On the approximation ability of evolutionary optimization with application to minimum set cover

Artificial Intelligence

Volumn 180-181, Issue , 2012, Pages 20-33

  Yu, Yang ^a   Yao, Xin ^b   Zhou, Zhi Hua ^a  

^a NANJING UNIVERSITY   (China)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Approximation algorithm; Approximation ratio; Evolutionary algorithms; k Set cover; Time complexity analysis

Indexed keywords

APPROXIMATION ABILITY; APPROXIMATION PERFORMANCE; APPROXIMATION RATIOS; EVOLUTIONARY OPTIMIZATIONS; GREEDY ALGORITHMS; K-SET COVER; K-SET COVER PROBLEM; LOWER BOUNDS; MINIMUM SET COVER; MULTI OBJECTIVE; NATURAL EVOLUTION; NP-HARD; OPTIMAL SOLUTIONS; SATISFICING; SET COVER PROBLEM; TIME COMPLEXITY;

EVOLUTIONARY ALGORITHMS; HEURISTIC ALGORITHMS;

APPROXIMATION ALGORITHMS;

EID: 84862795189     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.artint.2012.01.001     Document Type: Article

References (33)

1. N. Alon, D. Moshkovitz, and S. Safra Algorithmic construction of sets for k-restrictions ACM Transactions on Algorithms 2 2 2006 153 177 (Pubitemid 44273960)
2. A. Auger, and B. Doerr Theory of Randomized Search Heuristics - Foundations and Recent Developments 2011 World Scientific Singapore
3. T. Bäck Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms 1996 Oxford University Press Oxford, UK
4. E. Benkhelifa, G. Dragffy, A. Pipe, M. Nibouche, Design innovation for real world applications, using evolutionary algorithms, in: 2009 IEEE Congress on Evolutionary Computation, Trondheim, Norway, 2009, pp. 918-924.
5. V. Chvátal A greedy heuristic for the set-covering problem Mathematics of Operations Research 4 3 1979 233 235
6. B. Doerr, A.V. Eremeev, C. Horoba, F. Neumann, M. Theile, Evolutionary algorithms and dynamic programming, in: Proceedings of the 11th ACM Conference on Genetic and Evolutionary Computation Conference (GECCO09), Montreal, Canada, 2009, pp. 771-778.
7. S. Droste, T. Jansen, and I. Wegener A rigorous complexity analysis of the (1 + 1) evolutionary algorithm for linear functions with boolean inputs Evolutionary Computation 6 2 1998 185 196 (Pubitemid 128692902)
8. R. Duh, M. Fürer, Approximation of k-set cover by semi local optimization, in: Proceedings of the 29th Annual ACM Symposium on Theory of Computing (STOC97), El Paso, TX, 1997, pp. 256-264.
9. U. Feige A threshold of ln n for approximating set cover Journal of the ACM 45 4 1998 634 652 (Pubitemid 128488790)
10. T. Friedrich, J. He, N. Hebbinghaus, F. Neumann, and C. Witt Analyses of simple hybrid algorithms for the vertex cover problem Evolutionary Computation 17 1 2009 3 19
11. T. Friedrich, J. He, N. Hebbinghaus, F. Neumann, and C. Witt Approximating covering problems by randomized search heuristics using multi-objective models Evolutionary Computation 18 4 2010 617 633
12. O. Giel, I. Wegener, Evolutionary algorithms and the maximum matching problem, in: Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science, Berlin, Germany, 2003, pp. 415-426.
13. R. Hassin, and A. Levin A better-than-greedy approximation algorithm for the minimum set cover problem SIAM Journal on Computing 35 1 2005 189 200
14. J. He, and X. Yao Drift analysis and average time complexity of evolutionary algorithms Artificial Intelligence 127 1 2001 57 85 (Pubitemid 32264935)
15. J. He, X. Yao, An analysis of evolutionary algorithms for finding approximation solutions to hard optimisation problems, in: Proceedings of 2003 IEEE Congress on Evolutionary Computation (CEC03), Canberra, Australia, 2003, pp. 2004-2010.
16. T. Higuchi, M. Iwata, D. Keymeulen, H. Sakanashi, M. Murakawa, I. Kajitani, E. Takahashi, K. Toda, N. Salami, N. Kajihara, and N. Otsu Real-world applications of analog and digital evolvable hardware IEEE Transactions on Evolutionary Computation 3 3 1999 220 235
