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### Evolutionary Optimization in Noisy Environments Bibliography

Evolutionary optimization has often to be conducted in the presence of noise. Generally, two sorts of noise have been considered:
1. Noise in the fintee function. In this case, we mean the noise is additive and, in most cases unbiased. Research on this kind of noise focus mainly on how to reduce the influence of the noise. Two main approaches are available: explicit averaging and implicit avaraging.
2. Noise in the design variables or in the environmental parameters. When noise is present in designvariables or in environmental parameters, the main motivation is to find an optimal solution that is insensitive to noises. This is often known as search for robust solutions. The robustness can be defined based on the expected fitness given a certain distribution of the noise or the worst-case fitness, given a threshold of tolerance in performance or in design variables.

In both cases, an important issue is to reduce the additional computational cost in dealing with the nosie. To this end, adaptive sampling (change of sample size, use of ad hoc sample techniques instead of random sampling), introduction of local search and use of meta-models have been studied.

References on handling approximate fitness functions can be found here.

A survey of the research can be found here.

Please send me an email to include your papers (in bibtex format) in this bibliography. Thanks.

References sorted by year can be found here.

Last updated on August 12, 2005 by Yaochu Jin.

 All publications sorted by name
1. A. N. Aizawa and B. W. Wah. Scheduling of Genetic Algorithms in a Noisy Environment. Evolutionary Computation, pp 97-122, 1994. [bibtex-key = AiWa94]

2. A.N. Aizawa and B.W Wah. Dynamic control of genetic algorithms in a noisy environment. In Conference on Genetic Algorithms, pages 48--55, 1993. Morgan Kaufmann. [bibtex-key = AiWa93]

3. D. V. Arnold. Noisy Optimization with Evolution Strategies. Kluwer, 2002. [bibtex-key = Arn02]

4. D. Arnold. Evolution strategies in noisy environments -- A survey of existing work. In L. Kallel, B. Naudts, and A. Rogers, editors,Theoretical Aspects of Evolutionary Computing,, pages 239--249. Springer Verlag, Heidelberg, 2001. [bibtex-key = Arn01]

5. D. V. Arnold and H.-G. Beyer. A Comparison of Evolution Strategies with Other Direct Search Methods in the Presence of Noise. Computational Optimization and Applications, 24:135--159, 2003. [bibtex-key = ArBe03]

6. D. V. Arnold and H.-G. Beyer. Efficiency and Mutation Strength Adaptation of the $(\mu/\mu_I,\lambda)$-ES in a Noisy Environment. In M. Schoenauer et al., editor, Parallel Problem Solving from Nature, volume 1917 of LNCS, pages 39-48, 2000. Springer. [bibtex-key = ArBe00]

7. D. V. Arnold and H.-G. Beyer. Local Performance of the $(\mu/\mu_I,\lambda)$-ES in a Noisy Environment. In W. Martin and W. Spears, editors, Foundations of Genetic Algorithms, pages 127--142, 2000. Morgan Kaufmann. [bibtex-key = ArBe00b]

8. R. C. Ball, T. M. A. Fink, and N. E. Bowler. Stochastic Annealing. Physical Review Letters, 91, 2003.
Note: 030201. [bibtex-key = BFB03]

9. E.B. Baum, D. Boneh, and C. Garret. On genetic algorithms. In 8th Annual Conference on Computational Learning Theory, pages 230--239, 1995. Springer. [bibtex-key = BBG95]

10. S. Baumert and R.L. Smith. Pure random search for noisy objective functions. Technical report 01-03, Department of Industrial and Operations Engineering, The University of Michigan, 2001. [bibtex-key = BaSm01]

11. T. Beielstein and S. Markon. Threshold selection, Hypothesis test, and DOE methods. In Congress on Evolutionary Computation, pages 777-782, 2002. IEEE. [bibtex-key = BeMa02]

12. H.-G. Beyer. Actuator noise in recominant evolution strategies on general quadratic fitness models. In K. Deb et.al., editor, Genetic and Evolutionary Computation Conference, volume 3102 of LNCS, pages 654-665, 2004. Springer. [bibtex-key = Bey04]

13. H.-G. Beyer. Evolutionary Algorithms in Noisy Environments: Theoretical Issues and Guidelines for Practice. Computer methods in applied mechanics and engineering, 186:239-267, 2000. [bibtex-key = Bey00]

