Hybrid evolutionary algorithms on minimum vertex cover for random graphs

Proceedings of GECCO 2007: Genetic and Evolutionary Computation Conference

Volumn , Issue , 2007, Pages 547-554

  Pelikan, Martin ^a   Kalapala, Rajiv ^a   Hartmann, Alexander K ^b  

^a UNIVERSITY OF MISSOURI ST LOUIS   (United States)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Branch and bound; Genetic algorithm; Hierarchical BOA; Minimum vertex cover; Simulated annealing

Indexed keywords

BRANCH AND BOUND METHOD; GRAPH THEORY; HIERARCHICAL SYSTEMS; PROBLEM SOLVING; SIMULATED ANNEALING;

HIERARCHICAL BAYESIAN OPTIMIZATION ALGORITHM (HBOA); HYBRID EVOLUTIONARY ALGORITHMS; MINIMUM VERTEX COVERS; PARALLEL SIMULATED ANNEALING (PSA);

GENETIC ALGORITHMS;

EID: 34548075022     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1276958.1277073     Document Type: Conference Paper

References (43)

1. F. N. Abu-Khzam, R. L. Collins, M. R. Fellows, M. A. Langston, W. H. Suters, and C. T. Symons. Kernelization algorithms for the vertex cover problem: Theory and experiments. In Proceedings ACM-SIAM Workshop on Algorithm Engineering and Experiments (ALENEX '04), New Orleans, LA, 2004.
2. S. Baluja. 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.
3. M. Bauer and O. Golinelli. Core percolation in random graphs: a critical phenomena analysis. Eur. Phys. J. B, 24:339, 2001.
4. B. Bollobás. Random Graphs. Cambridge University Press, Cambridge, UK, 2nd edition, 2001.
5. 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.
6. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms. McGraw-Hill, New York, 2nd edition, 2001.
7. A. Das and B. K. Chakrabarti, editors. Quantum Annealing and Related Optimization Methods, volume 679. Springer, New York, 2005.
8. P. Erdös and A. Rényi. On the evolution of random graphs. Publ Math. Inst. Hung. Acad. Sci., 5:17, 1960.
9. N. Friedman and M. Goldszmidt. Learning Bayesian networks with local structure. In M. I. Jordan, editor, Graphical models, pages 421-459. MIT Press, Cambridge, MA, 1999.
10. M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York, 1979.
11. D. E. Goldberg. Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading, MA, 1989.
12. D. Gusfield, S. Eddhu, and C. Langley. Efficient reconstruction of phylogenetic networks with constrained recombination. In Proceedings of the Computational Systems Bioinformatics (CSAB 2006), 2006.
13. G. R. Harik. Finding multimodal solutions using restricted tournament selection. Proceedings of the International Conference on Genetic Algorithms (ICGA-95), pages 24-31, 1995.
14. A. K. Hartmann and H. Rieger, editors. New Optimization Algorithms in Physics, Weinheim, 2004. Wiley-VCH.
15. A. K. Hartmann and M. Weigt. Phase Transitions in Combinatorial Optimization Problems. Wiley-VCH, Weinheim, 2005.
16. J. H. Holland. Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI, 1975.
17. H. Hongwei, X. Xuezhou, X. Jin, and B. Zheng. Solving vertex covering problems using hybrid genetic algorithms. In Proceedings of the 5th International Conference on Signal Processing, pages 1663-1666, 2000.
18. X. Huang, J. Lai, and S. F. Jennings. Maximum common subgraph: Some upper bound and lower bound results. BMC Bioinformatics, 7(Suppl 4):S6, 2006.
19. R. M. Karp. Reducibility among combinatorial problems. In Symposium on the Complexity of Computer Computations, pages 85-103, Yorktown Heights, NY, 1972. Plenum, NY.
20. S. Khuri and T. Bäck. An evolutionary heuristic for the minimum vertex cover problem. Genetic Algorithms within the Framework of Evolutionary Computation: Proceedings of the KI-94 Workshop, pages 86-90, 1994.
21. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science, 220:671-680, 1983.
