Posterior exploration based sequential Monte Carlo for global optimization

Abstract

We propose a global optimization algorithm based on the Sequential Monte Carlo (SMC) sampling framework. In this framework, the objective function is normalized to be a probabilistic density function (pdf), based on which a sequence of annealed target pdfs is designed to asymptotically converge on the set of global optima. A sequential importance sampling (SIS) procedure is performed to simulate the resulting targets, and the maxima of the objective function is assessed from the yielded samples. The disturbing issue lies in the design of the importance sampling (IS) pdf, which crucially influences the IS efficiency. We propose an approach to design the IS pdf online by embedding a posterior exploration (PE) procedure into each iteration of the SMC framework. The PE procedure can also explore the important regions of the parameter space supported by the target pdf. A byproduct of the PE procedure is an adaptive mechanism to design the annealing temperature schedule online. We compare the performance of the proposed algorithm with those of several existing related alternatives by applying them to over a dozen standard benchmark functions. The result demonstrates the appealing properties of our algorithm.