Adaptive evolutionary Monte Carlo algorithm for optimization with applications to sensor placement problems

Abstract

In this paper, we present an adaptive evolutionary Monte Carlo algorithm (AEMC), which combines a treebased predictive model with an evolutionary Monte Carlo sampling procedure for the purpose of global optimization. Our development is motivated by sensor placement applications in engineering, which requires optimizing certain complicated "black-box" objective function. The proposed method is able to enhance the optimization efficiency and effectiveness as compared to a few alternative strategies. AEMC falls into the category of adaptive Markov chain Monte Carlo (MCMC) algorithms and is the first adaptive MCMC algorithm that simulates multiple Markov chains in parallel. A theorem about the ergodicity property of the AEMC algorithm is stated and proven. We demonstrate the advantages of the proposed method by applying it to a sensor placement problem in a manufacturing process, as well as to a standard Griewank test function.

Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter

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“…where B > 0 is the 'bananicity' constant. distribution was (28). The VBAM state space model was the random walk model (27) with A = I, H = I and Q = 10 −9 I.…”

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“…A state space model is employed to study the variation propagation, and the optimal solution is derived based on the analytical form of system reliability [66]. Wang et al [38] proposed a statistical analyses of the Fisher information matrix and the prediction matrix using the Powell's direct search to obtain an optimal sensor locations for an automated coordinate checking fixture.…”

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