17. G.S. Hornby, A. Globus, D.S. Linden, J.D. Lohn, Automated antenna design with evolutionary algorithms, in: Proceedings of 2006 American Institute of Aeronautics and Astronautics Conference on Space, San Jose, CA, 2006, pp. 19-21.
18. J.R. Koza, M.A. Keane, and M.J. Streeter Whats AI done for me lately? Genetic programmings human-competitive results IEEE Intelligent Systems 18 3 2003 25 31
19. M. Laumanns, L. Thiele, E. Zitzler, E. Welzl, K. Deb, Running time analysis of multi-objective evolutionary algorithms on a simple discrete optimization problem, in: Proceedings of the 7th International Conference on Parallel Problem Solving from Nature (PPSN02), London, UK, 2002, pp. 44-53.
20. A. Levin Approximating the unweighted k-set cover problem: Greedy meets local search SIAM Journal on Discrete Mathematics 23 1 2008 251 264
21. J. Mestre, Greedy in approximation algorithms, in: Proceedings of the 14th Annual European Symposium on Algorithms (ESA06), Zurich, Switzerland, 2006, pp. 528-539. (Pubitemid 44699677)
22. F. Neumann, M. Laumanns, Speeding up approximation algorithms for NP-hard spanning forest problems by multi-objective optimization, in: Proceedings of the 7th Latin American Symposium on Theoretical Informatics, Valdivia, Chile, 2006, pp. 745-756. (Pubitemid 43986653)
23. F. Neumann, J. Reichel, Approximating minimum multicuts by evolutionary multi-objective algorithms, in: Proceedings of the 10th International Conference on Parallel Problem Solving from Nature (PPSN08), Dortmund, Germany, 2008, pp. 72-81.
24. F. Neumann, I. Wegener, Minimum spanning trees made easier via multi-objective optimization, in: Proceedings of the 7th ACM Annual Conference on Genetic and Evolutionary Computation Conference (GECCO05), Washington DC, 2005, pp. 763-769. (Pubitemid 43226373)
25. F. Neumann, and I. Wegener Can single-objective optimization profit from multiobjective optimization? J. Knowles, D. Corne, K. Deb, Multiobjective Problem Solving from Nature - From Concepts to Applications 2007 Springer Berlin, Germany 115 130
26. F. Neumann, and C. Witt Bioinspired Computation in Combinatorial Optimization - Algorithms and Their Computational Complexity 2010 Springer-Verlag Berlin, Germany
27. F. Neumann, J. Reichel, M. Skutella, Computing minimum cuts by randomized search heuristics, in: Proceedings of the 10th ACM Annual Conference on Genetic and Evolutionary Computation (GECCO08), Atlanta, GA, 2008, pp. 779-786.
28. P. Oliveto, J. He, and X. Yao Analysis of the (1 + 1) -EA for finding approximate solutions to vertex cover problems IEEE Transactions on Evolutionary Computation 13 5 2009 1006 1029
29. R. Raz, S. Safra, A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP, in: Proceedings of the ACM Symposium on Theory of Computing (STOC97), El Paso, TX, 1997, pp. 475-484.
30. J. Scharnow, K. Tinnefeld, I. Wegener, Fitness landscapes based on sorting and shortest paths problems, in: Proceedings of the 7th International Conference on Parallel Problem Solving from Nature (PPSN02), Granada, Spain, 2002, pp. 54-63.
31. P. Slavík A tight analysis of the greedy algorithm for set cover Journal of Algorithms 25 2 1997 237 254 (Pubitemid 127451763)
32. C. Witt, Worst-case and average-case approximations by simple randomized search heuristics, in: Proceedings of the 22nd Annual Symposium on Theoretical Aspects of Computer Science (STACS05), Stuttgart, Germany, 2005, pp. 44-56. (Pubitemid 41241235)
33. Y. Yu, and Z.-H. Zhou A new approach to estimating the expected first hitting time of evolutionary algorithms Artificial Intelligence 172 15 2008 1809 1832