14. H.-G. Beyer. Toward a Theory of Evolution Strategies: Some Asymptotical Results from the $(1\stackrel{+}{,}\lambda)$-Theory. Evolutionary Computation, 1(2):165-188, 1993. [bibtex-key = Bey93]

15. C. Bierwirth and D. C. Mattfeld. Production Scheduling and Rescheduling with Genetic Algorithms. Evolutionary Computation, 7(1):1-18, 1999. [bibtex-key = BiMa99]

16. J. Branke. Evolutionary Optimization in Dynamic Environments. Kluwer, 2001. [bibtex-key = Bra01]

17. J. Branke. Reducing the Sampling Variance when Searching for Robust Solutions. In L. Spector et al., editor, Genetic and Evolutionary Computation Conference (GECCO '01), pages 235--242, 2001. Morgan Kaufmann. [bibtex-key = Branke:2001]

18. J. Branke. Creating robust solutions by means of evolutionary algorithms. In Parallel Problem Solving from Nature, LNCS, pages 119-128, 1998. Springer. [bibtex-key = Bra98]

19. J. Branke and C. Schmidt. Sequential Sampling in Noisy Environments. In Parallel Problem Solving from Nature, LNCS, 2004. Springer. [bibtex-key = BrSc04b]

20. J. Branke and C. Schmidt. Selection in the presence of noise. In E. Cantu-Paz, editor, Genetic and Evolutionary Computation Conference, volume 2723 of LNCS, pages 766-777, 2003. Springer. [bibtex-key = BrSc03]

21. J. Branke, C. Schmidt, and H. Schmeck. Efficient fitness estimation in noisy environment. In L. Spector et al., editor, Genetic and Evolutionary Computation, pages 243-250, 2001. Morgan Kaufmann. [bibtex-key = BSS01]

22. T. Bäck and U. Hammel. Evolution strategies applied to perturbed objective functions. In Congress on Evolutionary Computation, pages 40--45, 1994. IEEE. [bibtex-key = HB94a]

23. E. Cantu-Paz. Adaptive sampling for noisy problems. In Genetic and Evolutionary Computation Conference, pages 947--958, 2004. Springer. [bibtex-key = Can04]

24. D. Costa and E. A. Silver. Tabu Search When Noise is Present: An Illustration in the Context of Cause and Effect Analysis. Journal of Heuristics, 4:5-23, 1998. [bibtex-key = CoSi98]

25. P. Darwen and J. Pollack. Co-Evolutionary learning on noisy tasks. In Congress on Evolutionary Computation, pages 1724--1731, 1999. IEEE. [bibtex-key = DaPo99]

26. P.J. Darwen and X. Yao. On evolving robust strategies for iterated prisoner's dilemma. In X. Yao, editor,Progress in Evolutionary Computation, volume 956 of LNAI, pages 276--292. Springer, Berlin, 1995. [bibtex-key = DaYa95]

27. I. Das. Robustness optimization for constrained nonlinear programming problems. Engineering Optimization, 32(5):585-618, 2000. [bibtex-key = Das00]

28. A. Di Pietro, L. While, and L. Barone. Applying evolutionary algorithms to problems with noisy, time-consuming fitness functions. In Congress on Evolutionary Computation, pages 1254--1261, 2004. IEEE. [bibtex-key = DWL04]

29. S. Droste. Analysis of the $(1+1)$ EA for a noisy onemax. In K. Deb et.al., editor, Genetic and Evolutionary Computation Conference, volume 3102 of LNCS, pages 1088-1099, 2004. Springer. [bibtex-key = Dro04]

30. J. M. Fitzpatrick and J. J. Grefenstette. Genetic Algorithms in Noisy Environments. Machine Learning, 3:101-120, 1988. [bibtex-key = FiGr88]

31. M. Giacobini, M. Tomassini, and L. Vanneschi. Limiting the Number Fitness Cases in Genetic Programming Using Statistics. In J.J. Merelo Guervos, editor, Parallel Problem Solving from Nature, volume 2439 of LNCS, pages 371--380, 2002. Springer. [bibtex-key = gtv02]

32. D.E. Goldberg, K. Deb, and J.H. Clark. Genetic algorithms, noise, and the sizing of populations. Complex Systems, 6:333-362, 1992. [bibtex-key = GDC92]

33. A. Gosavi. The Effect of Noise on Artificial Intelligence and Meta-Heuristic Techniques. In Artificial Neural Networks in Engineering Conference, volume 12, pages 981--988, 2002. American Society of Mechanical Engineering Press. [bibtex-key = Gos02]

34. J. J. Grefenstette. Genetic algorithms for changing environments. In R. Maenner and B. Manderick, editors, Parallel Problem Solving from Nature, pages 137-144, 1992. North-Holland. [bibtex-key = Gre92]

35. H. Greiner. Robust optical coating design with evolution strategies. Applied Optics, 35(28):5477-5483, 1996. [bibtex-key = Gre96]

36. W. Gutjahr. A converging ACO algorithm for stochastic combinatorial optimization. In A. Albrecht and K. Steinhoefl, editors, Stochastic Algorithms: Foundations and Applications, volume 2827 of LNCS, pages 10--25, 2003. Springer. [bibtex-key = Gut03]

37. U. Hammel and T. Bäck. Evolution Strategies on Noisy Functions, How to Improve Convergence Properties. In Y. Davidor, H. -P. Schwefel, and R. Männer, editors, Parallel Problem Solving from Nature, volume 866 of LNCS, pages 159-168, 1994. Springer. [bibtex-key = HB94]

38. J. Hu, X. Zhong, and E. Goodman. Open-end robust design of analog filters using genetic programming. In Genetic and Evolutionary Computation Conference, pages 1619-1626, 2005. [bibtex-key = Hu05]

39. Evan J. Hughes. Evolutionary Multi-objective Ranking with Uncertainty and Noise. In E. Zitzler et al., editor, Evolutionary Multi-Criterion Optimization, volume 1993 of LNCS, pages 329-343, 2001. Springer. [bibtex-key = Hug01]

40. Gutjahr W. J. and Pflug G. C.. Simulated annealing for noisy cost functions. J. Global Optim., 8(1):1--13, 1996. [bibtex-key = GuPf96]

41. Y. Jin and B. Sendhoff. Trade-off between performance and robustness: An evolutionary multiobjective approach. In Evolutionary Multi-criterion Optimization, LNCS 2632, pages 237--251, 2003. Springer. [bibtex-key = JiSe03]

42. B. Levitan and S. Kauffman. Adaptive Walks with Noisy Fitness Measurements. Molecular Diversity, 1(1):53-68, 1994. [bibtex-key = LeKa95]

43. M. Li, S. Azarm, and V. Aute. A multi-objective genetic algorithm for robust design optimization. In Genetic and Evolutionary Computation Conference, pages 771-778, 2005. [bibtex-key = Li05]

44. S. Markon, D.V. Arnold, T. Bäck, T. Beielstein, and H.-G. Beyer. Thresholding - a selection operator for noisy ES. In Congress on Evolutionary Computation, pages 465--472, 2001. IEEE. [bibtex-key = MABBB01]

45. B. L. Miller. Noise, Sampling, and Efficient Genetic Algorithms. PhD thesis, Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1997.
Note: Available as TR 97001. [bibtex-key = Mi97]

46. B. L. Miller and D. E. Goldberg. Genetic Algorithms, Selection Schemes, and the Varying Effects of Noise. Evolutionary Computation, 4(2):113-131, 1996. [bibtex-key = MiGo97]

47. B.L. Miller and D.E. Goldberg. Genetic algorithms, selection schemes and the varying effects of noise. Technical report IlliGAL Report No. 95009, Department of General Engineering, University of Illinoise at Urbana-Champaign, 1995. [bibtex-key = MiGo95]

48. De.E. Moriarty and R. Miikkulainen. Forming neural networks through efficient and adaptive co-evolution. Evolutionary Computation, 5(4):373--399, 1997. [bibtex-key = MoMi97]

49. I. Paenke, J. Branke, and Y. Jin. Efficient search for robust solutions by means of evolutionary algorithms and fitness approximation. IEEE Transactions on Evolutionary Computation, 2004.
Note: To appear. [bibtex-key = PBJ04]

50. S. Rana, L. D. Whitley, and R. Cogswell. Searching in the Presence of Noise. In H.-M. Voigt, editor, Parallel Problem Solving from Nature, volume 1141 of LNCS, pages 198-207, 1996. Springer. [bibtex-key = RWC96]

