Structural and Multidisciplinary Optimization

, Volume 46, Issue 2, pp 239–259 | Cite as

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

  • Renato de S. Motta
  • Silvana M. B. Afonso
  • Paulo R. M. Lyra
Research Paper


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 optimization Multidimensional Pareto frontier NBI method NC method 



The authors acknowledges the financial support given by the Brazilian research agency CNPq and Pernambuco state research agency FACEPE to the execution of the present work.

The authors acknowledges too, all the reviewers, which comments help to improve the current paper. It was particularly important to our knowledge the suggestion, during the second round of revision, of the paper Mueller-Gritschneider et al. (2009) in which a similar methodology to the one presented here was proposed.


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Renato de S. Motta
    • 1
  • Silvana M. B. Afonso
    • 1
  • Paulo R. M. Lyra
    • 2
  1. 1.Department of Civil EngineeringUFPERecifeBrazil
  2. 2.Department of Mechanical EngineeringUFPECidade UniversitáriaBrazil

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