Permuted Orthogonal Block-Diagonal Transformation Matrices for Large Scale Optimization Benchmarking

Ouassim Ait Elhara 1 Anne Auger 1 Nikolaus Hansen 1
1 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
Abstract : We propose a general methodology to construct large-scale testbeds for the benchmarking of continuous optimization algorithms. Our approach applies an orthogonal transformation on raw functions that involve only a linear number of operations in order to obtain large scale optimization benchmark problems. The orthogonal transformation is sampled from a parametrized family of transformations that are the product of a permutation matrix times a block-diagonal matrix times a permutation matrix. We investigate the impact of the different parameters of the transformation on its shape and on the difficulty of the problems for separable CMA-ES. We illustrate the use of the above defined transformation in the BBOB-2009 testbed as replacement for the expensive orthogonal (rotation) matrices. We also show the practicability of the approach by studying the computational cost and its applicability in a large scale setting.
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Ouassim Ait Elhara, Anne Auger, Nikolaus Hansen. Permuted Orthogonal Block-Diagonal Transformation Matrices for Large Scale Optimization Benchmarking. GECCO 2016, Jul 2016, Denver, United States. pp.189-196, ⟨10.1145/2908812.2908937⟩. ⟨hal-01308566v3⟩

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