Benchmarking the Nelder-Mead Downhill Simplex Algorithm With Many Local Restarts

Nikolaus Hansen 1, 2
1 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : We benchmark the Nelder-Mead downhill simplex method on the noisefree BBOB-2009 testbed. A multistart strategy is applied on two levels. On a local level, at least ten restarts are conducted with a small number of iterations and reshaped simplex. On the global level independent restarts are launched until $10^5 D$ function evaluations are exceeded, for dimension $D\ge20$ ten times less. For low search space dimensions the algorithm shows very good results on many functions. It solves 24, 18, 11 and 7 of 24 functions in 2, 5, 10 and 40-D.
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Conference papers
ACM-GECCO Genetic and Evolutionary Computation Conference, Jul 2009, Montreal, Canada. 2009
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https://hal.inria.fr/inria-00382104
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Nikolaus Hansen. Benchmarking the Nelder-Mead Downhill Simplex Algorithm With Many Local Restarts. ACM-GECCO Genetic and Evolutionary Computation Conference, Jul 2009, Montreal, Canada. 2009. <inria-00382104>

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