A Generalized Multiobjective Metamodel-Based Online Optimization Method for Engine Development

Stefan Held, Arne Hildenbrand, Anatoli Herdt, Georg Wachtmeister

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


Further advancing key technologies requires the optimization of increasingly complex systems with strongly interacting parameters - like efficiency optimization in engine development for optimizing the use of energy. Systematic optimization approaches based on metamodels, so-called Metamodel-Based Design Optimization (MBDO), present one key solution to these demanding problems. Recent advanced methods either focus on Single-Objective Optimization (SoO) on local metamodels with online adaptivity or Multiobjective Optimization (MoO) on global metamodels with only limited adaptivity. In the scope of this work, a fully online adaptive ("in the loop") optimization approach, capable of both SoO and MoO, is developed which automatically approximates the global system response and determines the (Pareto) optimum. A combination of a new Design of Experiment (DoE) method for sampling points, Neural Networks as metamodel/Response Surface Model (RSM), and a Genetic Algorithm (GA) for global optimization performed on the RSM enables very high flexibility. Key features of the presented MBDO methodology are as follows: A new fully online, adaptive approach working in iterative loops combined with successive refinements of the RSM; Two novel boundary treatment approaches for handling arbitrarily complex constraints; A novel approach to automatically adapt the number of neurons of the Neural Network to the system complexity; An innovative uncertainty-based DoE method to maximize information gain for each new sample point; Comprehensive additional sampling strategies. Detailed benchmarks to popular DoE methods and MBDO approaches from the literature are conducted. The benchmarks show comparable to slightly better performance to current state-of-the-art SoO MBDO approaches with the significant benefit that a global RSM is obtained, providing valuable insight into the system behavior. Compared to state-of-the-art MoO MBDO approaches, the benchmark highlights a considerably better performance in terms of the needed number of samples (i.e., simulations or experiments), significantly fewer resources required, and high accuracy approximation of the Pareto front.

Original languageEnglish
JournalSAE Technical Papers
StatePublished - 2023
EventSAE Automotive Technical Papers, WONLYAUTO 2023 - Warrendale, United States
Duration: 1 Jan 2023 → …


  • Design of Experiment
  • Genetic Algorithm
  • Metamodel-Based Design Optimization
  • Multiobjective Optimization
  • Neural Networks
  • Online Adaptivity


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