Time dependent global optimization via Bayesian inference and Sequential Monte Carlo sampling

In many areas of application it is important to estimate unknown model parameters in order to model precisely the underlying dynamics of a physical system. In recent years, Sequential Monte Carlo (SMC) methods have become a very popular tool for Bayesian parameter estimation. In this case, the problem of finding the best parameters configuration comes to the optimization issue which is to determine the best fit. In this paper, the application of this approach to the classical global optimization problem is described. We consider the situation when optimized functions are dynamical i.e. the global extremum is changing in time. For this purpose, we adapt two dimensional Ackley and four-dimensional Wood functions. Our aim is to find the most probable localization of the extremum in each time with the use of the Bayesian approach joined with the Markov Chain Monte Carlo (MCMC) and SMC algorithms. We propose a mechanism for dynamic tuning of the proposal distribution in SMC. The approach is based on the Metropolis-Hastings algorithm, combined with a resampling mechanism to achieve better results. We have examined different version of the proposed SMC and MCMC algorithms in terms of effectiveness to estimate the probabilistic distributions. The effect is demonstrated using two benchmark optimization problems. Computed results show that the proposed mechanisms can significantly improve optimization results compared to standard MCMC.