+1)-CMA-ES algorithm presented in [6]. The latter algorithm combines a classic (1+1)-ES scheme with an improved Covariance Matrix Adaptation mechanism [3], where an incremental update of the covariance matrix Cholesky factors is performed instead of computing the Cholesky decomposition.…”

Section: Some With 1+1 Covariance Matrix Adaptation Evolution Strmentioning

confidence: 99%

“…Other relevant algorithms based on the CMA have been proposed in literature, e.g. [4], [5], and [6].…”

mentioning

confidence: 99%

Three variants of three Stage Optimal Memetic Exploration for handling non-separable fitness landscapes

Caraffini

Iacca²,

Neri

et al. 2012

2012 12th UK Workshop on Computational Intelligence (UKCI)

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Abstract-Three Stage Optimal Memetic Exploration (3SOME) is a recently proposed algorithmic framework which sequentially perturbs a single solution by means of three operators. Although 3SOME proved to be extremely successful at handling high-dimensional multi-modal landscapes, its application to non-separable fitness functions present some flaws. This paper proposes three possible variants of the original 3SOME algorithm aimed at improving its performance on non-separable problems. The first variant replaces one of the 3SOME operators, namely the middle distance exploration, with a rotation-invariant Differential Evolution (DE) mutation scheme , which is applied on three solutions sampled in a progressively shrinking search space. In the second proposed mechanism, a micro-population rotation-invariant DE is integrated within the algorithmic framework. The third approach employs the search logic (1+1)-Covariance Matrix Adaptation Evolution Strategy, aka (1+1)-CMA-ES. In the latter scheme, a Covariance Matrix adapts to the landscape during the optimization in order to determine the most promising search directions. Numerical results show that, at the cost of a higher complexity, the three approaches proposed are able to improve upon 3SOME performance for non-separable problems without an excessive performance deterioration in the other problems.

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“…For N C → ∞, the covariance remains isotropic and GaA becomes equivalent to the (1+1)-ES with a P th -success rule. Keeping N C finite results in an algorithm that is almost equivalent to the (1+1)-CMA-ES [12]. Four key differences, however, remain.…”

Section: ) Strategy Parameters Of Gaamentioning

confidence: 99%

Gaussian Adaptation as a unifying framework for continuous black-box optimization and adaptive Monte Carlo sampling

Müller

Sbalzarini

2010

IEEE Congress on Evolutionary Computation

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We present a unifying framework for continuous optimization and sampling. This framework is based on Gaussian Adaptation (GaA), a search heuristic developed in the late 1960's. It is a maximumentropy method that shares several features with the (1+1)-variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The algorithm samples single candidate solutions from a multivariate normal distribution and continuously adapts the first and second moments. We present modifications that turn the algorithm into both a robust continuous black-box optimizer and, alternatively, an adaptive Random Walk Monte Carlo sampler. In black-box optimization, sample-point selection is controlled by a monotonically decreasing, fitness-dependent acceptance threshold. We provide general strategy parameter settings, stopping criteria, and restart mechanisms that render GaA quasi parameter free. We also introduce Metropolis GaA (M-GaA), where sample-point selection is based on the Metropolis acceptance criterion. This turns GaA into a Monte Carlo sampler that is conceptually similar to the seminal Adaptive Proposal (AP) algorithm. We evaluate the performance of Restart GaA on the CEC 2005 benchmark suite. Moreover, we compare the efficacy of M-GaA to that of the Metropolis-Hastings and AP algorithms on selected target distributions.

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A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies

Cited by 147 publications

References 16 publications

Gaussian Adaptation Revisited – An Entropic View on Covariance Matrix Adaptation

Gaussian Adaptation Revisited – An Entropic View on Covariance Matrix Adaptation

Three variants of three Stage Optimal Memetic Exploration for handling non-separable fitness landscapes

Gaussian Adaptation as a unifying framework for continuous black-box optimization and adaptive Monte Carlo sampling

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