Real-Parameter Black-Box Optimisation: Benchmarking and Designing Algorithms

Raymond Ros 1
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 : In continuous optimisation a given problem can be stated as follows: given the objective function f from R^n to R with n the dimension of the problem, find a suitable vector that minimises f up to an arbitrary numerical precision. In this context, the black-box scenario assumes that no information but the evaluation of f is available to guide its optimisation. In the first part, we study the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) which is a well-established stochastic approach for solving Black-Box Optimisation (BBO) problems. We show its time and space complexity limits when addressing high-dimensional BBO problems. To overcome such limits, we provide variants of the CMA-ES that update only block-diagonal elements of the covariance matrix, and exploit the separability of the problem. We show that on non-separable functions these variants can outperform the standard CMA-ES, given that the dimension of the problem is large enough. In the second part, we define and exploit an experimental framework BBO Benchmarking (BBOB) in which practitioners of BBO can test and compare algorithms on function testbeds. Results show dependencies on the budget (number of function evaluations) assigned to the optimisation of the objective function. Some methods such as NEWUOA or BFGS are more appropriate for small budgets. The CMA-ES approach using restarts and a population size management policy performs well for larger budgets. The COmparing Continuous Optimisers (COCO) software, used for the BBOB, is described technically in the third part. COCO implements our experimental framework as well as outputs the results that we have been exploiting.
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  • HAL Id : tel-00595922, version 2



Raymond Ros. Real-Parameter Black-Box Optimisation: Benchmarking and Designing Algorithms. Modeling and Simulation. Université Paris Sud - Paris XI, 2009. English. ⟨tel-00595922v2⟩



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