17 Introduction to Evidence-Based Robust Optimisation
571
31. X. Zhuang, R. Pan, L. Wang, Robustness and reliability consideration in product design
optimization under uncertainty, in IEEE International Conference on Industrial Engineering
and Engineering Management (IEEE, Piscataway, 2011), pp. 132–159. https://doi.org/10.
1109/IEEM.2011.6118131
32. A. Lewis, Robust regularization, Technical Report, Simon Fraser University, Vancouver
(2002)
33. M. Trosset, Taguchi and robust optimization, Technical Report, 96-31, Department of
Computational & Applied Mathematics, Rice University (1996)
34. M. McIlhagga, P. Husbands, R. Ives, A comparison of search techniques on a wing-box
optimisation problem, in Parallel Problem Solving from Nature ed. by H.-M. Voigt, W.
Ebeling, I. Rechenberg, H.-P. Schwefel, vol. 4 (Springer, Berlin, 1996), pp. 614–623
35. J. Herrmann, A genetic algorithm for minimax optimization problems, in Proceedings of the
Congress on Evolutionary Computation, vol. 2 (IEEE Press, New York, 1999), pp. 1099–1103
36. L. El Ghaoui, H. Lebret, Robust solutions to least-squares problems with uncertain data.
SIAM J. Matrix Anal. Appl. 18(4), 1035–1064 (1997)
37. H.-G. Beyer, M. Olhofer, B. Sendhoff, On the behavior of μ/μ I , λ-ES optimizing functions
disturbed by generalized noise, in Foundations of Genetic Algorithms, ed. by K. De Jong, R.
Poli, J. Rowe, vol. 7 (Morgan Kaufman, San Francisco, 2003), pp. 307–328
38. I. Das, Robustness optimization for constrained, nonlinear programming problems, Tech.
Rep. TR97-01, Technical Reports, Department of Computational & Applied Mathematics,
Rice University, Houston, TX (1997)
39. J. Mulvey, R. Vanderbei, S. Zenios, Robust optimization of large-scale systems. Oper. Res.
43(2), 264–281 (1995)
40. W. Chen, M. Wiecek, J. Zhang, Quality utility a compromise programming approach to robust
design. ASME J. Mech. Des. 121(2), 179–187 (1999)
41. N. Rolander, J. Rambo, Y. Joshi, J. Allen, F. Mistree, An approach to robust design of
turbulent convective systems. J. Mech. Des. 128(4), 844–855 (2006)
42. Y. Jin, B. Sendhoff, Trade-off between performance and robustness: an evolutionary multiobjective approach, in Evolutionary Multi-Criterion Optimization: Second International
Conference, EMO 2003, ed. by C. Fonseca, P. Fleming, E. Zitzler, K. Deb (Springer,
Heidelberg, 2003), pp. 237–251
43. W.L. Oberkampf, J.C. Helton, Investigation of evidence theory for engineering applications,
in Fourth Non-Deterministic Approaches Forum, vol. 1569 (AIAA, Reston, 2002)
44. L. Simoes, Fuzzy optimization of structures by the two-phase method. Comput. Struct.
79(2628), 2481–2490 (2001)
45. F. Campos, J. Villar, M. Jimenez, Robust solutions using fuzzy chance constraints. Eng.
Optim. 38(6), 627–645 (2006)
46. J. Liu, J.-B. Yang, J. Wang, H.S. Sii, Review of uncertainty reasoning approaches as guidance
for maritime and offshore safety-based assessment. J. UK Saf. Reliab. Soc. 23(1), 63–80
(2002)
47. M. Vasile, Robust mission design through evidence theory and multiagent collaborative
search. Ann. New York Acad. Sci. 1065, 152–173 (2005)
48. N. Croisard, M. Vasile, S. Kemble, G. Radice, Preliminary space mission design under
uncertainty. Acta Astronaut. 66, 5–6 (2010)
49. R.W. Chaney, A method of centers algorithm for certain minimax problems. Math. Program.
22(1), 202–226 (1982)
50. R. Klessig, E. Polak, A method of feasible directions using function approximations, with
applications to min max problems. J. Math. Anal. Appl. 41(3) 583–602 (1973)
51. V. Panin, Linearization method for continuous min-max problem. Cybernetics 17(2), 239–243
(1981)
52. Y. Danilin, V. Panin, B. Pshenichnyi, On the Shannon Gapacity of a graph. Notes Control Inf.
Sci. 23(30), 51–57 (1982)
53. V.F. Damyanov, VN Malozemov (Wiley, New York, 1974)
571
31. X. Zhuang, R. Pan, L. Wang, Robustness and reliability consideration in product design
optimization under uncertainty, in IEEE International Conference on Industrial Engineering
and Engineering Management (IEEE, Piscataway, 2011), pp. 132–159. https://doi.org/10.
1109/IEEM.2011.6118131
32. A. Lewis, Robust regularization, Technical Report, Simon Fraser University, Vancouver
(2002)
33. M. Trosset, Taguchi and robust optimization, Technical Report, 96-31, Department of
Computational & Applied Mathematics, Rice University (1996)
34. M. McIlhagga, P. Husbands, R. Ives, A comparison of search techniques on a wing-box
optimisation problem, in Parallel Problem Solving from Nature ed. by H.-M. Voigt, W.
Ebeling, I. Rechenberg, H.-P. Schwefel, vol. 4 (Springer, Berlin, 1996), pp. 614–623
35. J. Herrmann, A genetic algorithm for minimax optimization problems, in Proceedings of the
Congress on Evolutionary Computation, vol. 2 (IEEE Press, New York, 1999), pp. 1099–1103
36. L. El Ghaoui, H. Lebret, Robust solutions to least-squares problems with uncertain data.
SIAM J. Matrix Anal. Appl. 18(4), 1035–1064 (1997)
37. H.-G. Beyer, M. Olhofer, B. Sendhoff, On the behavior of μ/μ I , λ-ES optimizing functions
disturbed by generalized noise, in Foundations of Genetic Algorithms, ed. by K. De Jong, R.
Poli, J. Rowe, vol. 7 (Morgan Kaufman, San Francisco, 2003), pp. 307–328
38. I. Das, Robustness optimization for constrained, nonlinear programming problems, Tech.
Rep. TR97-01, Technical Reports, Department of Computational & Applied Mathematics,
Rice University, Houston, TX (1997)
39. J. Mulvey, R. Vanderbei, S. Zenios, Robust optimization of large-scale systems. Oper. Res.
43(2), 264–281 (1995)
40. W. Chen, M. Wiecek, J. Zhang, Quality utility a compromise programming approach to robust
design. ASME J. Mech. Des. 121(2), 179–187 (1999)
41. N. Rolander, J. Rambo, Y. Joshi, J. Allen, F. Mistree, An approach to robust design of
turbulent convective systems. J. Mech. Des. 128(4), 844–855 (2006)
42. Y. Jin, B. Sendhoff, Trade-off between performance and robustness: an evolutionary multiobjective approach, in Evolutionary Multi-Criterion Optimization: Second International
Conference, EMO 2003, ed. by C. Fonseca, P. Fleming, E. Zitzler, K. Deb (Springer,
Heidelberg, 2003), pp. 237–251
43. W.L. Oberkampf, J.C. Helton, Investigation of evidence theory for engineering applications,
in Fourth Non-Deterministic Approaches Forum, vol. 1569 (AIAA, Reston, 2002)
44. L. Simoes, Fuzzy optimization of structures by the two-phase method. Comput. Struct.
79(2628), 2481–2490 (2001)
45. F. Campos, J. Villar, M. Jimenez, Robust solutions using fuzzy chance constraints. Eng.
Optim. 38(6), 627–645 (2006)
46. J. Liu, J.-B. Yang, J. Wang, H.S. Sii, Review of uncertainty reasoning approaches as guidance
for maritime and offshore safety-based assessment. J. UK Saf. Reliab. Soc. 23(1), 63–80
(2002)
47. M. Vasile, Robust mission design through evidence theory and multiagent collaborative
search. Ann. New York Acad. Sci. 1065, 152–173 (2005)
48. N. Croisard, M. Vasile, S. Kemble, G. Radice, Preliminary space mission design under
uncertainty. Acta Astronaut. 66, 5–6 (2010)
49. R.W. Chaney, A method of centers algorithm for certain minimax problems. Math. Program.
22(1), 202–226 (1982)
50. R. Klessig, E. Polak, A method of feasible directions using function approximations, with
applications to min max problems. J. Math. Anal. Appl. 41(3) 583–602 (1973)
51. V. Panin, Linearization method for continuous min-max problem. Cybernetics 17(2), 239–243
(1981)
52. Y. Danilin, V. Panin, B. Pshenichnyi, On the Shannon Gapacity of a graph. Notes Control Inf.
Sci. 23(30), 51–57 (1982)
53. V.F. Damyanov, VN Malozemov (Wiley, New York, 1974)