PPSN 2010: Parallel Problem Solving from Nature, PPSN XI pp 462-471 | Cite as
Performance of Network Crossover on NK Landscapes and Spin Glasses
Conference paper
Abstract
This paper describes a network crossover operator based on knowledge gathered from either prior problem-specific knowledge or linkage learning methods such as estimation of distribution algorithms (EDAs). This operator can be used in a genetic algorithm (GA) to incorporate linkage in recombination. The performance of GA with network crossover is compared to that of GA with uniform crossover and the hierarchical Bayesian optimization algorithm (hBOA) on 2D Ising spin glasses, NK landscapes, and SK spin glasses. The results are analyzed and discussed.
Keywords
Genetic Algorithm Execution Time Problem Size Spin Glass Crossover Operator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
- 1.Goldberg, D.E.: The design of innovation: Lessons from and for competent genetic algorithms. Kluwer, Dordrecht (2002)MATHGoogle Scholar
- 2.Baluja, S.: Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Tech. Rep. No. CMU-CS-94-163, Carnegie Mellon University, Pittsburgh, PA (1994)Google Scholar
- 3.Mühlenbein, H., Paaß, G.: From recombination of genes to the estimation of distributions I. Binary parameters. Parallel Problem Solving from Nature, 178–187 (1996)Google Scholar
- 4.Larrañaga, P., Lozano, J.A. (eds.): Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer, Boston (2002)MATHGoogle Scholar
- 5.Pelikan, M., Goldberg, D.E., Lobo, F.: A survey of optimization by building and using probabilistic models. Computational Optimization and Applications 21(1), 5–20 (2002)MathSciNetMATHCrossRefGoogle Scholar
- 6.Pelikan, M., Sastry, K., Cantú-Paz, E. (eds.): Scalable optimization via probabilistic modeling: From algorithms to applications. Springer, Heidelberg (2006)MATHGoogle Scholar
- 7.Cantú-Paz, E.: Efficient and Accurate Parallel Genetic Algorithms. Kluwer, Boston (2000)MATHCrossRefGoogle Scholar
- 8.Schwarz, J., Ocenasek, J.: A problem-knowledge based evolutionary algorithm KBOA for hypergraph partitioning, Personal communication (2000)Google Scholar
- 9.Pelikan, M.: Hierarchical Bayesian optimization algorithm: Toward a new generation of evolutionary algorithms. Springer, Heidelberg (2005)MATHGoogle Scholar
- 10.Hauschild, M., Pelikan, M., Sastry, K., Goldberg, D.E.: Using previous models to bias structural learning in the hierarchical BOA. In: Genetic and Evolutionary Comp. Conf (GECCO 2008), pp. 415–422 (2008)Google Scholar
- 11.Hauschild, M.W., Pelikan, M.: Intelligent bias of network structures in the hierarchical boa, pp. 413–420. ACM, New York (2009)Google Scholar
- 12.Pelikan, M., Goldberg, D.E.: Escaping hierarchical traps with competent genetic algorithms. In: Genetic and Evolutionary Comp. Conf. (GECCO 2001), pp. 511–518 (2001)Google Scholar
- 13.Goldberg, D.E.: Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading (1989)MATHGoogle Scholar
- 14.Thierens, D.: Scalability problems of simple genetic algorithms. Evolutionary Computation 7(4), 331–352 (1999)CrossRefGoogle Scholar
- 15.Yu, T.L., Goldberg, D.E., Sastry, K., Lima, C.F., Pelikan, M.: Dependency structure matrix, genetic algorithms, and effective recombination. Evolutionary Computation 17(4), 595–626 (2009)CrossRefGoogle Scholar
- 16.Drezner, Z., Salhi, S.: Using hybrid metaheuristics for the one-day and two-way network design problem. Naval Research Logistics 49(5), 449–463 (2002)MathSciNetMATHCrossRefGoogle Scholar
- 17.Drezner, Z.: A new genetic algorithm for the quadratic assignment problem. INFORMS Journal on Computing 15(3), 320–330 (2003)MathSciNetCrossRefGoogle Scholar
- 18.Stonedahl, F., Rand, W., Wilensky, U.: CrossNet: a framework for crossover with network-based chromosomal representations. In: Genetic and Evolutionary Comp. Conf. (GECCO 2008), pp. 1057–1064. ACM, New York (2008)CrossRefGoogle Scholar
- 19.Holland, J.H.: Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor (1975)Google Scholar
- 20.Ackley, D.H.: An empirical study of bit vector function optimization. Genetic Algorithms and Simulated Annealing, 170–204 (1987)Google Scholar
- 21.Deb, K., Goldberg, D.E.: Analyzing deception in trap functions. IlliGAL Report No. 91009, University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL (1991)Google Scholar
- 22.Kauffman, S.: Adaptation on rugged fitness landscapes. In: Stein, D.L. (ed.) Lecture Notes in the Sciences of Complexity, pp. 527–618. Addison Wesley, Reading (1989)Google Scholar
- 23.Wright, A.H., Thompson, R.K., Zhang, J.: The computational complexity of n-k fitness functions. IEEE Trans. Evolutionary Computation 4(4), 373–379 (2000)CrossRefGoogle Scholar
- 24.Pelikan, M., Sastry, K., Butz, M.V., Goldberg, D.E.: Performance of evolutionary algorithms on random decomposable problems. In: PPSN, pp. 788–797 (2006)Google Scholar
- 25.Pelikan, M., Sastry, K., Goldberg, D.E., Butz, M.V., Hauschild, M.: Performance of evolutionary algorithms on NK landscapes with nearest neighbor interactions and tunable overlap. MEDAL Report No. 2009002, Missouri Estimation of Distribution Algorithms Laboratory, University of Missour–St. Louis, St. Louis, MO (2009)Google Scholar
- 26.Pelikan, M.: Analysis of estimation of distribution algorithms and genetic algorithms on NK landscapes, pp. 1033–1040 (2008)Google Scholar
- 27.Mezard, M., Parisi, G., Virasoro, M.: Spin glass theory and beyond. World Scientific, Singapore (1987)MATHGoogle Scholar
- 28.Spin Glass Ground State Server. University of Köln, Germany (2004), http://www.informatik.uni-koeln.de/ls_juenger/research/sgs/sgs.html
- 29.Kirkpatrick, S., Sherrington, D.: Infinite-ranged models of spin-glasses. Phys. Rev. B 17(11), 4384–4403 (1978)CrossRefGoogle Scholar
- 30.Katzgraber, H.G.: Spin glasses and algorithm benchmarks: A one-dimensional view. Journal of Physics: Conf. Series 95(012004) (2008)Google Scholar
- 31.Barahona, F.: On the computational complexity of Ising spin glass models. Journal of Physics A: Mathematical, Nuclear and General 15(10), 3241–3253 (1982)MathSciNetCrossRefGoogle Scholar
- 32.Hartwig, A., Daske, F., Kobe, S.: A recursive branch-and-bound algorithm for the exact ground state of Ising spin-glass models. Computer Physics Communications 32(2), 133–138 (1984)CrossRefGoogle Scholar
- 33.Pelikan, M., Katzgraber, H.G., Kobe, S.: Finding ground states of Sherrington-Kirkpatrick spin glasses with hierarchical BOA and genetic algorithms. In: Genetic and Evolutionary Comp. Conf. (GECCO 2008), pp. 447–454. ACM, New York (2008)CrossRefGoogle Scholar
- 34.Harik, G.R.: Finding multimodal solutions using restricted tournament selection. In: International Conf. on Genetic Algorithms (ICGA 1995), pp. 24–31 (1995)Google Scholar
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