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Abstract: . The task of finding minimal elements of a partially ordered set is a generalization of the task of finding the global minimum of a real-valued function or of finding Pareto-optimal points of a multicriteria optimization problem. It is shown that evolutionary algorithms are able to converge to the set of minimal elements in finite time with probability one, provided that the search space is finite, the time-invariant variation operator is associated with a positive transition probability... (Update)
Context of citations to this paper: More
...problem classes since theoretical results concerning EAs are unknown apparently. This situation may change by the approach initiated in [6]. Instead of developing an own theory for each problem class, it suffices to develop a theory for EAs that can cope with partially ordered...
.... order and deploy EAs with those selection methods being explicitly designed for coping with arbitrary partially ordered fitness sets (Rudolph 1998, 2001a; Rudolph and Agapie 2000) Section 2 offers a brief introduction to partially ordered sets in general and in particular to...
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8: a multi--objective evolutionary algorithm and its convergence to the pareto set - Rudolph - 1998
6: the convergence of multiobjective evolutionary algorithms (context) - Hanne - 1999
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BibTeX entry: (Update)
G. Rudolph. Evolutionary search for minimal elements in partially ordered finite sets. In Proceedings of the 7th Annual Conference on Evolutionary Programming (EP'98). Springer, Berlin and Heidelberg, 1998. http://citeseer.ist.psu.edu/rudolph98evolutionary.html More
@inproceedings{ rudolph98evolutionary,
author = "G{\"u}nter Rudolph",
title = "Evolutionary Search for Minimal Elements in Partially Ordered Finite Sets",
booktitle = "Proceedings of {theSeventhAnnual} Conference on Evolutionary Programming({EP}\enskip {VII})",
volume = "1447",
publisher = "Springer",
address = "Berlin",
editor = "V. William ``Bill'' Porto and N. Saravanan and Don Waagen and Agoston E. Eiben",
pages = "345--353",
year = "1998",
url = "citeseer.ist.psu.edu/rudolph98evolutionary.html" }
Citations (may not include all citations):191 An overview of evolutionary algorithms in multiobjective opt.. - Fonseca, Fleming - 1995
37 Convergence rates for markov chains - Rosenthal - 1995
31 Multicriterion decision making (context) - Horn - 1997
26 Global convergence of genetic algorithms: A markov chain ana.. (context) - Eiben, Aarts et al. - 1991
17 Multi--objective optimization by genetic algorithms: a revie.. (context) - Tamaki, Kita et al. - 1996
15 A markov chain analysis on simple genetic algorithms (context) - Suzuki - 1995
13 Asymptotic convergence properties of genetic algorithms and .. (context) - Fogel - 1994
13 Partially ordered sets (context) - Trotter - 1995
11 Convergence properties of canonical genetic algorithms (context) - Rudolph - 1994
7 Convergence of evolutionary algorithms in general search spa.. - Rudolph - 1996
3 Use of vector optimization in multiobjective decision making (context) - Peschel, Riedel - 1977
2 Systemanalyse und mehrkriterielle Entscheidung (context) - Ester - 1987
2 Lineare Algebra und analytische Geometrie (context) - Klingenberg, Klein - 1971
The graph only includes citing articles where the year of publication is known.
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