Abstract
We develop new Markov chain Monte Carlo samplers for neighborhood generation in global optimization algorithms based on Hit-and-Run. The success of Hit-and-Run as a sampler on continuous domains motivated Discrete Hit-and-Run with random biwalk for discrete domains. However, the potential for efficiencies in the implementation, which requires a randomization at each move to create the biwalk, lead us to a different approach that uses fixed patterns in generating the biwalks. We define Sphere and Box Biwalks that are pattern-based and easily implemented for discrete and mixed continuous/discrete domains. The pattern-based Hit-and-Run Markov chains preserve the convergence properties of Hit-and-Run to a target distribution. They also converge to continuous Hit-and-Run as the mesh of the discretized variables becomes finer, approaching a continuum. Moreover, we provide bounds on the finite time performance for the discrete cases of Sphere and Box Biwalks. We embed our samplers in an Improving Hit-and-Run global optimization algorithm and test their performance on a number of global optimization test problems.
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This work has been funded in part by NSF grant DMI-0244286, DMI-0244291, and CMMI-0908317.
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Mete, H.O., Shen, Y., Zabinsky, Z.B. et al. Pattern discrete and mixed Hit-and-Run for global optimization. J Glob Optim 50, 597–627 (2011). https://doi.org/10.1007/s10898-010-9534-8
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DOI: https://doi.org/10.1007/s10898-010-9534-8
Keywords
- Global optimization
- Simulated annealing
- Markov chain Monte Carlo sampling
- Stochastic optimization
- Adaptive search algorithms
- Improving Hit-and-Run