A simplex-like search method for bi-objective optimization

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

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Item Type:Conference or Workshop contribution (Paper)
Item Status:Live Archive


We describe a new algorithm for bi-objective optimization, similar to the Nelder Mead simplex
algorithm, widely used for single objective optimization. For diferentiable 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 a simplex, so we term the technique the \cosine
seeking complex". An extra beneft of this approach is that a successful search identifes the direction
of the effcient 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.

Keywords:Multi-objective optimization, Simplex, Complex
Subjects:G Mathematical and Computer Sciences > G140 Numerical Analysis
G Mathematical and Computer Sciences > G160 Engineering/Industrial Mathematics
Divisions:College of Science > School of Engineering
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ID Code:12079
Deposited On:07 Oct 2013 07:56

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