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Decomposition-based Inner- and Outer-Refinement Algorithms for Global Optimization

Abstract

Traditional deterministic global optimization methods are often based on a Branch-and-Bound (BB) search tree, which may grow rapidly, preventing the method to find a good solution. Motivated by decomposition-based inner approximation (column generation) methods for solving transport scheduling problems with over 100 million variables, we present a new deterministic decomposition-based successive approximation method for general modular and/or sparse MINLPs. The new method, called Decomposition-based Inner- and Outer-Refinement, is based on a block-separable reformulation of the model into sub-models. It generates inner- and outer-approximations using column generation, which are successively refined by solving many easier MINLP and MIP subproblems in parallel (using BB), instead of searching over one (global) BB search tree. We present preliminary numerical results with Decogo (Decomposition-based Global Optimizer), a new parallel decomposition MINLP solver implemented in Python and Pyomo.

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Correspondence to Ivo Nowak.

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This work has been funded by Grant TIN2015-66688-C2-2-R from the Spanish Ministry in part financed by the European Regional Development Fund (ERDF). We are grateful to the anonymous referees for their encouragement and many remarks and to Stefan Vigerske for the MINLPlib results.

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Nowak, I., Breitfeld, N., Hendrix, E.M.T. et al. Decomposition-based Inner- and Outer-Refinement Algorithms for Global Optimization. J Glob Optim 72, 305–321 (2018). https://doi.org/10.1007/s10898-018-0633-2

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  • DOI: https://doi.org/10.1007/s10898-018-0633-2

Keywords

  • Global optimization
  • Decomposition method
  • MINLP
  • Successive approximation
  • Column generation