research-article

Analysis of epistasis correlation on NK landscapes with nearest-neighbor interactions

Author:

Martin PelikanAuthors Info & Claims

GECCO '11: Proceedings of the 13th annual conference on Genetic and evolutionary computation

Pages 1013 - 1020

https://doi.org/10.1145/2001576.2001714

Published: 12 July 2011 Publication History

Abstract

Epistasis correlation is a measure that estimates the strength of interactions between problem variables. This paper presents an empirical study of epistasis correlation on a large number of random problem instances of NK landscapes with nearest neighbor interactions. The results are analyzed with respect to the performance of hybrid variants of two evolutionary algorithms: (1) the genetic algorithm with uniform crossover and (2) the hierarchical Bayesian optimization algorithm.

References

[1]

S. Baluja. Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Tech. Rep. No. Carnegie Mellon University-CS-94--163, Carnegie Mellon University, Pittsburgh, PA, 1994.

Digital Library

[2]

D. M. Chickering, D. Heckerman, and C. Meek. A Bayesian approach to learning Bayesian networks with local structure. Technical Report MSR-TR-97-07, Microsoft Research, Redmond, WA, 1997.

[3]

Y. Davidor. Epistasis variance: Suitability of a representation to genetic algorithms. Complex Systems, 4:369--383, 1990.

[4]

Y. Davidor. Genetic algorithms and robotics: a heuristic strategy for optimization. World Scientific Publishing, Singapore, 1991.

Digital Library

[5]

K. Deb and D. E. Goldberg. Analyzing deception in trap functions. IlliGAL Report No. 91009, University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL, 1991.

[6]

N. Friedman and M. Goldszmidt. Learning Bayesian networks with local structure. In M. I. Jordan, editor, Graphical models, pages 421--459. MIT Press, 1999.

Digital Library

[7]

N. Friedman and Z. Yakhini. On the sample complexity of learning Bayesian networks. Proc. of the Conf. on Uncertainty in Artificial Intelligence (UAI-96), pages 274--282, 1996.

Digital Library

[8]

D. E. Goldberg. Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading, MA, 1989.

Digital Library

[9]

D. E. Goldberg. The design of innovation: Lessons from and for competent genetic algorithms. Kluwer, 2002.

Digital Library

[10]

D. E. Goldberg, K. Deb, and J. H. Clark. Genetic algorithms, noise, and the sizing of populations. Complex Systems, 6:333--362, 1992.

[11]

G. R. Harik. Finding multimodal solutions using restricted tournament selection. Proc. of the Int. Conf. on Genetic Algorithms (ICGA-95), pages 24--31, 1995.

Digital Library

[12]

G. R. Harik, E. Cantú-Paz, D. E. Goldberg, and B. L. Miller. The gambler's ruin problem, genetic algorithms, and the sizing of populations. Proc. of the Int. Conf. on Evolutionary Computation (ICEC-97), pages 7--12, 1997.

[13]

G. R. Harik and D. E. Goldberg. Learning linkage. Foundations of Genetic Algorithms, 4:247--262, 1996.

[14]

J. H. Holland. Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI, 1975.

Digital Library

[15]

T. Jones and S. Forrest. Fitness distance correlation as a measure of problem difficulty for genetic algorithms. Proc. of the Int. Conf. on Genetic Algorithms (ICGA-95), pages 184--192, 1995.

Digital Library

[16]

S. Kauffman. Adaptation on rugged fitness landscapes. In D. L. Stein, editor, Lecture Notes in the Sciences of Complexity, pages 527--618. Addison Wesley, 1989.

[17]

P. Larranaga and J. A. Lozano, editors. Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer, Boston, MA, 2002.

Digital Library

[18]

J. A. Lozano, P. Larranaga, I. Inza, and E. Bengoetxea, editors. Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms. Springer, 2006.

Digital Library

[19]

M. Manela and J. A. Campbell. Harmonic analysis, epistasis and genetic algorithms. Parallel Problem Solving from Nature, pages 59--66, 1992.

