An algorithm for solving the system-level problem in multilevel optimization

A multilevel optimization approachwhich is applicableto nonhierarchiccoupledsystems is presented.The approachincludesa generaltreatment of design(or behavior) constraints and coupling constraints at the discipline level through the useof norms. Three different types of normsareexamined-themax norm, the Kreisselmeier-Steinhauser (KS) norm, and the lp norm. The max norm is recommended.The approachis demonstratedon a classof hub frame structures which simulatemultidisciplinary systems.The max norm is shownto producesystem-levelconstraint functions which arenon-smooth. A cutting-plane algorithm is presentedwhich adequatelydealswith the resulting cornersin the constraint functions. The algorithm is testedon hub frameswith increasingnumberof members(which simulate disciplines), and the resultsare summarized. *Thisresearch wassupportedbytheNational Aeronautics andSpaceAdministration underNASAContract No. NASl-19480 while the first author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001.

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