Optimization by ℓ1-Constrained Markov Fitness Modelling

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 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 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.