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Grid-Enhanced Polylithic Modeling and Solution Approaches for Hard Optimization Problems

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Modeling, Simulation and Optimization of Complex Processes HPSC 2018

Abstract

We present a grid enhancement approach (GEA) for hard mixed integer or nonlinear non-convex problems to improve and stabilize the quality of the solution if only short time is available to compute it, e.g., in operative planning or scheduling problems. Branch-and-bound algorithms and polylithic modeling & solution approaches (PMSA)—tailor-made techniques to compute primal feasible points—usually involve problem-specific control parameters \(\mathbf {p}\). Depending on data instances, different choices of \(\mathbf {p}\) may lead to variations in run time or solution quality. It is not possible to determine optimal settings of \(\mathbf {p}\) a priori. The key idea of the GEA is to exploit parallelism on the application level and to run the polylithic approach on several cores of the CPU, or on a cluster of computers in parallel for different settings of \(\mathbf {p}\). Especially scheduling problems benefit strongly from the GEA, but it is also useful for computing Pareto fronts of multi-criteria problems or computing minimal convex hulls of circles and spheres. In addition to improving the quality of the solution, the GEA helps us maintain a test suite of data instances for the real world optimization problem, to improve the best solution found so far, and to calibrate the tailor-made polylithic approach.

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Acknowledgements

The authors are indebted to the anonymous referees whose comments helped to improve this paper. We thank Dr. Michael Bussieck (GAMS GmbH, Frechen, Germany) for discussion on parallelism used in optimization, Dr. Jens Schulz & Dr. Susanne Heipcke (FICO, Berlin, Germany & Marseille, France) for hints and details on parallelization in XPRESS, and Prof. Dr. Michael Torsten Koch (ZIB Berlin, Berlin, Germany), Dr. Jens Schulz and Dr. Steffen Klosterhalfen (Mannheim, Germany) for their careful reading of and feedback on the manuscript.

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Authors and Affiliations

  1. Department of Astronomy, University of Florida, Gainesville, FL, 32611, USA

    Josef Kallrath

  2. Discrete Optimization and Logistics, Karlsruhe Institute of Technology, 76133, Karlsruhe, Germany

    Robert Blackburn

  3. Technical University of Darmstadt, 64289, Darmstadt, Germany

    Julius Näumann

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  1. Josef Kallrath
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  2. Robert Blackburn
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Correspondence to Josef Kallrath .

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Editors and Affiliations

  1. Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Heidelberg, Germany

    Hans Georg Bock

  2. Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Heidelberg, Germany

    Willi Jäger

  3. Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Heidelberg, Germany

    Ekaterina Kostina

  4. Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam

    Hoang Xuan Phu

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Kallrath, J., Blackburn, R., Näumann, J. (2021). Grid-Enhanced Polylithic Modeling and Solution Approaches for Hard Optimization Problems. In: Bock, H.G., Jäger, W., Kostina, E., Phu, H.X. (eds) Modeling, Simulation and Optimization of Complex Processes HPSC 2018. Springer, Cham. https://doi.org/10.1007/978-3-030-55240-4_4

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