Structural and Multidisciplinary Optimization

, Volume 46, Issue 2, pp 239–259

A modified NBI and NC method for the solution of N-multiobjective optimization problems


    • Department of Civil EngineeringUFPE
  • Silvana M. B. Afonso
    • Department of Civil EngineeringUFPE
  • Paulo R. M. Lyra
    • Department of Mechanical EngineeringUFPE
Research Paper

DOI: 10.1007/s00158-011-0729-5

Cite this article as:
de S. Motta, R., Afonso, S.M.B. & Lyra, P.R.M. Struct Multidisc Optim (2012) 46: 239. doi:10.1007/s00158-011-0729-5


Multiobjective optimization (MO) techniques allow a designer to model a specific problem considering a more realistic behavior, which commonly involves the satisfaction of several targets simultaneously. A fundamental concept, which is adopted in the multicriteria optimization task, is that of Pareto optimality. In this paper we test several well-known procedures to deal with multiobjective optimization problems (MOP) and propose a novel modified procedure that when applied to the existing Normal Boundary Intersection (NBI) method and Normal Constraint (NC) method for more than two objectives overcomes some of their deficiencies. For the three and four objective applications analyzed here, the proposed scheme presents the best performance both in terms of quality and efficiency to obtain a set of proper Pareto points, when compared to the analyzed existing approaches.


Multiobjective optimizationMultidimensional Pareto frontierNBI methodNC method

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© Springer-Verlag 2011