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New Approximation Assisted Multi-objective collaborative Robust Optimization (new AA-McRO) under interval uncertainty

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Abstract

Existing collaborative optimization techniques with multiple coupled subsystems are predominantly focused on single-objective deterministic optimization. However, many engineering optimization problems have system and subsystems that can each be multi-objective, constrained and with uncertainty. The literature reports on a few deterministic Multi-objective Multi-Disciplinary Optimization (MMDO) techniques. However, these techniques in general require a large number of function calls and their computational cost can be exacerbated when uncertainty is present. In this paper, a new Approximation-Assisted Multi-objective collaborative Robust Optimization (New AA-McRO) under interval uncertainty is presented. This new AA-McRO approach uses a single-objective optimization problem to coordinate all system and subsystem multi-objective optimization problems in a Collaborative Optimization (CO) framework. The approach converts the consistency constraints of CO into penalty terms which are integrated into the system and subsystem objective functions. The new AA-McRO is able to explore the design space better and obtain optimum design solutions more efficiently. Also, the new AA-McRO obtains an estimate of Pareto optimum solutions for MMDO problems whose system-level objective and constraint functions are relatively insensitive (or robust) to input uncertainties. Another characteristic of the new AA-McRO is the use of online approximation for objective and constraint functions to perform system robustness evaluation and subsystem-level optimization. Based on the results obtained from a numerical and an engineering example, it is concluded that the new AA-McRO performs better than previously reported MMDO methods.

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Acknowledgments

The work presented in this paper was supported in part by The Petroleum Institute (PI), Abu Dhabi, United Arab Emirates, as part of the Education and Energy Research Collaboration (EERC) agreement between the PI and University of Maryland, College Park. The work was also supported in part by an ONR grant. Such support does not constitute an endorsement by the funding agency of the opinions expressed in the paper. A previous version of this paper was presented at the 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Fort Worth, TX (Hu et al. 2010).

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Maryland, College Park, MD, 20742, USA

    Weiwei Hu & Shapour Azarm

  2. Department of Chemical Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, UAE

    Ali Almansoori

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  1. Weiwei Hu
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  2. Shapour Azarm
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  3. Ali Almansoori
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Correspondence to Shapour Azarm.

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Hu, W., Azarm, S. & Almansoori, A. New Approximation Assisted Multi-objective collaborative Robust Optimization (new AA-McRO) under interval uncertainty. Struct Multidisc Optim 47, 19–35 (2013). https://doi.org/10.1007/s00158-012-0816-2

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  • DOI: https://doi.org/10.1007/s00158-012-0816-2

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