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On the Pareto optimum sensitivity analysis in multicriteria optimization
Author(s) -
Zhang W. H.
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.890
Subject(s) - pareto principle , sensitivity (control systems) , mathematical optimization , pareto interpolation , differentiable function , constraint (computer aided design) , tangent , multi objective optimization , mathematics , set (abstract data type) , projection (relational algebra) , pareto analysis , computer science , algorithm , engineering , geometry , mathematical analysis , statistics , generalized pareto distribution , extreme value theory , electronic engineering , programming language
To analyse the trade‐off relations among the set of criteria in multicriteria optimization, Pareto optimum sensitivity analysis is systematically studied in this paper. Original contributions cover two parts: theoretical demonstrations are firstly made to validate the gradient projection method in Pareto optimum sensitivity analysis. It is shown that the projected gradient direction evaluated at a given Pareto optimum in the design variable space rigorously corresponds to the tangent direction of the Pareto curve/surface at that point in the objective space. This statement holds even for the change of the set of active constraints in the perturbed problem. Secondly, a new active constraint updating strategy is proposed, which permits the identification of the active constraint set change, to determine the influence of this change upon the differentiability of the Pareto curve and finally to compute directional derivatives in non‐differentiable cases. This work will highlight some basic issues in multicriteria optimization. Some numerical problems are solved to illustrate these novelties. Copyright © 2003 John Wiley & Sons, Ltd.