scholarly journals An Application of the Maximum Theorem in Multi-Criteria Optimization, Properties of Pareto-Retract Mappings, and the Structure of Pareto Sets

2012 ◽  
Vol 03 (10) ◽  
pp. 1415-1422
Author(s):  
Zdravko Dimitrov Slavov ◽  
Christina Slavova Evans
Keyword(s):  
Pareto Sets ◽  
Maximum Theorem

Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems

2010 ◽  
Vol 39 (4) ◽  
pp. 1340-1371 ◽  
Author(s):  
Ilias Diakonikolas ◽  
Mihalis Yannakakis
Keyword(s):  
Shortest Paths ◽  
Pareto Sets

scholarly journals Bergeʼs maximum theorem for noncompact image sets

2014 ◽  
Vol 413 (2) ◽  
pp. 1040-1046 ◽  
Author(s):  
Eugene A. Feinberg ◽  
Pavlo O. Kasyanov ◽  
Mark Voorneveld
Keyword(s):  
Maximum Theorem

scholarly journals Multiobjective Monotonicity Analysis: Pareto Set Dependency and Tradeoffs Causality in Configuration Design

2021 ◽  
pp. 1-18
Author(s):  
Nökkvi S. Sigurdarson ◽  
Tobias Eifler ◽  
Martin Ebro ◽  
Panos Y. Papalambros
Keyword(s):  
Oral Drug Delivery ◽  
Pareto Set ◽  
Oral Drug ◽  
Configuration Design ◽  
Analysis Process ◽  
Trade Offs ◽  
Design Changes ◽  
Pareto Sets ◽  
Multiobjective Design ◽  
Monotonicity Analysis

Abstract Multiobjective design optimization studies typically derive Pareto sets or use a scalar substitute function to capture design trade-offs, leaving it up to the designer's intuition to use this information for design refinements and decision making. Understanding the causality of trade-offs more deeply, beyond simple post-optimality parametric studies, would be particularly valuable in configuration design problems to guide configuration redesign. This paper presents the method of Multiobjective Monotonicity Analysis to identify root causes for the existence of trade-offs and the particular shape of Pareto sets. This analysis process involves reducing optimization models through constraint activity identification to a point where dependencies specific to the Pareto set and the constraints that cause them are revealed. The insights gained can then be used to target configuration design changes. We demonstrate the proposed approach in the preliminary design of a medical device for oral drug delivery

Covering Pareto Sets by Multilevel Subdivision Techniques

2005 ◽  
Vol 124 (1) ◽  
pp. 113-136 ◽  
Author(s):  
M. Dellnitz ◽  
O. Sch�tze ◽  
T. Hestermeyer
Keyword(s):  
Pareto Sets
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