Surrogate-Assisted Evolutionary Algorithms

Ilya Loshchilov 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 : Evolutionary Algorithms (EAs) have received a lot of attention regarding their potential to solve complex optimization problems using problem-specific variation operators. A search directed by a population of candidate solutions is quite robust with respect to a moderate noise and multi-modality of the optimized function, in contrast to some classical optimization methods such as quasi-Newton methods. The main limitation of EAs, the large number of function evaluations required, prevents from using EAs on computationally expensive problems, where one evaluation takes much longer than 1 second. The present thesis focuses on an evolutionary algorithm, Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which has become a standard powerful tool for \textit{continuous black-box optimization}. We present several state-of-the-art algorithms, derived from CMA-ES, for solving single- and multi-objective black-box optimization problems. First, in order to deal with expensive optimization, we propose to use comparison-based surrogate (approximation) models of the optimized function, which do not exploit function values of candidate solutions, but only their quality-based ranking. The resulting self-adaptive surrogate-assisted CMA-ES represents a tight coupling of statistical machine learning and CMA-ES, where a surrogate model is build, taking advantage of the function topology given by the covariance matrix adapted by CMA-ES. This allows to preserve two key invariance properties of CMA-ES: invariance with respect to i). monotonous transformation of the function, and ii). orthogonal transformation of the search space. For multi-objective optimization we propose two mono-surrogate approaches: i). a mixed variant of One Class Support Vector Machine (SVM) for dominated points and Regression SVM for non-dominated points; ii). Ranking SVM for preference learning of candidate solutions in the multi-objective space. We further integrate these two approaches into multi-objective CMA-ES (MO-CMA-ES) and discuss aspects of surrogate-model exploitation. Second, we introduce and discuss various algorithms, developed to understand, explore and expand frontiers of the Evolutionary Computation domain, and CMA-ES in particular. We introduce linear time Adaptive Coordinate Descent method for non-linear optimization, which inherits a CMA-like procedure of adaptation of an appropriate coordinate system without losing the initial simplicity of Coordinate Descent. For multi-modal optimization we propose to adaptively select the most suitable regime of restarts of CMA-ES and introduce corresponding alternative restart strategies. For multi-objective optimization we analyze case studies, where original parent selection procedures of MO-CMA-ES are inefficient, and introduce reward-based parent selection strategies, focused on a comparative success of generated solutions.
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https://tel.archives-ouvertes.fr/tel-00823882
Contributor : Loshchilov Ilya <>
Submitted on : Saturday, May 18, 2013 - 9:47:18 PM
Last modification on : Thursday, April 5, 2018 - 12:30:12 PM
Long-term archiving on : Monday, August 19, 2013 - 5:00:59 AM

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Ilya Loshchilov. Surrogate-Assisted Evolutionary Algorithms. Optimization and Control [math.OC]. Université Paris Sud - Paris XI; Institut national de recherche en informatique et en automatique - INRIA, 2013. English. ⟨tel-00823882⟩

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