Pattern discrete and mixed Hit-and-Run for global optimization

  • Authors:

  • Huseyin Onur Mete;Yanfang Shen;Zelda B. Zabinsky;Seksan Kiatsupaibul;Robert L. Smith

  • Affiliations:

  • Industrial and Systems Engineering, University of Washington, Seattle, USA 98195-2650;Citigroup Alternative Investments, New York, USA 10022;Industrial and Systems Engineering, University of Washington, Seattle, USA 98195-2650;Faculty of Commerce and Accountancy, Chulalongkorn University, Bangkok, Thailand 10330;Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, USA 48109-2117

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2011

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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.