License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.04461.13
URN: urn:nbn:de:0030-drops-2346
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2005/234/
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Nakayama, Hirotaka

Multi-objective Optimization and its Engineering Applications

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04461.NakayamaHirotaka2.Other.234.pdf (0.4 MB)

Abstract

Many practical optimization problems usually have several conflicting objectives. In those multi-objective optimization, no solution optimizing all objective functions simultaneously exists in general. Instead, Pareto optimal solutions, which are ``efficient" in terms of all objective functions, are introduced. In general we have many Pareto optimal solutions. Therefore, we need to decide a final solution among Pareto optimal solutions taking into account the balance among objective functions, which is called ``trade-off analysis". It is no exaggeration to say that the most important task in multi-objective optimization is trade-off analysis. Consequently, the methodology should be discussed in view of how it is easy and understandable for trade-off analysis.

In cases with two or three objective functions, the set of Pareto optimal solutions in the objective function space (i.e., Pareto frontier) can be depicted relatively easily. Seeing Pareto frontiers, we can grasp the trade-off relation among objectives totally. Therefore, it would be the best way to depict Pareto frontiers in cases with two or three objectives. (It might be difficult to read the trade-off relation among objectives with three dimension, though). In cases with more than three objectives, however, it is impossible to depict Pareto forntier. Under this circumstance, interactive methods can help us to make local trade-off analysis showing a ``certain" Pareto optimal solution. A number of methods differing in which Pareto optimal solution is to be shown, have been developed. This paper discusses critical issues among those methods for multi-objective optimization, in particular applied to engineering design problems.

BibTeX - Entry

@InProceedings{nakayama:DagSemProc.04461.13,
  author =	{Nakayama, Hirotaka},
  title =	{{Multi-objective Optimization and its Engineering Applications}},
  booktitle =	{Practical Approaches to Multi-Objective Optimization},
  pages =	{1--13},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4461},
  editor =	{J\"{u}rgen Branke and Kalyanmoy Deb and Kaisa Miettinen and Ralph E. Steuer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2005/234},
  URN =		{urn:nbn:de:0030-drops-2346},
  doi =		{10.4230/DagSemProc.04461.13},
  annote =	{Keywords: Multi-Objective Optimization, Interactive Multi-Objective Optimization, Evolutionary Algorithms, Pareto Frontier}
}

Keywords: Multi-Objective Optimization, Interactive Multi-Objective Optimization, Evolutionary Algorithms, Pareto Frontier
Collection: 04461 - Practical Approaches to Multi-Objective Optimization
Issue Date: 2005
Date of publication: 10.08.2005

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