Abstract
In industrial applications, several objectives are often managed simultaneously (e.g., minimizing the cost and the weight of a mechanical structure satisfying some constraints). Although lots of optimization studies deal with only one objective, this approach is often not realistic for engineering optimization. Therefore, improvements in multiobjective optimization methods are required. This paper presents the formulation of a new utopia hyperplane that improves the proposal of the original normalized normal constraint method using two approaches: a redefinition of the anchor points and an exact linear transformation between the design objectives space and the normalized space. Both approaches always produce a normalized space with equal scales that improves the even distribution of the solutions over the Pareto frontier. Examples of the method proposed are presented related with mechanical engineering and structure design including a challenging non-convex Pareto frontier.
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References
Cheng F, Li D (1999) Quality utility—a compromise programming approach to robust design. J Mech Des 121:179–187
Das I, Dennis JE (1998) Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicrieteria optimization problems. SIAM J Optim 8:631–657
Fonseca C, Fleming P (1993) Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Fifth Int Conf on Genetic Algorithms, pp 416–423
Horn J, Nafpliotis N, Goldberg D (1994) A niched Pareto genetic algorithm for multiobjective optimization. In: First IEEE Conf on Evolutionary Computation, pp 82–87
Huang HZ, Gu YK, Du X (2006) An interactive fuzzy multi-objective optimization method for engineering design. Eng Appl Artif Intell 19(5):451–460
Koski J (1985) Defectiveness of weighting methods in multicriterion optimization of structures. Commun Appl Numer Methods 1:333–337
Kurapati A, Azarm S (2000) Immune network simulation with multiobjective genetic algoritms for multidisciplinary design optimization. Eng Opt 33:245–260
Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidisc Optim 26:369–395
Martínez M, Sanchis J, Blasco X (2006) Global and well-distributed Pareto frontier by modified normalized normal constraint methods for bicriterion problems. Struct Multidisc Optim 34:197–209. doi:10.1007/s00158-006-0071-5
Mattson CA, Mullur AA, Messac A (2004) Smart Pareto filter: obtaining a minimal represesntation of multiojective design space. Eng Optimiz 26(6):721–740
Messac A (1996) Physical programming: effective optimization for computational design. AIAA J 34(1):149–158
Messac A, Ismail-Yahaya A, Mattson CA (2003) The normalized normal constraint method for generating the Pareto frontier. Struct Multidisc Optim 25:86–98
Messac A, Mattson CA (2004) Normal constraint method with guarantee of even representation of complete Pareto frontier. AIAA J 42:2101–2111
Srinivas N, Deb K (1994) Multiobjective function optimization using non-dominated sorting genetic algorithms. Evolutionary Computation 2:221–248
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Partially supported by FEDER DPI2005-07835, FEDER DPI2004-8383-C03-02 projects (MEC—Spain) and GV06/26 (Generalitat Valenciana)
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Sanchis, J., Martínez, M., Blasco, X. et al. A new perspective on multiobjective optimization by enhanced normalized normal constraint method. Struct Multidisc Optim 36, 537–546 (2008). https://doi.org/10.1007/s00158-007-0185-4
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DOI: https://doi.org/10.1007/s00158-007-0185-4