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Posterior exploration based sequential Monte Carlo for global optimization

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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 optimum. A sequential importance sampling procedure is performed to simulate the resulting targets and the maxima of the objective function are 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 by embedding a posterior exploration (PE) procedure into each iteration of the SMC framework. The PE procedure can explore the important regions of the solution space supported by the target pdf. A byproduct of the PE procedure is an adaptive mechanism to design the annealing temperature schedule. We compare the proposed algorithm with related existing methods using a dozen benchmark functions. The result demonstrates the appealing properties of our algorithm.

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Acknowledgements

This work was partly supported by the National Natural Science Foundation (NSF) of China (No. 61571238), the China Postdoctoral Science Foundation (Nos. 2015M580455 and 2016T90483) and Scientific and Technological Support Project (Society) of Jiangsu Province (No. BE2016776).

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Authors and Affiliations

  1. School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Bin Liu

  2. Jiangsu Key Laboratory of Big Data Security & Intelligent Processing, Nanjing University of Posts and Telecommunications, Nanjing, 210023, Jiangsu, China

    Bin Liu

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  1. Bin Liu
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Correspondence to Bin Liu.

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Liu, B. Posterior exploration based sequential Monte Carlo for global optimization. J Glob Optim 69, 847–868 (2017). https://doi.org/10.1007/s10898-017-0543-8

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  • DOI: https://doi.org/10.1007/s10898-017-0543-8

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