Structural and Multidisciplinary Optimization

, Volume 34, Issue 4, pp 301–315 | Cite as

2D decision-making for multicriteria design optimization

Research Paper
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Abstract

The high dimensionality encountered in engineering design optimization due to large numbers of performance criteria and specifications leads to cumbersome and sometimes unachievable trade-off analyses. To facilitate those analyses and enhance decision-making and design selection, we propose to decompose the original problem by considering only pairs of criteria at a time, thereby making trade-off evaluation the simplest possible. For the final design integration, we develop a novel coordination mechanism that guarantees that the selected design is also preferred for the original problem. The solution of an overall large-scale problem is therefore reduced to solving a family of bicriteria subproblems and allows designers to effectively use decision-making in merely two dimensions for multicriteria design optimization.

Keywords

Multicriteria design optimization Interactive decision-making Decomposition Coordination Trade-off visualization Sensitivity 

Nomenclature

MOP

multiobjective problem

MOPi

i-th multiobjective subproblem

COP

coordination problem

COPi

i-th coordination problem

SEP

sensitivity problem

SEPij

j-th sensitivity problem for COP i

f

vector objective function for MOP

\(f^{i}\)

vector objective function for MOP i , COP i

g, h

vector constraint functions

x

vector of design variables

xi

vector of design variables selected in COP i

εi

vector of tolerance values in COP i

\(\lambda ^{{i \cdot }}_{{j \cdot }}\)

vector of Langragean multipliers in SEP ij

Convention

subscripts denote vector components superscripts distinguish different vectors 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesClemson UniversityClemsonUSA
  2. 2.Department of Mechanical EngineeringClemson UniversityClemsonUSA

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