A new method for lower bounds on the running time of evolutionary algorithms

IEEE Transactions on Evolutionary Computation

Volumn 17, Issue 3, 2013, Pages 418-435

  Sudholt, Dirk ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Evolutionary algorithms; fitness level method; runtime analysis; theory

Indexed keywords

EVOLUTIONARY ALGORITHMS (EAS); EXPECTED RUNNING TIME; FITNESS EVALUATIONS; FITNESS-LEVEL METHOD; RUN-TIME ANALYSIS; SELECTION OPERATORS; THEORY; TRANSITION PROBABILITIES;

ALGORITHMS; EVOLUTIONARY ALGORITHMS; OPTIMIZATION;

HEALTH;

EID: 84878387126     PISSN: 1089778X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TEVC.2012.2202241     Document Type: Article

References (54)

1. D. Sudholt, "General lower bounds for the running time of evolutionary algorithms," Proc. 11th Int. Conf. Parallel Problem Solving From Nature (PPSN), LNCS 6238. 2010, pp. 124-133.
2. S. Droste, T. Jansen, and I. Wegener, "On the analysis of the (1+1) evolutionary algorithm," Theor. Comput. Sci., vol. 276, nos. 1-2, pp. 51-81, 2002.
3. J. He and X. Yao, "A study of drift analysis for estimating computation time of evolutionary algorithms," Natural Comput., vol. 3, no. 1, pp. 21-35, 2004. (Pubitemid 39127657)
4. J. J̈agersk̈upper, "Combining Markov-chain analysis and drift analysis: The (1+1) evolutionary algorithm on linear functions reloaded," Algorithmica, vol. 59, no. 3, pp. 409-424, 2011.
5. B. Doerr, D. Johannsen, and C. Winzen, "Drift analysis and linear functions revisited," Proc. IEEE Congr. Evol. Comput., Jul. 2010, pp. 1967-1974.
6. C. Witt, "Optimizing linear functions with randomized search heuristics: The robustness of mutation," Proc. 29th Int. Symp. Theor. Aspects Comput. Sci., 2012, pp. 420-431.
7. T. Jansen and I. Wegener, "Evolutionary algorithms: How to cope with plateaus of constant fitness and when to reject strings of the same fitness," IEEE Trans. Evol. Comput., vol. 5, no. 6, pp. 589-599, Dec. 2001. (Pubitemid 34091917)
8. I. Wegener and C. Witt, "On the optimization of monotone polynomials by simple randomized search heuristics," Combinatorics, Probability Comput., vol. 14, nos. 1-2, pp. 225-247, 2005. (Pubitemid 40303861)
9. B. Doerr, T. Jansen, D. Sudholt, C. Winzen, and C. Zarges, "Optimizing monotone functions can be difficult," Proc. 11th Int. Conf. Parallel Problem Solving From Nature (PPSN), LNCS 6238. 2010, pp. 42-51.
10. P. S. Oliveto, J. He, and X. Yao, "Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results," Int. J. Autom. Comput., vol. 4, no. 3, pp. 281-293, 2007. (Pubitemid 47167355)
11. F. Neumann and C. Witt, Bioinspired Computation in Combinatorial Optimization-Algorithms and Their Computational Complexity. Berlin, Germany: Springer, 2010.
12. D. Sudholt, "The impact of parametrization in memetic evolutionary algorithms," Theor. Comput. Sci., vol. 410, no. 26, pp. 2511-2528, 2009.
13. D. Sudholt, "Hybridizing evolutionary algorithms with variable-depth search to overcome local optima," Algorithmica, vol. 59, no. 3, pp. 343-368, 2011.
14. D. Sudholt and C. Zarges, "Analysis of an iterated local search algorithm for vertex coloring," Proc. 21st Int. Symp. Algorithms Comput., LNCS 6506. 2010, pp. 340-352.
15. S. Droste, "A rigorous analysis of the compact genetic algorithm for linear functions," Natural Comput., vol. 5, no. 3, pp. 257-283, 2006. (Pubitemid 44304901)
16. T. Chen, K. Tang, G. Chen, and X. Yao, "Analysis of computational time of simple estimation of distribution algorithms," IEEE Trans. Evol. Comput., vol. 14, no. 1, pp. 1-22, Feb. 2010.
17. W. J. Gutjahr and G. Sebastiani, "Runtime analysis of ant colony optimization with best-so-far reinforcement," Methodol. Comput. Appl. Probab., vol. 10, no. 3, pp. 409-433, 2008.
18. F. Neumann and C. Witt, "Runtime analysis of a simple ant colony optimization algorithm," Algorithmica, vol. 54, no. 2, pp. 243-255, 2009.
19. F. Neumann, D. Sudholt, and C. Witt, "Analysis of different MMAS ACO algorithms on unimodal functions and plateaus," Swarm Intell., vol. 3, no. 1, pp. 35-68, 2009.
20. D. Sudholt and C. Thyssen, "Running time analysis of ant colony optimization for shortest path problems," J. Discrete Algorithms, vol. 10, pp. 165-180, 2012.
21. D. Sudholt and C. Witt, "Runtime analysis of a binary particle swarm optimizer," Theor. Comput. Sci., vol. 411, no. 21, pp. 2084-2100, 2010.
22. C. Witt, "Why standard particle swarm optimizers elude a theoretical runtime analysis," Proc. 10th Found. Genet. Algorithms, 2009, pp. 13-20.
23. C. Zarges, "Rigorous runtime analysis of inversely fitness proportional mutation rates," Proc. 10th Parallel Problem Solving From Nature (PPSN X), LNCS 5199. 2008, pp. 112-122.
24. T. Jansen and C. Zarges, "Analysis of evolutionary algorithms: From computational complexity analysis to algorithm engineering," Proc. 11th Workshop Found. Genet. Algorithms, 2011, pp. 1-14.
25. A. Auger and B. Doerr, Eds., Theory of Randomized Search Heuristics-Foundations and Recent Developments (Series on Theoretical Computer Science, no. 1). Singapore: World Scientific, 2011.
26. G. Rudolph, Convergence Properties of Evolutionary Algorithms. Hamburg, Germany: Kova?c, 1997.
27. B. Doerr, M. Fouz, and C. Witt, "Quasirandom evolutionary algorithms," Proc. Genet. Evol. Comput. Conf., 2010, pp. 1457-1464.
28. P. S. Oliveto and C. Witt, "Simplified drift analysis for proving lower bounds in evolutionary computation," Algorithmica, vol. 59, no. 3, pp. 369-386, 2011.
29. B. Doerr, D. Johannsen, and C. Winzen, "Multiplicative drift analysis," Proc. Genet. Evol. Comput. Conf., 2010, pp. 1449-1456.
30. P. K. Lehre, "Negative drift in populations," Proc. 11th Int. Conf. Parallel Problem Solving From Nature (PPSN), LNCS 6238. 2011, pp. 244-253.
31. B. Doerr, M. Fouz, and C. Witt, "Sharp bounds by probability-generating functions and variable drift," Proc. 13th Annu. Genet. Evol. Comput. Conf., 2011, pp. 2083-2090.
32. J. Horn, D. E. Goldberg, and K. Deb, "Long path problems," Proc. 3rd Parallel Problem Solving From Nature (PPSN III), LNCS 866. 1994, pp. 149-158.
33. G. Rudolph, "How mutation and selection solve long-path problems in polynomial expected time," Evol. Comput., vol. 4, no. 2, pp. 195-205, 1997. (Pubitemid 126706156)
34. S. B̈ottcher, B. Doerr, and F. Neumann, "Optimal fixed and adaptive mutation rates for the leading ones problem," Proc. 11th Int. Conf. Parallel Problem Solving From Nature (PPSN), LNCS 6238. 2010, pp. 1-10.
