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Gaussian Process Regression Based Multi-Objective Bayesian Optimization for Power System Design

Author

Listed:
  • Nicolai Palm

    (Systems Engineering Laboratory, University of Applied Sciences, Lothstrasse 64, 80335 München, Germany)

  • Markus Landerer

    (Systems Engineering Laboratory, University of Applied Sciences, Lothstrasse 64, 80335 München, Germany)

  • Herbert Palm

    (Systems Engineering Laboratory, University of Applied Sciences, Lothstrasse 64, 80335 München, Germany)

Abstract

Within a disruptively changing environment, design of power systems becomes a complex task. Meeting multi-criteria requirements with increasing degrees of freedom in design and simultaneously decreasing technical expertise strengthens the need for multi-objective optimization (MOO) making use of algorithms and virtual prototyping. In this context, we present Gaussian Process Regression based Multi-Objective Bayesian Optimization (GPR-MOBO) with special emphasis on its profound theoretical background. A detailed mathematical framework is provided to derive a GPR-MOBO computer implementable algorithm. We quantify GPR-MOBO effectiveness and efficiency by hypervolume and the number of required computationally expensive simulations to identify Pareto-optimal design solutions, respectively. For validation purposes, we benchmark our GPR-MOBO implementation based on a mathematical test function with analytically known Pareto front and compare results to those of well-known algorithms NSGA-II and pure Latin Hyper Cube Sampling. To rule out effects of randomness, we include statistical evaluations. GPR-MOBO turnes out as an effective and efficient approach with superior character versus state-of-the art approaches and increasing value-add when simulations are computationally expensive and the number of design degrees of freedom is high. Finally, we provide an example of GPR-MOBO based power system design and optimization that demonstrates both the methodology itself and its performance benefits.

Suggested Citation

  • Nicolai Palm & Markus Landerer & Herbert Palm, 2022. "Gaussian Process Regression Based Multi-Objective Bayesian Optimization for Power System Design," Sustainability, MDPI, vol. 14(19), pages 1-23, October.
  • Handle: RePEc:gam:jsusta:v:14:y:2022:i:19:p:12777-:d:935522
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    References listed on IDEAS

    as
    1. Kaifeng Yang & Michael Emmerich & André Deutz & Thomas Bäck, 2019. "Efficient computation of expected hypervolume improvement using box decomposition algorithms," Journal of Global Optimization, Springer, vol. 75(1), pages 3-34, September.
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