Probabilistic analytical target cascading: A moment matching formulation for multilevel optimization under uncertainty

Huibin Liu, Wei Chen, Michael Kokkolaras, Panos Y. Papalambros, Harrison M. Kim

Research output: Contribution to journalArticlepeer-review


Analytical target cascading (ATC) is a methodology for hierarchical multilevel system design optimization. In previous work, the deterministic ATC formulation was extended to account for random variables represented by expected values to be matched among subproblems and thus ensure design consistency. In this work, the probabilistic formulation is augmented to allow the introduction and matching of additional probabilistic characteristics. A particular probabilistic analytical target cascading (PATC) formulation is proposed that matches the first two moments of interrelated responses and linking variables. Several implementation issues are addressed, including representation of probabilistic design targets, matching responses and linking variables under uncertainty, and coordination strategies. Analytical and simulation-based optimal design examples are used to illustrate the new formulation. The accuracy of the proposed PATC formulation is demonstrated by comparing PATC results to those obtained using a probabilistic all-in-one formulation.

Original languageEnglish (US)
Pages (from-to)991-1000
Number of pages10
JournalJournal of Mechanical Design
Issue number4
StatePublished - Jul 2006


  • Analytical target cascading
  • Coordination strategy
  • Design targets and consistency
  • Hierarchical multilevel optimization
  • Moments
  • Probabilistic approach
  • Uncertainty

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


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