51. L. M. Rattray and J. Shapiro. Noisy Fitness Evaluation in Genetic Algorithms and the Dynamics of Learning. In R. K. Belew and M. D. Vose, editors, Foundations of Genetic Algorithms, pages 117-139, 1997. Morgan Kaufmann. [bibtex-key = RaSh97]

52. T. Ray. Constrained robust optimal design using a multi-objective evolutionary algorithm. In Congress on Evolutionary Computation, pages 419--424, 2002. IEEE. [bibtex-key = Ray02]

53. J. Redmond and G. Parker. Actuator placement based on reachable set optimization for expected disturbance. Journal Optimization Theory and Applications, 90(2):279-300, August 1996. [bibtex-key = RePa96]

54. G. Rudolph. A Partial Order Approach to Noisy Fitness Functions. In Congress on Evolutionary Computation, pages 318-325, 2001. IEEE. [bibtex-key = rud01]

55. G. Rudolph. Evolutionary search for minimal elements in partially ordered fitness sets. In Annual Conference on Evolutionary Programming, Berlin, pages 345--353, 1998. Springer. [bibtex-key = Rud98]

56. Y. Sano and H. Kita. Optimization of noisy fitness functions by means of genetic algorithms using history of search with test of estimation. In Congress on Evolutionary Computation, pages 360-365, 2002. IEEE. [bibtex-key = SaKi02]

57. Y. Sano and H. Kita. Optimization of Noisy Fitness Functions by Means of Genetic Algorithms Using History of Search. In M. Schoenauer et al., editor, Parallel Problem Solving from Nature, volume 1917 of LNCS, pages 571-580, 2000. Springer. [bibtex-key = SaKi00]

58. Y. Sano, H. Kita, I. Kamihira, and M. Yamaguchi. Online Optimization of an Engine Controller by means of a Genetic Algorithm using History of Search. In Asia-Pacific Conference on Simulated Evolution and Learning, pages 2929-2934, 2000. Springer. [bibtex-key = SKKY00]

59. A.V. Sebald and D.B. Fogel. Design of fault tolerant neural networks for pattern classification. In D.B. Fogel and W. Atmar, editors, Annual Conference on Evolutionary Programming, pages 90-99, 1992. [bibtex-key = SeFo92]

60. B. Sendhoff, H.-G. Beyer, and M. Olhofer. On noise induced multi-modality in evolutionary algorithms. In Asia-Pacific Conference on Simulated Evolution and Learning, volume 1, pages 219--224, 2002. [bibtex-key = BBO02]

61. P. Stagge. Averaging Efficiently in the Presence of Noise. In A. E. Eiben et al., editor, Parallel Problem Solving from Nature V, volume 1498 of LNCS, pages 188-197, 1998. Springer. [bibtex-key = Sta98]

62. Phillip D. Stroud. Kalman-Extended Genetic Algorithm for Search in Nonstationary Environments with Noisy Fitness Evaluations. IEEE Transactions on Evolutionary Computation, 5(1):66--77, 2001. [bibtex-key = str01]

63. J. Teich. Pareto-Front Exploration with Uncertain Objectives. In E. Zitzler et al., editor, Evolutionary Multi-Criterion Optimization, volume 1993 of LNCS, pages 314-328, 2001. Springer. [bibtex-key = Tei01]

64. A. Thompson. On the automatic design of robust electronics through artificial evolution. In International Conference on Evolvable Systems, pages 13-24, 1998. Springer. [bibtex-key = Tho98]

65. S. Tsutsui and A. Ghosh. Genetic algorithms with a robust solution searching scheme. IEEE Transactions on Evolutionary Computation, 1(3):201--208, 1997. [bibtex-key = TsGh97]

66. S. Tsutsui, A. Ghosh, and Y. Fujimoto. A robust solution searching scheme in genetic search. In Parallel Problem Solving from Nature, pages 543--552, 1996. Springer. [bibtex-key = TGF96]

67. D. Wiesmann, U. Hammel, and T. Bäck. Robust design of multilayer optical coatings by means of evolutionary algorithms. IEEE Transactions on Evolutionary Computation, 2(4):162-167, 1998. [bibtex-key = WHB98]

68. K. deb and H. Gupta. Searching for robust Pareto-optimal solutons in multi-objective optimization. In Evolutionary Multi-Criterion Optimization, LNCS 3410, pages 150-164. Springer, 2005. [bibtex-key = Deb05]

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