A simplex-like search method for bi-objective optimization

Peachey, T. C., Riley, M. J., Abramson, D. and Stewart, J. (2012). A simplex-like search method for bi-objective optimization. In: EngOpt 2012: 3rd International Conference on Engineering Optimization: Proceedings. EngOpt 2012: 3rd International Conference on Engineering Optimization, Rio de Janeiro, Brazil, (1-10). 1-5 July 2012.

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Name Description MIMEType Size Downloads
Author Peachey, T. C.
Riley, M. J.
Abramson, D.
Stewart, J.
Title of paper A simplex-like search method for bi-objective optimization
Conference name EngOpt 2012: 3rd International Conference on Engineering Optimization
Conference location Rio de Janeiro, Brazil
Conference dates 1-5 July 2012
Proceedings title EngOpt 2012: 3rd International Conference on Engineering Optimization: Proceedings
Place of Publication Rio de Janeiro, Brazil
Publisher Federal University of Rio de Janeiro
Publication Year 2012
Sub-type Fully published paper
Start page 1
End page 10
Total pages 10
Language eng
Abstract/Summary We describe a new algorithm for bi-objective optimization, similar to the Nelder Mead simplex algorithm, widely used for single objective optimization. For differentiable bi-objective functions on a continuous search space, internal Pareto optima occur where the two gradient vectors point in opposite directions. So such optima may be located by minimizing the cosine of the angle between these vectors. This requires a complex rather than than a simplex, so we term the technique the “cosine seeking complex”. An extra benefit of this approach is that a successful search identifies the direction of the efficient curve of Pareto points, expediting further searches. Results are presented for some standard test functions. The method presented is quite complicated and space considerations here preclude complete details. We hope to publish a fuller description in another place.
Keyword Multi-objective optimization
Simplex
complex
Q-Index Code E1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Proceedings via conference website: http://www.engopt.org/proceedings.html

 
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