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Toward the Use of Pareto Performance Solutions and Pareto Robustness Solutions for Multi-Objective Robust Optimization Problems

[+] Author Affiliations
Weijun Wang, Stéphane Caro, Fouad Bennis

Institut de Recherche en Communications et Cybernétique de Nantes, Nantes, France

Oscar Brito Augusto

University of Sao Paulo, Sao Paulo, SP, Brazil

Paper No. ESDA2012-82099, pp. 541-550; 10 pages
doi:10.1115/ESDA2012-82099
From:
  • ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis
  • Volume 3: Advanced Composite Materials and Processing; Robotics; Information Management and PLM; Design Engineering
  • Nantes, France, July 2–4, 2012
  • Conference Sponsors: International
  • ISBN: 978-0-7918-4486-1
  • Copyright © 2012 by ASME

abstract

For Multi-Objective Robust Optimization Problem (MOROP), it is important to obtain design solutions that are both optimal and robust. To find these solutions, usually, the designer need to set a threshold of the variation of Performance Functions (PFs) before optimization, or add the effects of uncertainties on the original PFs to generate a new Pareto robust front. In this paper, we divide a MOROP into two Multi-Objective Optimization Problems (MOOPs). One is the original MOOP, another one is that we take the Robustness Functions (RFs), robust counterparts of the original PFs, as optimization objectives. After solving these two MOOPs separately, two sets of solutions come out, namely the Pareto Performance Solutions (PP) and the Pareto Robustness Solutions (PR). Make a further development on these two sets, we can get two types of solutions, namely the Pareto Robustness Solutions among the Pareto Performance Solutions (PR(PP)), and the Pareto Performance Solutions among the Pareto Robustness Solutions (PP(PR)). Further more, the intersection of PR(PP) and PP(PR) can represent the intersection of PR and PP well. Then the designer can choose good solutions by comparing the results of PR(PP) and PP(PR). Thanks to this method, we can find out the optimal and robust solutions without setting the threshold of the variation of PFs nor losing the initial Pareto front. Finally, an illustrative example highlights the contributions of the paper.

Copyright © 2012 by ASME

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