article

Embedded landscapes

Author:

Robert B. HeckendornAuthors Info & Claims

Evolutionary Computation, Volume 10, Issue 4

Pages 345 - 369

https://doi.org/10.1162/106365602760972758

Published: 01 December 2002 Publication History

Abstract

In this paper we introduce embedded landscapes as an extension of NK landscapes and MAXSAT problems. This extension is valid for problems where the representation can be expressed as a simple sum of subfunctions over subsets of the representation domain. This encompasses many additive constraint problems and problems expressed as the interaction of subcomponents, where the critical features of the subcomponents are represented by subsets of bits in the domain. We show that embedded landscapes of fixed maximum epistasis K are exponentially sparse in epistatic space with respect to all possible functions. We show we can compute many important statistical features of these functions in polynomial time including all the epistatic interactions and the statistical moments of hyperplanes about the function mean and hyperplane mean. We also show that embedded landscapes of even small fixed K can be NP-complete. We can conclude that knowing the epistasis and many of the hyperplane statistics is not enough to solve the exponentially difficult part of these general problems and that the difficulty of the problem lies not in the epistasis itself but in the interaction of the epistatic parts.

References

[1]

Altenberg, L. (1994). Evolving better representations through selective genome growth. In Proceedings of the IEEE World Congress on Computational Intelligence, pages 182-187, IEEE Press, Piscataway, New Jersey.

[2]

Altenberg, L. (1996). Nk fitness landscapes. In Bäck, T., Fogel, D., and Michalewicz, Z., editors, The Handbook of Evolutionary Computation, Oxford University Press, Oxford, UK.

[3]

Bethke, A. D. (1981). Genetic Algorithms as Function Optimizers. Ph.D. thesis, Department of Computer and Communication Sciences, University of Michigan, Ann Arbor, Michigan.

Digital Library

[4]

Cormen, T. H., Leiserson, C. E., and Rivest, R. L. (1990). Introduction to Algorithms. McGraw-Hill, New York, New York.

Digital Library

[5]

Goldberg, D. (1989a). Genetic algorithms and walsh functions: Part i, a gentle introduction. Complex Systems, 3:129-152.

[6]

Goldberg, D. (1989b). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading, Massachusetts.

Digital Library

[7]

Heckendorn, R. B. and Whitley, D. (1997). A walsh analysis of nk-landscapes. In Bäck, T., editor, Proceedings of the Seventh International Conference on Genetic Algorithms, pages 41-48, Morgan Kaufmann, San Francisco, California.

[8]

Heckendorn, R. B. and Whitley, D. (1999). Predicting epistasis from mathematical models. Evolutionary Computation, 7(1):69-101.

Digital Library

[9]

Heckendorn, R. B., Rana, S., and Whitley, D. (1999a). Polynomial time summary statistics for a generalization of maxsat. In Banzhaf, W. et al., editors, Proceedings of the Genetic and Evolutionary Computation Conference, volume 1, pages 281-288, Morgan Kaufmann, San Francisco, California.

[10]

Heckendorn, R. B., Rana, S., and Whitley, D. (1999b). Test function generators as embedded landscapes. In Bäck, T. and Banzhaf, W., editors, Foundations of Genetic Algorithms - 5, pages 183-198, Morgan Kaufmann, San Francisco, California.

[11]

Heckendorn, R. B., Whitley, L. D., and Rana, S. (1997). Nonlinearity, hyperplane ranking and the simple genetic algorithm. In Belew, R. K. and Vose, M., editors, Foundations of Genetic Algorithms - 4, pages 181-202, Morgan Kaufmann, San Francisco, California.

Digital Library

[12]

Hogg, T., Huberman, B. A., and Williams, C. P. (1996). Special issue sat problems. Artificial Intelligence, 81(1-2).

Digital Library

[13]

Holland, J. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, Michigan.

Digital Library

[14]

Jones, T. (1995a). Evolutionary Algorithms, Fitness Landscapes and Search. Ph.D. thesis, University of New Mexico, Albuquerque, New Mexico.

[15]

Jones, T. (1995b). One operator, one landscape. Technical Report SFI TR 95-02-025, Santa Fe Institute, Santa Fe, New Mexico.

[16]

De Jong, K. A., Potter, M. A., and Spears, W. M. (1997). Using problem generators to explore the effects of epistasis. In Bäck, T., editor, Proceedings of the Seventh International Conference on Genetic Algorithms, pages 338-339, Morgan Kaufmann, San Francisco, California.

[17]

Kargupta, H. and Park, B. H. (1999). Fast construction of distributed and decomposed evolutionary representation. In Brave, S. and Wu, A. S., editors, Late Breaking Papers at the 1999 Genetic and Evolutionary Computation Conference, pages 139-148, Morgan Kaufmann, San Francisco, California.

[18]

Kauffman, S. A. (1993). The Origins of Order. Oxford University Press, Oxford, UK.

[19]

Kauffman, S. A. (1995). At Home in the Universe. Oxford University Press, Oxford, UK.

[20]

Mendenhall, W. (1967). Introduction to Probability and Statistics. Second Edition. Wadsworth Publishing, Belmont, California.

Digital Library

[21]

Niven, I. (1965). Mathematics of Choice. Mathematical Association of America, Washington, DC.

[22]

Papadimitriou, C. H. (1994). Computational Complexity. Addison-Wesley, Reading, Massachusetts.

