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Optimization by ℓ 1-constrained Markov fitness modelling

par Valentini, Gabriele ;Malagò, Luigi;Matteucci, Matteo
Référence Lecture notes in computer science, 7219 LNCS, page (250-264)
Publication Publié, 2012

Article révisé par les pairs

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Résumé :

When the function to be optimized is characterized by a limited and unknown number of interactions among variables, a context that applies to many real world scenario, it is possible to design optimization algorithms based on such information. Estimation of Distribution Algorithms learn a set of interactions from a sample of points and encode them in a probabilistic model. The latter is then used to sample new instances. In this paper, we propose a novel approach to estimate the Markov Fitness Model used in DEUM. We combine model selection and model fitting by solving an ℓ 1-constrained linear regression problem. Since candidate interactions grow exponentially in the size of the problem, we first reduce this set with a preliminary coarse selection criteria based on Mutual Information. Then, we employ ℓ 1-regularization to further enforce sparsity in the model, estimating its parameters at the same time. Our proposal is analyzed against the 3D Ising Spin Glass function, a problem known to be NP-hard, and it outperforms other popular black-box meta-heuristics. © 2012 Springer-Verlag.