22. K. Kotecha and N. Gambhava. A hybrid genetic algorithm for minimum vertex cover problem. In B. Prasad, editor, The First Indian International Conference on Artificial Intelligence, pages 904-913, Hyderabad, 2003. IICAI.
23. P. Larrañaga and J. A. Lozano, editors. Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer, Boston, MA, 2002.
24. E. L. Lawler and D. E. Wood. Branch-and-bound methods: a survey. Operational Research 14:699, University of Michigan, Ann Arbor, Ann Arbor, MI, 1966.
25. R. Luling and B. Monien. Load balancing for distributed branch and bound algorithms. In The 6th International Parallel Processing Symposium, pages 543-549, Los Alamitos, USA, 1992. IEEE Computer Society Press.
26. M. Mézard, G. Parisi, and R. Zecchina. Analytic and algorithmic solution of random satisfiability problems. Science, 297:812, 2002.
27. R. Monasson and S. Coceo, rajectories in phase diagrams, growth processes, and computational complexity: How search algorithms solve the 3-satisfiability problem. Phys. Rev. Lett., 86:1654, 2001.
28. R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyansky. Determining computational complexity from characteristic phase transitions. Nature, 400:133, 1999.
29. H. Mühlenbein and G. Paaß. From recombination of genes to the estimation of distributions I. Binary parameters. In A. Eiben, T. Back, M. Shoenauer, and H. Schwefel, editors, Parallel Problem Solving from Nature, pages 178-187, Berlin, 1996. Springer Verlag.
30. M. Pelikan. Hierarchical Bayesian optimization algorithm: Toward a new generation of evolutionary algorithms. Springer-Verlag, 2005.
31. M. Pelikan and D. E. Goldberg. Escaping hierarchical traps with competent genetic algorithms. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), pages 511-518, 2001. Also IlliGAL Report No. 2000020.
32. 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. Also IlliGAL Report No. 99018.
33. M. Pelikan and A. Hartmann. Searching for ground states of Ising spin glasses with hierarchical BOA and cluster exact approximation. In E. Cantú-Paz, M. Pelikan, and K. Sastry, editors, Scalable optimization via probabilistic modeling: From algorithms to applications. Springer, 2006.
34. M. Pelikan, K. Sastry, and E. Cantú-Paz, editors. Scalable Optimization via Probabilistic Modeling: From Algorithms to Applications. Springer, 2006.
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. Also IlliGAL Report No. 2002004.
36. E. Tsang. Foundations of Constraint Satisfaction. Academic Press, London, 1993.
37. P.-J. Wan, L. Liu, and O. Frieder. Optimal placement of wavelength converters in trees and trees of rings. In Proceedings. Eight International Conference on Computer Communications and Networks, pages 392-397, 1999.
38. M. Weigt and A. K. Hartmann. Minimal vertex covers on finite-connectivity random graphs - A hard-sphere lattice-gas picture. Phys. Rev. E, 63:056127, 2000.
39. M. Weigt and A. K. Hartmann. The number guards needed by a museum - a phase transition in vertex covering of random graphs. Phys. Rev. Lett., 84:6118, 2000.
40. M. Weigt and A. K. Hartmann. The typical-case complexity of a vertex-covering algorithm on finite-connectivity random graphs. Phys. Rev. Lett., 86:1658, 2001.
41. K. Xu, F. Boussemart, F. Hemery, and C. Lecoutre. A simple model to generate hard satisfiable instances. In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI), pages 337-342, Edinburgh, Scotland, 2005.
42. K. Xu and W. Li. Exact phase transitions in random constraint satisfaction problems. Artificial Intelligence Research, 12:93103, 2000.
43. K. Xu and W. Li. Many hard examples in exact phase transitions with application to generating hard satisfiable instances. Technical Report cs.CC/0302001, 2003.