[23]

Reeves, C. and Wright, C. (1995). An experimental design perspective on genetic algorithms. In Whitley, D. and Vose, M., editors, Foundations of Genetic Algorithms - 3, pages 7-22, Morgan Kaufmann, San Francisco, California.

Digital Library

[24]

Solé R. and Goodman, B. (2000). Signs of Life: How Complexity Pervades Biology. Basic Books, New York, New York.

[25]

Weinberger, E. (1990). Correlated and uncorrelated fitness landscapes and how to tell the difference. Biological Cybernetics, 63:325-226.

Digital Library

[26]

Weinberger, E. (1996). Np completeness of kauffman's n-k model, a tuneably rugged fitness landscape, www. santafe. edu/sfi/publications/Working-Papers/96-02-003 .ps.

[27]

Whitley, D., Mathias, K., and Pyeatt, L. (1995). Hyperplane ranking in simple genetic algorithms. In Eshelman, L. J., editor, Proceedings of the Sixth International Conference on Genetic Algorithms, pages 231-238, Morgan Kaufmann, San Francisco, California.

Digital Library

Cited By

Tinós RPrzewozniczek MWhitley DChicano F(2024)Iterated Local Search with Linkage LearningACM Transactions on Evolutionary Learning and Optimization10.1145/36511654:2(1-29)Online publication date: 2-Mar-2024
https://dl.acm.org/doi/10.1145/3651165
Tulczyjew LPrzewozniczek MTinós RWijata ANalepa JLi XHandl J(2024)CANNIBAL Unveils the Hidden Gems: Hyperspectral Band Selection via Clustering of Weighted Variable Interaction GraphsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654203(412-421)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654203
Przewozniczek MTinós RKomarnicki MSilva SPaquete L(2023)First Improvement Hill Climber with Linkage Learning -- on Introducing Dark Gray-Box Optimization into Statistical Linkage Learning Genetic AlgorithmsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590495(946-954)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1145/3583131.3590495
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Index Terms

Embedded landscapes
1. Computing methodologies
  1. Artificial intelligence
    1. Search methodologies
      1. Heuristic function construction
2. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness
  2. Design and analysis of algorithms

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cover image Evolutionary Computation

Evolutionary Computation Volume 10, Issue 4

December 2002

104 pages

ISSN:1063-6560

EISSN:1530-9304

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MIT Press

Cambridge, MA, United States

Publication History

Published: 01 December 2002

Published in EVOL Volume 10, Issue 4

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Cited By

Tinós RPrzewozniczek MWhitley DChicano F(2024)Iterated Local Search with Linkage LearningACM Transactions on Evolutionary Learning and Optimization10.1145/36511654:2(1-29)Online publication date: 2-Mar-2024
https://dl.acm.org/doi/10.1145/3651165
Tulczyjew LPrzewozniczek MTinós RWijata ANalepa JLi XHandl J(2024)CANNIBAL Unveils the Hidden Gems: Hyperspectral Band Selection via Clustering of Weighted Variable Interaction GraphsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654203(412-421)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654203
Przewozniczek MTinós RKomarnicki MSilva SPaquete L(2023)First Improvement Hill Climber with Linkage Learning -- on Introducing Dark Gray-Box Optimization into Statistical Linkage Learning Genetic AlgorithmsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590495(946-954)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1145/3583131.3590495
Tinós RPrzewozniczek MWhitley DChicano FSilva SPaquete L(2023)Genetic Algorithm with Linkage LearningProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590349(981-989)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1145/3583131.3590349
Przewozniczek MTinós RFrej BKomarnicki MWagner M(2022)On turning black - into dark gray-optimization with the direct empirical linkage discovery and partition crossoverProceedings of the Genetic and Evolutionary Computation Conference10.1145/3512290.3528734(269-277)Online publication date: 8-Jul-2022
https://dl.acm.org/doi/10.1145/3512290.3528734
Tinós RPrzewozniczek MWhitley DWagner M(2022)Iterated local search with perturbation based on variables interaction for pseudo-boolean optimizationProceedings of the Genetic and Evolutionary Computation Conference10.1145/3512290.3528716(296-304)Online publication date: 8-Jul-2022
https://dl.acm.org/doi/10.1145/3512290.3528716
Dushatskiy AAlderliesten TBosman P(2021)A Novel Approach to Designing Surrogate-assisted Genetic Algorithms by Combining Efficient Learning of Walsh Coefficients and DependenciesACM Transactions on Evolutionary Learning and Optimization10.1145/34531411:2(1-23)Online publication date: 29-Jul-2021
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Alghamdi THeckendorn R(2021)An Evolutionary Computation Based Model for Testing Transfer Learning Strategies2021 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC45853.2021.9504888(1380-1389)Online publication date: 28-Jun-2021
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Leprêtre FVerel SFonlupt CMarion VAuger AStützle T(2019)Walsh functions as surrogate model for pseudo-boolean optimization problemsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3321707.3321800(303-311)Online publication date: 13-Jul-2019
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Whitley LChicano FGoldman B(2016)Gray box optimization for mk landscapes nk landscapes and max-ksatEvolutionary Computation10.1162/EVCO_a_0018424:3(491-519)Online publication date: 1-Sep-2016
https://dl.acm.org/doi/10.1162/EVCO_a_00184
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