[20]

H. Mühlenbein and G. Paaß. From recombination of genes to the estimation of distributions I. Binary parameters. Parallel Problem Solving from Nature, pages 178--187, 1996.

Digital Library

[21]

B. Naudts and L. Kallel. Some facts about so called GA-hardness measures. Technical Report 379, Ecole Polytechnique, CMAP, France, 1998.

[22]

B. Naudts, D. Suys, and A. Verschoren. Epistasis as a basic concept in formal landscape analysis. Proc. of the Int. Conf. on Genetic Alg. (ICGA-97), pages 65--72, 1997.

[23]

M. Pelikan. Hierarchical Bayesian optimization algorithm: Toward a new generation of evolutionary algorithms. Springer, 2005.

[24]

M. Pelikan. NK landscapes, problem difficulty, and hybrid evolutionary algorithms. Genetic and Evol. Comp. Conf. (GECCO-2010), pages 665--672, 2010.

Digital Library

[25]

M. Pelikan and D. E. Goldberg. Escaping hierarchical traps with competent genetic algorithms. Genetic and Evol. Comp. Conf. (GECCO-2001), pages 511--518, 2001.

[26]

M. Pelikan and D. E. Goldberg. A hierarchy machine: Learning to optimize from nature and humans. Complexity, 8(5):36--45, 2003.

Digital Library

[27]

M. Pelikan, D. E. Goldberg, and F. Lobo. A survey of optimization by building and using probabilistic models. Computational Optimization and Applications, 21(1):5--20, 2002.

Digital Library

[28]

M. Pelikan, K. Sastry, and E. Cantú-Paz, editors. Scalable optimization via probabilistic modeling: From algorithms to applications. Springer-Verlag, 2006.

Digital Library

[29]

M. Pelikan, K. Sastry, and D. E. Goldberg. Scalability of the Bayesian optimization algorithm. International Journal of Approximate Reasoning, 31(3):221--258, 2002.

[30]

M. Pelikan, K. Sastry, D. E. Goldberg, M. V. Butz, and M. Hauschild. Performance of evolutionary algorithms on NK landscapes with nearest neighbor interactions and tunable overlap. Genetic and Evol. Comp. Conf. (GECCO-2009), pages 851--858, 2009.

Digital Library

[31]

Y. ping Chen, T.-L. Yu, K. Sastry, and D. E. Goldberg. A survey of genetic linkage learning techniques. IlliGAL Report No. 2007014, University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL, 2007.

[32]

C. R. Reeves and C. C. Wright. Epistasis in genetic algorithms: An experimental design perspective. Proceedings of the 6th International Conference on Genetic Algorithms, pages 217--224, 1995.

Digital Library

[33]

S. Rochet, M. Slimane, and G. Venturini. Epistasis for real encoding in genetic algorithms. In Proceedings of the Australian New Zealand Conference on Intelligent Information Systems, ANZIIS 96, Adelaide, South Australia, 18--20 November 1996, pages 268--271, 1996.

[34]

S. Rochet, G. Venturini, M. Slimane, and E. M. E. Kharoubi. A critical and empirical study of epistasis measures for predicting ga performances: A summary. In Selected Papers from the Third European Conference on Artificial Evolution, AE '97, pages 275--286, London, UK, 1998. Springer-Verlag.

Digital Library

[35]

K. Sastry. Evaluation-relaxation schemes for genetic and evolutionary algorithms. Master's thesis, University of Illinois at Urbana-Champaign, Department of General Engineering, Urbana, IL, 2001.

[36]

K. Sastry, D. E. Goldberg, and M. Pelikan. Don't evaluate, inherit. Genetic and Evol. Comp. Conf. (GECCO-2001), pages 551--558, 2001.

[37]

K. Sastry, M. Pelikan, and D. E. Goldberg. Efficiency enhancement of estimation of distribution algorithms. In M. Pelikan, K. Sastry, and E. Cantú-Paz, editors, Scalable Optimization via Probabilistic Modeling: From Algorithms to Applications, pages 161--185. Springer, 2006.

[38]

G. Syswerda. Uniform crossover in genetic algorithms. Proc. of the Int. Conf. on Genetic Algorithms (ICGA-89), pages 2--9, 1989.

