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References
Barahona, F. (1982). On the computational complexity of Ising spin glass models. Journal of Physics A: Mathematical, Nuclear and General, 15 (10):3241-3253
Barahona, F., Maynard, R., Rammal, R., and Uhry, J. (1982). Morphology of ground states of a two dimensional frustration model. Journal of Physics A, 15:673
Berg, B. A. and Neuhaus, T. (1992). Multicanonical ensemble - a new approach to simulate first order phasetransition. Physical Review Letters, 68(9)
Bieche, I., Maynard, R., Rammal, R., and Uhry, J. (1980). On the ground states of the frustration model of a spin glass by a matching method of graph theory. Journal of Physics A, 13:2553
Binder, K. and Young, A. (1986). Spin-glasses: Experimental facts, theoretical concepts and open questions. Review of Modern Physics, 58:801
Chickering, D. M., Heckerman, D., and Meek, C. (1997). A Bayesian approach to learning Bayesian networks with local structure. Technical Report MSR-TR-97-07, Microsoft Research, Redmond, WA
Claiborne, J. (1990). Mathematical Preliminaries for Computer Net-working. Wiley, New York
Dayal, P., Trebst, S., Wessel, S., ürtz, D., Troyer, M., Sabhapandit, S., and Coppersmith, S. (2004). Performance limitations of flat histogram methods and optimality of Wang-Langdau sampling. Physical Review Letters, 92(9):097201
Fischer, K. and Hertz, J. (1991). Spin Glasses. Cambridge University Press, Cambridge
Fischer, S. and Wegener, I. (2004). The Ising model on the ring: Mutation versus recombination. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2004), pages 1113-1124
Friedman, N. and Goldszmidt, M. (1999). Learning Bayesian networks with local structure. In Jordan, M. I., editor, Graphical models, pages 421-459. MIT Press, Cambridge, MA
Galluccio, A. and Loebl, M. (1999a). A theory of Pfaffian orientations. I. Perfect matchings and permanents. Electronic Journal of Combinatorics, 6(1). Research Paper 6
Galluccio, A. and Loebl, M. (1999b). A theory of Pfaffian orientations. II. T-joins, k-cuts, and duality of enumeration. Electronic Journal of Combinatorics, 6(1). Research Paper 7
Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading, MA
Harik, G. R. (1995). Finding multimodal solutions using restricted tournament selection. Proceedings of the International Conference on Genetic Algorithms (ICGA-95), pages 24-31
Hartmann, A. K. (1996). Cluster-exact approximation of spin glass ground states. Physica A, 224:480
Hartmann, A. K. (2001). Ground-state clusters of two, three and fourdimensional +/-J Ising spin glasses. Physical Review E, 63:016106
Hartmann, A. K. and Rieger, H. (2001). Optimization Algorithms in Physics. Wiley-VCH, Weinheim
Hartmann, A. K. and Rieger, H., editors (2004). New Optimization Algorithms in Physics. Wiley-VCH, Weinheim
Hartmann, A. K. and Weigt, M. (2005). Phase Transitions in Combinatorial Optimization Problems. Wiley-VCH, Weinheim
Holland, J. H. (1975). Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI
Mezard, M., Parisi, G., and Virasoro, M. (1987). Spin glass theory and beyond. World Scientific, Singapore
Middleton, A. and Fisher, D. S. (2002). The three-dimensional random field Ising magnet: Interfaces, scaling, and the nature of states. Physical Review B, 65:134411
Mühlenbein, H. and Mahnig, T. (1999). Convergence theory and applications of the factorized distribution algorithm. Journal of Computing and Information Technology, 7(1):19-32
Mühlenbein, H. and Paaß, G. (1996). From recombination of genes to the estimation of distributions I. Binary parameters. Parallel Problem Solving from Nature, pages 178-187
Mühlenbein, H. and Schlierkamp-Voosen, D. (1993). Predictive models for the breeder genetic algorithm: I. Continuous parameter optimization. Evolutionary Computation, 1(1):25-49
Naudts, B. and Naudts, J. (1998). The effect of spin-flip symmetry on the performance of the simple GA. Parallel Problem Solving from Nature, pages 67-76
Newman, C. and Stein, D. (2003). Finite-dimensional spin glasses: states, excitations and interfaces. preprint cond-mat/0301022
Pelikan, M.(2005).Hierarchical Bayesian optimization algorithm: Toward a new generation of evolutionary algorithms. Springer, Berlin Heidelberg New York
Pelikan, M. and Goldberg, D. E. (2001). Escaping hierarchical traps with competent genetic algorithms. Proceedings of the Genetic and Evolution-ary Computation Conference (GECCO-2001), pages 511-518
Pelikan, M. and Goldberg, D. E. (2003). Hierarchical BOA solves Ising spin glasses and MAXSAT. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2003), II:1275-1286
Pelikan, M., Ocenasek, J., Trebst, S., Troyer, M., and Alet, F. (2004). Computational complexity and simulation of rare events of Ising spin glasses. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2004), 2:36-47
Picard, J.-C. and Ratliff, H. (1975). Minimum cuts and related problems.Networks, 5:357
Sastry, K. and Goldberg, D. E. (2002). Analysis of mixing in genetic algorithms: A survey. IlliGAL Report No. 2002012, University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL 15 Searching for Ground States of Ising Spin Glasses349
Spin Glass Ground State Server (2004). http://www.informatik.uni-koeln.de/ls juenger/research/sgs/sgs.html University of Köln, Germany
Swamy, M. and Thulasiraman, K. (1991). Graphs, Networks and Algorithms. Wiley, New York
Tarjan, R. (1983). Data Structures and Network Algorithms. Society for industrial and applied mathematics, Philadelphia
Thierens, D., Goldberg, D. E., and Pereira, A. G. (1998). Domino con-vergence, drift, and the temporal-salience structure of problems. Pro-ceedings of the International Conference on Evolutionary Computation (ICEC-98), pages 535-540
Träff, J. (1996). A heuristic for blocking flow algorithms. European Journal of Operations Research, 89:564
Van Hoyweghen, C. (2001). Detecting spin-flip symmetry in optimization problems. In Kallel, L. et al., editors, Theoretical Aspects of Evolutionary Computing, pages 423-437. Springer, Berlin Heidelberg New York
Wang, F. and Landau, D. P. (2001). Efficient, multiple-range random walk algorithm to calculate the density of states. Physical Review Letters, 86 (10):2050-2053
Young, A., editor (1998). Spin glasses and random fields. World Scientific, Singapore
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Pelikan, M., Hartmann, A.K. (2006). Searching for Ground States of Ising Spin Glasses with Hierarchical BOA and Cluster Exact Approximation. In: Pelikan, M., Sastry, K., CantúPaz, E. (eds) Scalable Optimization via Probabilistic Modeling. Studies in Computational Intelligence, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34954-9_15
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