ABSTRACT
This paper proposes a population-sizing model for entropy-based model building in discrete estimation of distribution algorithms. Specifically, the population size required for building an accurate model is investigated. The effect of selection pressure on population sizing is also preliminarily incorporated. The proposed model indicates that the population size required for building an accurate model scales as Θ(m log m), where m is the number of substructures of the given problem and is proportional to the problem size. Experiments are conducted to verify the derivations, and the results agree with the proposed model.
- M. Abramowitz and L. Stegun. Handbook of Mathematical Functions. Dover, New York, 1970. Google ScholarDigital Library
- C. Aporntewan and P. Chongstitvatana. Building-block identification by simultaneity matrix. Proceedings of the Genetic and Evolutionary Computation Conference, pages 1566--1567, 2003. Google ScholarDigital Library
- T. Bäck. Generalized convergence models for tournament and (λ;μ) selection. Proceedings of the Sixth International Conference on Genetic Algorithms (ICGA 1995), pages 2--8, 1995. Google ScholarDigital Library
- T. Blickle and L. Thiele. A mathematical analysis of tournament selection. Proceedings of the Sixth International Conference on Genetic Algorithms (ICGA'95), pages 9--16, 1995. Google ScholarDigital Library
- T. M. Cover and J. A. Thomas. Elements of Information Theory, pages 18--26. Wiley, New York, 1991. Google ScholarDigital Library
- R. Etxeberria and P. Larranaga. Global optimization using bayesian networks. Proceedings of the Second Symposium on Artificial Intelligence Adaptive Systems, pages 332--339, 1999.Google Scholar
- W. Feller. An Introduction to Probability Theory, volume 2. Wiley, New York, 1966.Google Scholar
- D. E. Goldberg. Simple genetic algorithms and the minimal, deceptive problem. In Genetic Algorithms and Simulated Annealing, chapter 6, pages 74--88. Pitman Publishing, London, 1987.Google Scholar
- D. E. Goldberg. Sizing populations for serial and parallel genetic algorithms. Proceedings of the Third International Conference on Genetic Algorithms, pages 70--79, 1989. Google ScholarDigital Library
- D. E. Goldberg. The design of innovation: Lessons from and for competent genetic algorithms. Kluwer Academic Publishers, Boston, MA, 2002. Google ScholarDigital Library
- D. E. Goldberg, K. Deb, and J. H. Clark. Genetic algorithms, noise, and the sizing of populations. Complex Systems, 6:333--362, 1992.Google Scholar
- D. E. Goldberg, K. Sastry, and T. Latoza. On the supply of building blocks. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), pages 336--342, 2001.Google Scholar
- G. Harik. Linkage learning via probabilistic modeling in the ecga. IlliGAL Report No. 99010, University of Illinois at Urbana-Champaign, Urbana, IL, February 1999.Google Scholar
- G. Harik, E. Cantu-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.Google ScholarCross Ref
- J. H. Holland. Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI, 1975. Google ScholarDigital Library
- M. Hutter and M. Zaffalon. Distribution of mutual information from complete and incomplete data. Computational Statistics and Data Analysis, 48(3):633--657, 2005.Google ScholarCross Ref
- P. Larranaga and J. Lozano, editors. Estimation of Distribution Algorithms. Kluwer Academic Publishers, Boston, MA, 2002.Google ScholarCross Ref
- M. Mitchell, S. Forrest, and J. H. Holland. The royal road for genetic algorithms: Fitness landscapes and GA performance. Towards a Practice of Autonomous Systems: Proceedings of the First European Conference on Artificial Life, pages 245--254, 1992.Google Scholar
- H. Muhlenbein and R. Hons. The estimation of distributions and the minimum relative entropy principle. Evolutionary Computation, 13(1):1--27, 2005. Google ScholarDigital Library
- M. Munetomo and D. E. Goldberg. Identifying linkage groups by nonlinearity/non-monotonicity detection. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-1999), 1:433--440, 1999.Google Scholar
- J. Ocenasek. Entropy--based convergence measurement in discrete estimation of distribution algorithms. In L. Jose A., L. Pedro, and I. Inaki, editors, Towards a New Evolutionary Computation: Advances in Estimation of Distribution Algorithms, pages 39--49. Springer Verlag, New Yorks, 2006.Google Scholar
- M. Pelikan, D. E. Goldberg, and E. Cantu-Paz. BOA: The Bayesian optimization algorithm. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO--1999), I:525--532, 1999.Google Scholar
- M. Pelikan, D. E. Goldberg, and E. Cantu-Paz. Bayesian optimization algorithm, population sizing, and time to convergence. Proceedings of the Genetic and Evolutionary Computation Conference, pages 275--282, 2000.Google Scholar
- M. Pelikan, K. Sastry, and E. Cantu-Paz, editors. Scalable Optimization via Probabilistic Modeling from Algorithms to Applications. Springer, Berlin, 2006. Google ScholarDigital Library
- M. Pelikan, K. Sastry, and D. E. Goldberg. Scalability of the Bayesian optimization algorithm. International Journal of Approximate Reasoning, 31(3):221--258, 2003.Google ScholarCross Ref
- C. Reeves. Using genetic algorithms with small populations. Proceedings of the Fifth International Conference on Genetic Algorithms, pages 92--99, 1993. Google ScholarDigital Library
- K. Sastry and D. E. Goldberg. On extended compact genetic algorithm. Late-Breaking Paper at the Genetic and Evolutionary Computation Conference, pages 352--359, 2000.Google Scholar
- K. Sastry and D. E. Goldberg. Designing competent mutation operators via probabilistic model building of neighborhoods. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2004), 2:114--125, 2004.Google ScholarCross Ref
- C. E. Shannon. A mathematical theory of communication. The Bell System Technical Journal, 27:379--423, 1948.Google ScholarCross Ref
- A. Wright, R. Poli, C. Stephens, W. B. Landgon, and S. Pulavarty. An estimation of distribution algorithm based on maximum entropy. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2004), pages 343--354, 2004.Google ScholarCross Ref
- T.-L. Yu and D. E. Goldberg. Conquering hierarchical difficulty by explicit chunking: Substructural chromosome compression. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2006), pages 1385--1392, 2006. Google ScholarDigital Library
- T.-L. Yu, D. E. Goldberg, A. Yassine, and Y.-p. Chen. Genetic algorithm design inspired by organizational theory: Pilot study of a dependency structure matrix driven genetic algorithm. Proceedings of Artificial Neural Networks in Engineering (ANNIE 2003), pages 327--332, 2003.Google ScholarCross Ref
Index Terms
- Population sizing for entropy-based model building in discrete estimation of distribution algorithms
Recommendations
Sub-structural niching in estimation of distribution algorithms
GECCO '05: Proceedings of the 7th annual conference on Genetic and evolutionary computationWe propose a sub-structural niching method that fully exploits the problem decomposition capability of linkage-learning methods such as the estimation distribution algorithms and concentrate on maintaining diversity at the sub-structural level. The ...
To explore or to exploit: An entropy-driven approach for evolutionary algorithms
An evolutionary algorithm is an optimization process comprising two important aspects: exploration discovers potential offspring in new search regions; and exploitation utilizes promising solutions already identified. Intelligent balance between these ...
Probabilistic model-building genetic algorithms
GECCO '07: Proceedings of the 9th annual conference companion on Genetic and evolutionary computationProbabilistic model-building algorithms (PMBGAs) replace traditional variation of genetic and evolutionary algorithms by (1) building a probabilistic model of promising solutions and (2) sampling the built model to generate new candidate solutions. ...
Comments