A new perspective on multiobjective optimization by enhanced normalized normal constraint method |
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Authors: | J Sanchis M Martínez X Blasco J V Salcedo |
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Affiliation: | (1) Department of Systems Engineering and Control, Polytechnic University of Valencia, Valencia, Spain |
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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.
Partially supported by FEDER DPI2005-07835, FEDER DPI2004-8383-C03-02 projects (MEC—Spain) and GV06/26 (Generalitat Valenciana) |
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Keywords: | Multiobjective optimization Pareto frontier Nonlinear optimization Engineering design |
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