Digital Library

[39]

D. Thierens. Scalability problems of simple genetic algorithms. Evolutionary Computation, 7(4):331--352, 1999.

Digital Library

[40]

D. Thierens, D. E. Goldberg, and A. G. Pereira. Domino convergence, drift, and the temporal-salience structure of problems. Proc. of the Int. Conf. on Evolutionary Computation (ICEC-98), pages 535--540, 1998.

[41]

E. Weinberger. Correlated and uncorrelated fitness landscapes and how to tell the difference. Biological Cybernetics, 63(5):325--336, 1990.

Digital Library

[42]

A. H. Wright, R. K. Thompson, and J. Zhang. The computational complexity of N-K fitness functions. IEEE Trans. on Evolutionary Computation, 4(4):373--379, 2000.

Digital Library

Cited By

Martins JDelbem A(2016)Pairwise independence and its impact on Estimation of Distribution AlgorithmsSwarm and Evolutionary Computation10.1016/j.swevo.2015.10.00127(80-96)Online publication date: Apr-2016
https://doi.org/10.1016/j.swevo.2015.10.001
Li MHill SO'Riordan C(2012)Analysis of a triploid genetic algorithm over deceptive and epistatic landscapesACM SIGAPP Applied Computing Review10.1145/2387358.238736212:3(51-59)Online publication date: 1-Sep-2012
https://dl.acm.org/doi/10.1145/2387358.2387362

Index Terms

Analysis of epistasis correlation on NK landscapes with nearest-neighbor interactions

Recommendations

Adaptation of a multiagent evolutionary algorithm to NK landscapes
GECCO '13 Companion: Proceedings of the 15th annual conference companion on Genetic and evolutionary computation

Multiagent evolutionary algorithm (MEA) is a relatively new optimization technique, where a life cycle of a population of agents, which perform local search, is simulated. The algorithm was originally intended as a method for solving the graph coloring ...
NK landscapes, problem difficulty, and hybrid evolutionary algorithms
GECCO '10: Proceedings of the 12th annual conference on Genetic and evolutionary computation

This paper presents an experimental study of NK landscapes with the main focus on the relationship between (1) problem parameters, (2) various measures of problem difficulty of fitness landscapes, and (3) performance of hybrid evolutionary algorithms. ...
Maximally rugged NK landscapes contain the highest peaks
GECCO '05: Proceedings of the 7th annual conference on Genetic and evolutionary computation

NK models provide a family of tunably rugged fitness landscapes used in a wide range of evolutionary computation studies. It is well known that the average height of local optima regresses to the mean of the landscape with increasing epistasis, k. This ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

GECCO '11: Proceedings of the 13th annual conference on Genetic and evolutionary computation

July 2011

2140 pages

ISBN:9781450305570

DOI:10.1145/2001576

Editor:
Natalio Krasnogor
University of Nottingham, UK
,
General Chair:
Pier Luca Lanzi
Politecnico di Milano, Italy

Copyright © 2011 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

SIGEVO: ACM Special Interest Group on Genetic and Evolutionary Computation

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 July 2011

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

GECCO '11

Sponsor:

SIGEVO

GECCO '11: Genetic and Evolutionary Computation Conference

July 12 - 16, 2011

Dublin, Ireland

Acceptance Rates

Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
117
Total Downloads

Downloads (Last 12 months)1
Downloads (Last 6 weeks)0

Reflects downloads up to 16 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Martins JDelbem A(2016)Pairwise independence and its impact on Estimation of Distribution AlgorithmsSwarm and Evolutionary Computation10.1016/j.swevo.2015.10.00127(80-96)Online publication date: Apr-2016
https://doi.org/10.1016/j.swevo.2015.10.001
Li MHill SO'Riordan C(2012)Analysis of a triploid genetic algorithm over deceptive and epistatic landscapesACM SIGAPP Applied Computing Review10.1145/2387358.238736212:3(51-59)Online publication date: 1-Sep-2012
https://dl.acm.org/doi/10.1145/2387358.2387362

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents