The use of tail inequalities on the probable computational time of randomized search heuristics

Theoretical Computer Science

Volumn 436, Issue , 2012, Pages 106-117

  Zhou, Dong ^a   Luo, Dan ^a   Lu, Ruqian ^b   Han, Zhangang ^a  

^a BEIJING NORMAL UNIVERSITY   (China)

^b CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Computational complexity; Evolutionary algorithms (EAs); Expected running time; Probable computational time (PCT); Randomized search heuristics (RSHs); Tail inequalities

Indexed keywords

COMPUTATIONAL TIME; EVOLUTIONARY ALGORITHMS (EAS); RANDOMIZED SEARCH HEURISTICS; RUNNING TIME; TAIL INEQUALITIES;

ARTIFICIAL INTELLIGENCE; BOOLEAN FUNCTIONS; COMPUTATIONAL COMPLEXITY; PARTICLE SWARM OPTIMIZATION (PSO);

HEURISTIC ALGORITHMS;

EID: 84860717041     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2012.01.010     Document Type: Article

References (53)

1. S. Droste, T. Jansen, and I. Wegener On the analysis of the (1 + 1) evolutionary algorithm Theoretical Computer Science 276 1-2 2002 51 81
2. I. Wegener Methods for the analysis of evolutionary algorithms on pseudo-Boolean functions Evolutionary Optimization 48 2002 349 369
3. H.G. Beyer, H.-P. Schwefel, and I. Wegener How to analyse evolutionary algorithms Theoretical Computer Science 287 1 2002 101 130
4. J. He, and X. Yao Drift analysis and average time complexity of evolutionary algorithms Artificial Intelligence 127 1 2001 57 85
5. J. He, and X. Yao Towards an analytic framework for analysing the computation time of evolutionary algorithms Artificial Intelligence 145 1-2 2003 59 97
6. J. He, and X. Yao A study of drift analysis for estimating computation time of evolutionary algorithms Natural Computing 3 1 2004 21 35
7. S. Nijssen, and T. Bäck An analysis of the behavior of simplified evolutionary algorithms on trap functions IEEE Transactions on Evolutionary Computation 7 1 2003 11 22
8. P.S. Oliveto, J. He, and X. Yao Time complexity of evolutionary algorithms for combinatorial optimization: a decade of results International Journal of Automation and Computing 4 3 2007 281 293
9. J. He, and X. Yao From an individual to a population: an analysis of the first hitting time of population-based evolutionary algorithms IEEE Transactions on Evolutionary Computation 6 5 2002 495 511
10. C. Witt Runtime analysis of the (μ + 1) EA on simple pseudo-Boolean functions Evolutionary Computation 14 1 2006 65 86
11. 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
12. T. Jansen, and I. Wegener The analysis of evolutionary algorithms - a proof that crossover really can help Algorithmica 34 2002 47 66
13. T. Jansen, K.A. De Jong, and I. Wegener On the choice of the offspring population size in evolutionary algorithms Evolutionary Computation 13 4 2005 413 440
14. T. Jansen, and I. Wegener Real royal road functions - where crossover provably is essential Discrete Applied Mathematics 149 1-3 2005 111 125
15. T. Chen, J. He, G. Sun, G. Chen, and X. Yao A new approach for analyzing average time complexity of population-based evolutionary algorithms on unimodal problems IEEE Transactions on Systems, Man, and Cybernetics, Part B 39 5 2009 1092 1106
16. P. Lehre, X. Yao, On the impact of mutation-selection balance on the runtime of evolutionary algorithms, IEEE Transactions on Evolutionary Computation (2011), doi:10.1109/TEVC.2011.2112665.
17. P. Lehre, and X. Yao Crossover can be constructive when computing unique input-output sequences Soft Computing 2010 1 13
18. T. Chen, K. Tang, G. Chen, X. Yao, A large population size can be unhelpful in evolutionary algorithms, Theoretical Computer Science (2011), doi:10.1016/j.tcs.2011.02.016.
19. O. Giel, and I. Wegener Evolutionary algorithms and the maximum matching problem Proceedings of 20th Annual Symposium on Theoretical Aspects of Computer Science STACS'03 2003 Springer-Verlag London 415 426
20. C. Witt Worst-case and average-case approximations by simple randomized search heuristics Proceedings of the 22th Symposium on Theoretical Aspects of Computer Science STACS Lecture Notes in Computer Science vol. 3404 2005 Springer Berlin, Heidelberg 44 56
21. 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
22. P. S. Oliveto, J. He, X. Yao, Analysis of population-based evolutionary algorithms for the vertex cover problem, in: Proceedings of IEEE World Congress on Computational Intelligence, WCCI, WCCI'08, Hong Kong, 2008, pp. 1563-1570.
23. 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
24. T. Neumann, and C. Witt Bioinspired computation in combinatorial optimization Algorithms and their Computational Complexity 2010 Springer Berlin, Heidelberg
25. A. Auger, and B. Doerr Theory of Randomized Search Heuristics: Foundations and Recent Developments 2011 World Scientific Singapore
26. W. Gutjahr Mathematical runtime analysis of ACO algorithms: survey on an emerging issue Swarm Intelligence 1 2007 59 79
