Min–max formulation of the balance number in multiobjective global optimization

Min–max formulation of the balance number in multiobjective global optimization

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Article ID: iaor2004764
Country: United Kingdom
Volume: 44
Issue: 7
Start Page Number: 899
End Page Number: 907
Publication Date: Oct 2002
Journal: Computers & Mathematics with Applications
Authors: ,
Keywords: pareto-optimality
Abstract:

The notion of the balance number introduced by Galperin through a certain set contraction procedure for nonscalarized multiobjective global optimization is representd via a min–max operation on the data of the problem. This representation yields a different computational procedure for the calculation of the balance number and allows us to generalize the approach for problems with countably many performance criteria. Comparisons with Pareto optimality and compromise solutions are discussed and illustrated by examples. It is demonstrated that lp-norm scalarizations (1 ≤ p < ∞), do not cover the entire Pareto set.

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