Quality-time analysis of multi-objective evolutionary algorithms
Pages 1455 - 1462
Abstract
A quality-time analysis of multi-objective evolutionary algorithms (MOEAs) based on schema theorem and building blocks hypothesis is developed. A bicriteria OneMax problem, a hypothesis of niche and species, and a definition of dissimilar schemata are introduced for the analysis. In this paper, the convergence time, the first and last hitting time models are constructed for analyzing the performance of MOEAs. Population sizing model is constructed for determining appropriate population sizes. The models are verified using the bicriteria OneMax problem. The theoretical results indicate how the convergence time and population size of a MOEA scale up with the problem size, the dissimilarity of Pareto-optimal solutions, and the number of Pareto-optimal solutions of a multi-objective optimization problem.
References
[1]
T. Bàck, D. B. Fogel, and Z. Michalewics. Handbook of evolutionary computation. Institute of Physics Publishing, 1998.]]
[2]
T. Blickle and L. Thiele. A mathematical analysis of tournament selection. Proceedings of the Six International Conference on Genetic Algorithms, pages 9--16, 1995.]]
[3]
C. A. Coello Coello, D. A. Van Veldhuizen, and G. B. Lamont. Evolutionary algorithms for solving multi-objective problems. Genetic algorithms and evolutionary computation ; 5. Kluwer Academic, New York, 2002.]]
[4]
K. Deb. Multi-objective optimization using evolutionary algorithms. Wiley-Interscience series in systems and optimization. John Wiley & Sons, 2001.]]
[5]
K. Deb and D. E. Goldberg. An investigation of niche and species formation in genetic function optimization. Proceedings of the Third International Conference on Genetic Algorithms, pages 42--50, 1989.]]
[6]
D. E. Goldberg. Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Pub. Co., 1989.]]
[7]
D. E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Publishing Co., Reading, MA, January 1989. ISBN: 0-201-15767-5.]]
[8]
D. E. Goldberg. The Design of Innovation: Lessons from and for Competent Genetic Algorithms, volume 7 of Genetic Algorithms and Evoluationary Computation. Kluwer Academic Publishers, June 2002. ISBN: 1-4020-7098-5.]]
[9]
D. E. Goldberg and K. Deb. A comparative analysis of selection schemes used in genetic algorithms. Foundations of Genetic Algorithms, 1:69--93, 1991.]]
[10]
D. E. Goldberg and G. Liepens. Theory tutorial, 1991. (Tutorial presented at the 1991 International Conference on Genetic Algorithms, La Jolla, CA).]]
[11]
G. Harik, E. Cantú-Paz, D. E. Goldberg, and B. L. Miller. The gambler's ruin problem, genetic algorithms, and the sizing of populations. Proceedings of the 1997 IEEE International Conference on Evolutionary Computation, pages 7--12, 1997.]]
[12]
S.-Y. Ho and X.-I. Chang. An efficient generalized multiobjective evolutionary algorithm. In Proceedings of the Genetic and Evolutionary Computation Conference 1999: Volume 1, pages 871--878. Morgan Kaufmann Publishers, 1999.]]
[13]
S.-Y. Ho, L.-S. Shu, and J.-H. Chen. Intelligent evolutionary algorithms for large parameter optimization problems. IEEE Transaction on Evolutionary Computation, 8(6):522--541, December 2004.]]
[14]
J. H. Holland. Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI, 1975. ISBN: 0-262-58111-6.]]
[15]
H. Ishibuchi and Y. Shibata. Mating scheme for controlling the diversity-convergence balance for multiobjective optimization. In Proceeding of Genetic and Evolutionary Computation - GECCO 2004, Part I, volume 3102 of Lecture Notes in Computer Science, pages 1259--1271. Springer, 2004.]]
[16]
K. KrishnaKumar, S. Narayanaswamy, and S. Garg. Solving large parameter optimization problems using a genetic algorithm with stochastic coding. Genetic Algorithms in Engineering and Computer Science, 1995. G. Winter, J. Periaux, M. Galán, P. Cuesta (Eds), John Wiley & Sons.]]
[17]
M. Laumanns, L. Thiele, and E. Zitzler. Running time analysis of multiobjective evolutionary algorithms on pseudo-boolean functions. IEEE Transactions on Evolutionary Computation, 8(2):170--182, April 2004.]]
[18]
B. L. Miller. Noise, sampling, and efficient genetic algorithms. doctoral dissertation, University of Illinois at Urbana-Champaign, Urbana, 1997.]]
[19]
B. L. Miller. Noise, Sampling, and Efficient Genetic Algorithms. PhD thesis, University of Illinois at Urbana-Champaign, Urbana, IL, May 1997.]]
[20]
B. L. Miller and D. E. Goldberg. Genetic algorithms, selection schemes, and the varying effects of noise. Evolutionary Computation, 4(2):113--131, 1996.]]
[21]
H. Mühlenbein and D. Schlierkamp-Voosen. Predictive models for the breeder genetic algorithm: I. Continuous parameter optimization. Evolutionary Computation, 1(1):25--49, 1993.]]
Index Terms
- Quality-time analysis of multi-objective evolutionary algorithms
Recommendations
Theoretical analyses of multi-objective evolutionary algorithms on multi-modal objectives: (hot-off-the-press track at GECCO 2021)
GECCO '21: Proceedings of the Genetic and Evolutionary Computation Conference CompanionPrevious theory work on multi-objective evolutionary algorithms considers mostly easy problems that are composed of unimodal objectives. This paper takes a first step towards a deeper understanding of how evolutionary algorithms solve multi-modal multi-...
An effective model of multiple multi-objective evolutionary algorithms with the assistance of regional multi-objective evolutionary algorithms: VIPMOEAs
Division of the evolutionary search among multiple multi-objective evolutionary algorithms (MOEAs) is a recent advantage in MOEAs design, particularly in effective parallel and distributed MOEAs. However, most these algorithms rely on such a central (re)...
An improved multi-objective population-based extremal optimization algorithm with polynomial mutation
As a recently developed evolutionary algorithm inspired by far-from-equilibrium dynamics of self-organized criticality, extremal optimization (EO) has been successfully applied to a variety of benchmark and engineering optimization problems. However, ...
Comments
Information & Contributors
Information
Published In
June 2005
2272 pages
Copyright © 2005 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]
Sponsors
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 25 June 2005
Check for updates
Author Tags
Qualifiers
- Article
Conference
Acceptance Rates
Overall Acceptance Rate 1,669 of 4,410 submissions, 38%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 332Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 25 Dec 2024
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in