Population model-based optimization with sequential Monte Carlo

Model-based optimization algorithms are effective for solving optimization problems with little structure. The algorithms iteratively find candidate solutions by generating samples from a parameterized probabilistic model on the solution space. In order to better capture the multi-modality of the objective function than the traditional model-based methods which use only a single model, we propose a framework of using a population of models with an adaptive mechanism to propagate the population over iterations. The adaptive mechanism is derived from estimating the optimal parameter of the probabilistic model in a Bayesian manner, and thus provides a proper way to determine the diversity in the population of the models. We develop two practical algorithms under this framework by applying sequential Monte Carlo methods, provide some theoretical justification on the convergence of the proposed methods, and carry out numerical experiments to illustrate their performance.