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

Nikolaus Hansen (1, 2)

1 TAO - Machine Learning and Optimisation
2 MSR - INRIA - Microsoft Research - Inria Joint Centre

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.

Domaines: Apprentissage [cs.LG]

Nikolaus Hansen. Benchmarking the Nelder-Mead Downhill Simplex Algorithm With Many Local Restarts. ACM-GECCO Genetic and Evolutionary Computation Conference, Jul 2009, Montreal, Canada. ⟨inria-00382104⟩