27. C. Witt Rigorous runtime analysis of swarm intelligence algorithms - An overview Swarm Intelligence for Multi-objective Problems in Data Mining vol. 242 2009 Springer Berlin, Heidelberg 157 177
28. T. Chen, K. Tang, G. Chen, and X. Yao Analysis of computational time of simple estimation of distribution algorithms IEEE Transactions on Evolutionary Computation 14 1 2010 1 22
29. W.J. Gutjahr First steps to the runtime complexity analysis of ant colony optimization Computers and Operations Research 35 9 2008 2711 2727
30. W. Gutjahr, and G. Sebastiani Runtime analysis of ant colony optimization with best-so-far reinforcement Methodology and Computing in Applied Probability 10 2008 409 433
31. F. Neumann, and C. Witt Runtime analysis of a simple ant colony optimization algorithm Algorithmica 54 2009 243 255
32. F. Neumann, D. Sudholt, and C. Witt Analysis of different MMAS ACO algorithms on unimodal functions and plateaus Swarm Intelligence 3 2009 35 68
33. D. Sudholt, and C. Witt Runtime analysis of a binary particle swarm optimizer Theoretical Computer Science 411 2010 2084 2100
34. F. Neumann, and C. Witt Ant colony optimization and the minimum spanning tree problem Theoretical Computer Science 411 25 2010 2406 2413
35. T. Kötzing, F. Neumann, H. Röglin, and C. Witt Theoretical properties of two ACO approaches for the traveling salesman problem Proceedings of ANTS 2010 Lecture Notes in Computer Science 2010 Springer-Verlag Berlin, Heidelberg 324 335
36. T. Kötzing, P.K. Lehre, F. Neumann, and P.S. Oliveto Ant colony optimization and the minimum cut problem Proceedings of the 12th Genetic and Evolutionary Computation Conference GECCO'10 2010 ACM New York 1393 1400
37. C. Horoba, and D. Sudholt Running time analysis of ACO systems for shortest path problems Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics Lecture Notes in Computer Science vol. 5752 2009 Springer Berlin, Heidelberg 76 91
38. C. Horoba, and D. Sudholt Ant colony optimization for stochastic shortest path problems Proceedings of the 12th Genetic and Evolutionary Computation Conference GECCO'10 2010 ACM New York 1465 1472
39. I. Wegener Simulated annealing beats metropolis in combinatorial optimization Automata, Languages and Programming Lecture Notes in Computer Science vol. 3580 2005 Springer Berlin, Heidelberg 589 601
40. B. Doerr, and L.A. Goldberg Drift analysis with tail bounds Proceedings of the 11th International Conference on Parallel Problem Solving from Nature: Part I PPSN'10 2010 Springer-Verlag Berlin, Heidelberg 174 183
41. P. Lehre Fitness-levels for non-elitist populations Proceedings of the 13th Genetic and Evolutionary Computation Conference GECCO'11 2011 ACM New York 2075 2082
42. D. Sudholt General lower bounds for the running time of evolutionary algorithms Parallel Problem Solving from Nature PPSN I Lecture Notes in Computer Science 2010 Springer Berlin, Heidelberg 124 133
43. J. Lässig, and D. Sudholt General scheme for analyzing running times of parallel evolutionary algorithms Parallel Problem Solving from Nature PPSN I Lecture Notes in Computer Science 2010 Springer Berlin, Heidelberg 234 243
44. J. Lässig, and D. Sudholt Analysis of speedups in parallel evolutionary algorithms for combinatorial optimization Proceedings of the 22nd International Symposium on Algorithms and Computation, ISAAC 2011 Lecture Notes in Computer Science 2011 Springer Berlin, Heidelberg 405 414
45. S. Droste Analysis of the (1 + 1) EA for a dynamically bitwise changing OneMax Proceedings of the 5th Genetic and Evolutionary Computation Conference series GECCO'03 vol. 2723 2003 Springer-Verlag Berlin, Heidelberg 909 921
46. I. Wegener, and C. Witt On the analysis of a simple evolutionary algorithm on quadratic pseudo-Boolean functions Journal of Discrete Algorithms 3 1 2005 61 78
47. I. Wegener, and C. Witt On the optimization of monotone polynomials by simple randomized search heuristics Combinatorics, Probability and Computing 14 1-2 2005 225 247
48. T. Jansen, and I. Wegener On the choice of the mutation probability for the (1 + 1) EA Parallel Problem Solving from Nature PPSN VI Lecture Notes in Computer Science 2000 Springer Berlin, Heidelberg 89 98
49. R. Meester A natural introduction to probability theory 2008 Birkhauser Berlin
50. M. Mitzenmacher, and E. Upfal Probability and Computing: Randomized Algorithms and Probabilistic Analysis 2005 Cambridge University Press New York
51. L.G. Valiant A theory of the learnable Communications of the ACM 27 11 1984 1134 1142
52. S. Baswana, S. Biswas, B. Doerr, T. Friedrich, P.P. Kurur, and F. Neumann Computing single source shortest paths using single-objective fitness Proceedings of the 10th ACM SIGEVO Workshop on Foundations of Genetic Algorithms FOGA'09 2009 ACM New York 59 66
53. J. Kennedy, R. Eberhart, A discrete binary version of the particle swarm algorithm, in: Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, vol. 5, 1997, pp. 4104-4109.