Adaptive step size random search

Schumer, M.; Steiglitz, K.

doi:10.1109/tac.1968.1098903

Cited by 242 publications

(109 citation statements)

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“…Creeping random methods have been studied by Korn and Korn (1964), Rastrigin (1967), and Belcey and Karplus (1968). Schumer and Steiglitz (1968) provided additional information on adaptive step size random searches.…”

Section: Methods Of Solutionmentioning

confidence: 99%

Hybrid Computer Methods for Direct Functional Optimization

Andrews

Korn

1975

IEEE Trans. Comput.

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Section: Methods Of Solutionmentioning

confidence: 99%

Hybrid Computer Methods for Direct Functional Optimization

Andrews

Korn

1975

IEEE Trans. Comput.

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“…The λ offspring are evaluated (line 2 with B = I the identity matrix). Depending on the choice of the step-size adaptation rule, the step-size is then adapted, either by some rule similar to the one-fifth rule [13,11] (line 4), or using the Cumulative Stepsize Adaptation [6] (line 6). CMA-ES differs from standard ES on lines 2 and 7, that describe the use of the Adaptive Encoding procedure.…”

Section: Adaptive Encodingmentioning

confidence: 99%

Adaptive coordinate descent

Loshchilov

Schoenauer

Sebag

2011

Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation

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Independence from the coordinate system is one source of efficiency and robustness for the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The recently proposed Adaptive Encoding (AE) procedure generalizes CMA-ES adaptive mechanism, and can be used together with any optimization algorithm. Adaptive Encoding gradually builds a transformation of the coordinate system such that the new coordinates are as decorrelated as possible with respect to the objective function. But any optimization algorithm can then be used together with Adaptive Encoding, and this paper proposes to use one of the simplest of all, that uses a dichotomy procedure on each coordinate in turn. The resulting algorithm, termed Adaptive Coordinate Descent (ACiD), is analyzed on the Sphere function, and experimentally validated on BBOB testbench where it is shown to outperform the standard (1 + 1)-CMA-ES, and is found comparable to other state-of-the-art CMA-ES variants.

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“…The penalty argument has the defect that it may yield fictitious solutions when the problem is ill-posed. More discussion on this subject has been given by Beltrami (1970 Gurin (1966), Schumer and Steiglitz (1968), Zakharev (1969) and Hill (1969). Good survey papers on random search methods were also given by Karnopp (1963) and White (1972).…”

Section: Objectivesmentioning

confidence: 99%