Solving multi-objective inverse problems of chained manufacturing processes

J.G. Hoffer*, B.C. Geiger, R. Kern

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This research presents an approach that combines stacked Gaussian processes (stacked GP) with target vector Bayesian optimization (BO) to solve multi-objective inverse problems of chained manufacturing processes. In this context, GP surrogate models represent individual manufacturing processes and are stacked to build a unified surrogate model that represents the entire manufacturing process chain. Using stacked GPs, epistemic uncertainty can be propagated through all chained manufacturing processes. To perform target vector BO, acquisition functions make use of a noncentral χ-squared distribution of the squared Euclidean distance between a given target vector and surrogate model output. In BO of chained processes, there are the options to use a single unified surrogate model that represents the entire joint chain, or that there is a surrogate model for each individual process and the optimization is cascaded from the last to the first process. Literature suggests that a joint optimization approach using stacked GPs overestimates uncertainty, whereas a cascaded approach underestimates it. For improved target vector BO results of chained processes, we present an approach that combines methods which under- or overestimate uncertainties in an ensemble for rank aggregation. We present a thorough analysis of the proposed methods and evaluate on two artificial use cases and on a typical manufacturing process chain: preforming and final pressing of an Inconel 625 superalloy billet.

Original languageEnglish
Pages (from-to)213-231
Number of pages19
JournalCIRP Journal of Manufacturing Science and Technology
Publication statusPublished - Feb 2023


  • Bayesian optimization
  • Gaussian process regression
  • Manufacturing
  • Multi-objective optimization
  • Process optimization

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering

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