Tight bounds on the optimization time of a randomized search heuristic on linear functions

Combinatorics Probability and Computing

Volumn 22, Issue 2, 2013, Pages 294-318

  Witt, Carsten ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

AMS 2010 Mathematics subject classification: Primary 68W20; Secondary 68Q25

Indexed keywords

EXPECTED OPTIMIZATION TIME; HIGH PROBABILITY; LARGE NEIGHBOURHOOD; LINEAR FUNCTIONS; MUTATION OPERATORS; MUTATION PROBABILITY; POLYNOMIAL OPTIMIZATION; RANDOMIZED SEARCH; RANDOMIZED SEARCH HEURISTICS; SECONDARY 68Q25; SUBJECT CLASSIFICATION; TIGHT BOUND; UPPER AND LOWER BOUNDS;

CLASSIFICATION (OF INFORMATION); HEURISTIC ALGORITHMS; RANDOM PROCESSES;

OPTIMIZATION;

EID: 84873365647     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548312000600     Document Type: Article

References (27)

1. Auger, A. and Doerr, B. (2011) Theory of Randomized Search Heuristics: Foundations and Recent Developments, World Scientific.
2. Back, T. (1993) Optimal mutation rates in genetic search. In Proc. International Conference on Genetic Algorithms, ICGA '93, Morgan Kaufmann, pp. 2-8.
3. Doerr, B., Fouz, M., and Witt, C. (2010). Quasirandom evolutionary algorithms. In Proc. Genetic and Evolutionary Computation Conference, GECCO '10, ACM Press, pp. 1457-1464.
4. Doerr, B., Fouz, M., and Witt, C. (2011). Sharp bounds by probability-generating functions and variable drift. In Proc. Genetic and Evolutionary Computation Conference, GECCO '11, ACM Press, pp. 2083-2090.
5. Doerr, B. and Goldberg, L. A. (2010). Adaptive drift analysis. In Proc. Parallel Problem Solving from Nature XI, PPSN '10, Vol. 6238 of Lecture Notes in Computer Science, Springer, pp. 32-41.
6. Doerr, B. and Goldberg, L. A. (2012). Adaptive drift analysis. Algorithmica, in press. Available online: http://www.springerlink.com/content/ v0n75x65k016r477
7. Doerr, B., Johannsen, D., and Winzen, C. (2010). Drift analysis and linear functions revisited. In Proc. Congress on Evolutionary Computation, CEC '10, IEEE Press, pp. 1-8.
8. Doerr, B., Johannsen, D., and Winzen, C. (2010). Multiplicative drift analysis. In Proc. Genetic and Evolutionary Computation Conference, GECCO '10, ACM Press, pp. 1449-1456.
9. Droste, S., Jansen, T., and Wegener, I. (2000). A natural and simple function which is hard for all evolutionary algorithms. In Proc. 26th Annual Conference of the IEEE Industrial Electronics Society, IECON '00, pp. 2704-2709. (Pubitemid 34089641)
10. Droste, S., Jansen, T., and Wegener, I. (2002). On the analysis of the (1+1) evolutionary algorithm. Theoret. Comput. Sci. 276 51-81.
11. Hajek, B. (1982). Hitting-time and occupation-time bounds implied by drift analysis with applications. Adv. Appl. Probab. 13 502-525.
12. He, J. and Yao, X. (2001). Drift analysis and average time complexity of evolutionary algorithms. Artificial Intelligence 127 57-85. (Pubitemid 32264935)
13. He, J. and Yao, X. (2004). A study of drift analysis for estimating computation time of evolutionary algorithms. Natural Computing 3 21-35. (Pubitemid 39127657)
14. Jagerskupper, J. (2007). Algorithmic analysis of a basic evolutionary algorithm for continuous optimization. Theoret. Comput. Sci. 379 329-347. (Pubitemid 46754584)
15. Jagerskupper, J. (2008). A blend of Markov-chain and drift analysis. In Proc. Parallel Problem Solving from Nature X, PPSN '08, Vol. 5199 of Lecture Notes in Computer Science, Springer, pp. 41-51.
16. Jagerskupper, J. (2011). Combining Markov-chain analysis and drift analysis: The (1+1) evolutionary algorithm on linear functions reloaded. Algorithmica 59 409-424.
17. Lehre, P. K. and Witt, C. (2012). Black-box search by unbiased variation. Algorithmica 64 623-642.
18. Marshall, A. W., Olkin, I. and Arnold, B. (2011). Inequalities: Theory of Majorization and its Applications, second edition, Springer.
19. Motwani, R. and Raghavan, P. (1995). Randomized Algorithms, Cambridge University Press.
20. Muhlenbein, H. (1992). How genetic algorithms really work I: Mutation and hillclimbing. In Proc. Parallel Problem Solving from Nature I, PPSN '92, Elsevier, pp. 15-26.
21. Neumann, F. and Witt, C. (2010). Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity, Natural Computing Series, Springer.
22. Sudholt, D. (2010). General lower bounds for the running time of evolutionary algorithms. In Proc. Parallel Problem Solving from Nature XI, PPSN '10, Vol. 6238 of Lecture Notes in Computer Science, Springer, pp. 124-133.
23. Sudholt, D. (2012). A new method for lower bounds on the running time of evolutionary algorithms. IEEE Trans. Evolutionary Computation, to appear. Preprint: http://dx.doi.org/10.1109/TEVC.2012.2202241
24. Wegener, I. (2001). Methods for the analysis of evolutionary algorithms on pseudo-Boolean functions. In Evolutionary Optimization (R. Sarker, M. Mohammadian and X. Yao, eds), Kluwer.
25. Wegener, I. and Witt, C. (2005). On the analysis of a simple evolutionary algorithm on quadratic pseudo-boolean functions. J. Discrete Algorithms 3 61-78. (Pubitemid 40219773)
26. Wegener, I. and Witt, C. (2005). On the optimization of monotone polynomials by simple randomized search heuristics. Combin. Probab. Comput. 14 225-247. (Pubitemid 40303861)
27. Witt, C. (2012). Optimizing linear functions with randomized search heuristics: The robustness of mutation. In Proc. Symposium on Theoretical Aspects of Computer Science, STACS '12, Leibniz International Proceedings in Informatics, pp. 420-431. Open access: http://drops.dagstuhl.de/opus/volltexte/ 2012/3392/.