35. I. Wegener, "Methods for the analysis of evolutionary algorithms on pseudo-Boolean functions," in Evolutionary Optimization, R. Sarker, X. Yao, and M. Mohammadian, Eds. Dordrecht, The Netherlands: Kluwer, 2002, pp. 349-369.
36. S. Droste, T. Jansen, and I. Wegener, "Upper and lower bounds for randomized search heuristics in black-box optimization," Theory Comput. Syst., vol. 39, no. 4, pp. 525-544, 2006. (Pubitemid 43876884)
37. P. K. Lehre and C. Witt, "Black box search by unbiased variation," Proc. Genet. Evol. Comput. Conf., 2010, pp. 1441-1448.
38. J. E. Rowe and M. D. Vose, "Unbiased black box search algorithms," Proc. 13th Annu. Genet. Evol. Comput. Conf., 2011, pp. 2035-2042.
39. B. Doerr, D. Johannsen, T. K̈otzing, P. K. Lehre, M. Wagner, and C. Winzen, "Faster black-box algorithms through higher arity operators," Proc. 11th Workshop Found. Genet. Algorithms, 2011, pp. 163-172.
40. B. Doerr and C. Winzen, "Toward a complexity theory of randomized search heuristics: Ranking-based black-box complexity," Proc. 6th Int. Comput. Sci. Symp. Russia (CSR), LNCS 6651. 2011, pp. 15-28.
41. P. A. Borisovsky and A. V. Eremeev, "Comparing evolutionary algorithms to the (1+1)-EA," Theor. Comput. Sci., vol. 403, no. 1, pp. 33-41, 2008.
42. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2nd ed. Cambridge, MA: MIT Press, 2001.
43. J. L̈assig and D. Sudholt, "Adaptive population models for offspring populations and parallel evolutionary algorithms," Proc. 11th Workshop Found. Genet. Algorithms, 2011, pp. 181-192.
44. C. Witt, "Runtime analysis of the (μ+1) EA on simple pseudo-Boolean functions," Evol. Comput., vol. 14, no. 1, pp. 65-86, 2006. (Pubitemid 43955273)
45. P. K. Lehre, "Fitness-levels for non-elitist populations," Proc. 13th Annu. Genet. Evol. Comput. Conf., 2011, pp. 2075-2082.
46. J. Rowe, personal communication, 2011.
47. J. L̈assig and D. Sudholt, "General scheme for analyzing running times of parallel evolutionary algorithms," Proc. 11th Int. Conf. Parallel Problem Solving From Nature (PPSN), LNCS 6238. 2010, pp. 234-243.
48. F. Neumann, D. Sudholt, and C. Witt, "A few ants are enough: ACO with iteration-best update," Proc. Genet. Evol. Comput. Conf., 2010, pp. 63-70.
49. S. Droste, T. Jansen, and I. Wegener, "A rigorous complexity analysis of the (1+1) evolutionary algorithm for separable functions with Boolean inputs," Evol. Comput., vol. 6, no. 2, pp. 185-196, 1998. (Pubitemid 128692902)
50. T. Jansen and D. Sudholt, "Analysis of an asymmetric mutation operator," Evol. Comput., vol. 18, no. 1, pp. 1-26, 2010.
51. T. K̈otzing, D. Sudholt, and M. Theile, "How crossover helps in pseudo-Boolean optimization," Proc. 13th Annu. Genet. Evol. Comput. Conf., 2011, pp. 989-996.
52. D. Sudholt, "Crossover speeds up building-block assembly," Proc. Genet. Evol. Comput. Conf., 2012, to be published.
53. B. Mitavskiy, J. Rowe, and C. Cannings, "Theoretical analysis of local search strategies to optimize network communication subject to preserving the total number of links," Int. J. Intell. Comput. Cybern., vol. 2, no. 2, pp. 243-284, 2009.
54. D. Zhou, D. Luo, R. Lu, and Z. Han, "The use of tail inequalities on the probable computational time of randomized search heuristics," Theor. Comput. Sci., vol. 436, pp. 106-117, 2012.