Abstract

A simple formula describing the dependence of the index of refraction of water on wavelength in the visible and the near-UV ranges and at temperature from 0 °C to 100 °C is given. Parameters of the formula were determined by minimization of discrepancies between calculated and experimental data by use of an elite genetic algorithm with adaptive mutations. This algorithm was devised with a particular application in mind, the determination of model parameters. Its superiority over the simple genetic algorithm in locating the global minimum was demonstrated on a family of multiminima test functions for as many as 100 variables.

© 1999 Optical Society of America

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  1. S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, pp. 671–680 (1983).
    [CrossRef]
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  3. A. B. Djurišić, A. D. Rakić, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
    [CrossRef]
  4. A. D. Rakić, J. M. Elazar, A. B. Djurišić, “Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
    [CrossRef]
  5. T. H. Han, W. W. Chang, “Estimation of the Gilbert model parameters using the simulated annealing method,” Electron. Lett. 32, 1256–1258 (1996).
    [CrossRef]
  6. A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogeneously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
    [CrossRef]
  7. A. D. Rakić, M. L. Majewski, “Modeling the optical dielectric function of GaAs and AlAs: Extension of Adachi’s model,” J. Appl. Phys. 80, 5909–5914 (1996).
    [CrossRef]
  8. M. K. Vai, S. Prasad, N. C. Li, F. Kai, “Modeling the microwave devices using simulated annealing optimization,” IEEE Trans. Electron. Devices 36, 761–762 (1989).
    [CrossRef]
  9. M. W. Gutowski, “Smooth genetic algorithm,” J. Phys. A Math. Gen. 27, 7893–7905 (1994).
    [CrossRef]
  10. H. Műhlenbein, D. Schlierkamp-Voosen, “Predictive models for the breeder genetic algorithm I. Continuous parameter optimization,” Evol. Comput. 1, 25–41 (1993).
    [CrossRef]
  11. K. P. Wong, Y. W. Wong, “Floating-point number coding method for genetic algorithms,” in Proceedings of IEEE Australian and New Zealand Conference on Intelligent Information Systems 93 (University of Perth, Western Australia, 1993), pp. 512–516.
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    [CrossRef]
  13. A. B. Djurišić, J. M. Elazar, A. D. Rakić, “Modeling the optical constants of solids using genetic algorithms with parameter space size adjustment,” Opt. Commun. 134, 407–414 (1997).
    [CrossRef]
  14. A. Chipperfield, R. Fleming, “Genetic algorithms in control system engineering,” Control Comput. 23, 88–94 (1995).
  15. R. Vemuri, R. Vemuri, “Genetic algorithm for MCM partitioning,” Electron. Lett. 30, 1270–1272 (1994).
    [CrossRef]
  16. S. H. Clearwater, T. Hogg, “Problem structure heuristics and scaling behavior for genetic algorithm,” Artif. Intell. 81, 327–347 (1996).
    [CrossRef]
  17. R. R. Brooks, S. S. Iyengar, J. Chen, “Automatic correlation and calibration of noisy sensor readingsusing elite genetic algorithms,” Artif. Intell. 81, 329–354 (1996).
  18. F. Curatelli, “Implementation and evaluation of genetic algorithms for system partitioning,” Int. J. Electron. 78, 435–437 (1995).
    [CrossRef]
  19. T. Bäck, H.-P. Schwefel, “Evolution strategies I: variants and their computational application,” in Genetic Algorithms in Engineering and Computer Science, G. Winter, J. Periaux, M. Galan, P. Cuesta, eds. (Wiley, New York, 1995), pp. 111–126.
  20. D. Raynolds, J. Gonatann, “Stochastic modelling of genetic algorithms,” Artif. Intell. 82, 303–330 (1996).
    [CrossRef]
  21. F. Aluffi-Pentini, V. Parisi, F. Zirilli, “Global optimization and stochastic differential equations,” J. Optim. Theory Appl. 47, 1–16 (1985).
    [CrossRef]
  22. A. Dekkers, E. Aarts, “Global optimization and simulated annealing,” Math. Programming, 50, 367–393 (1991).
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  24. P. D. T. Huibers, “Models for the wavelength dependence of the index of refraction of water,” Appl. Opt. 36, 3785–3787 (1997).
    [CrossRef] [PubMed]
  25. G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
    [CrossRef]
  26. W. Matthaus, “Empirische Gleichungen fúr den Brechungsindex des Meerwassers,” Beitr. Meereskd. 33, 73–78 (1974).
  27. X. Quan, E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. 34, 3477–3480 (1995).
    [CrossRef] [PubMed]
  28. P. Schiebener, J. Straub, J. M. H. Levelt, S. Engers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
    [CrossRef]

1997 (3)

A. B. Djurišić, A. D. Rakić, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

A. B. Djurišić, J. M. Elazar, A. D. Rakić, “Modeling the optical constants of solids using genetic algorithms with parameter space size adjustment,” Opt. Commun. 134, 407–414 (1997).
[CrossRef]

P. D. T. Huibers, “Models for the wavelength dependence of the index of refraction of water,” Appl. Opt. 36, 3785–3787 (1997).
[CrossRef] [PubMed]

1996 (6)

S. H. Clearwater, T. Hogg, “Problem structure heuristics and scaling behavior for genetic algorithm,” Artif. Intell. 81, 327–347 (1996).
[CrossRef]

R. R. Brooks, S. S. Iyengar, J. Chen, “Automatic correlation and calibration of noisy sensor readingsusing elite genetic algorithms,” Artif. Intell. 81, 329–354 (1996).

D. Raynolds, J. Gonatann, “Stochastic modelling of genetic algorithms,” Artif. Intell. 82, 303–330 (1996).
[CrossRef]

T. H. Han, W. W. Chang, “Estimation of the Gilbert model parameters using the simulated annealing method,” Electron. Lett. 32, 1256–1258 (1996).
[CrossRef]

A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogeneously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
[CrossRef]

A. D. Rakić, M. L. Majewski, “Modeling the optical dielectric function of GaAs and AlAs: Extension of Adachi’s model,” J. Appl. Phys. 80, 5909–5914 (1996).
[CrossRef]

1995 (4)

A. D. Rakić, J. M. Elazar, A. B. Djurišić, “Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

F. Curatelli, “Implementation and evaluation of genetic algorithms for system partitioning,” Int. J. Electron. 78, 435–437 (1995).
[CrossRef]

A. Chipperfield, R. Fleming, “Genetic algorithms in control system engineering,” Control Comput. 23, 88–94 (1995).

X. Quan, E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. 34, 3477–3480 (1995).
[CrossRef] [PubMed]

1994 (3)

R. Vemuri, R. Vemuri, “Genetic algorithm for MCM partitioning,” Electron. Lett. 30, 1270–1272 (1994).
[CrossRef]

K. P. Wong, Y. W. Wong, “Genetic and genetic/simulated annealing approaches to economic dispatch,” IEE Proc. Gen. Transm. Distrib. 141, 507–513 (1994).
[CrossRef]

M. W. Gutowski, “Smooth genetic algorithm,” J. Phys. A Math. Gen. 27, 7893–7905 (1994).
[CrossRef]

1993 (1)

H. Műhlenbein, D. Schlierkamp-Voosen, “Predictive models for the breeder genetic algorithm I. Continuous parameter optimization,” Evol. Comput. 1, 25–41 (1993).
[CrossRef]

1991 (1)

A. Dekkers, E. Aarts, “Global optimization and simulated annealing,” Math. Programming, 50, 367–393 (1991).

1990 (1)

P. Schiebener, J. Straub, J. M. H. Levelt, S. Engers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

1989 (1)

M. K. Vai, S. Prasad, N. C. Li, F. Kai, “Modeling the microwave devices using simulated annealing optimization,” IEEE Trans. Electron. Devices 36, 761–762 (1989).
[CrossRef]

1985 (1)

F. Aluffi-Pentini, V. Parisi, F. Zirilli, “Global optimization and stochastic differential equations,” J. Optim. Theory Appl. 47, 1–16 (1985).
[CrossRef]

1983 (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, pp. 671–680 (1983).
[CrossRef]

1977 (1)

G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
[CrossRef]

1974 (1)

W. Matthaus, “Empirische Gleichungen fúr den Brechungsindex des Meerwassers,” Beitr. Meereskd. 33, 73–78 (1974).

Aarts, E.

A. Dekkers, E. Aarts, “Global optimization and simulated annealing,” Math. Programming, 50, 367–393 (1991).

Aluffi-Pentini, F.

F. Aluffi-Pentini, V. Parisi, F. Zirilli, “Global optimization and stochastic differential equations,” J. Optim. Theory Appl. 47, 1–16 (1985).
[CrossRef]

Bäck, T.

T. Bäck, H.-P. Schwefel, “Evolution strategies I: variants and their computational application,” in Genetic Algorithms in Engineering and Computer Science, G. Winter, J. Periaux, M. Galan, P. Cuesta, eds. (Wiley, New York, 1995), pp. 111–126.

Brooks, R. R.

R. R. Brooks, S. S. Iyengar, J. Chen, “Automatic correlation and calibration of noisy sensor readingsusing elite genetic algorithms,” Artif. Intell. 81, 329–354 (1996).

Chang, W. W.

T. H. Han, W. W. Chang, “Estimation of the Gilbert model parameters using the simulated annealing method,” Electron. Lett. 32, 1256–1258 (1996).
[CrossRef]

Chen, J.

R. R. Brooks, S. S. Iyengar, J. Chen, “Automatic correlation and calibration of noisy sensor readingsusing elite genetic algorithms,” Artif. Intell. 81, 329–354 (1996).

Chipperfield, A.

A. Chipperfield, R. Fleming, “Genetic algorithms in control system engineering,” Control Comput. 23, 88–94 (1995).

Clearwater, S. H.

S. H. Clearwater, T. Hogg, “Problem structure heuristics and scaling behavior for genetic algorithm,” Artif. Intell. 81, 327–347 (1996).
[CrossRef]

Curatelli, F.

F. Curatelli, “Implementation and evaluation of genetic algorithms for system partitioning,” Int. J. Electron. 78, 435–437 (1995).
[CrossRef]

Dekkers, A.

A. Dekkers, E. Aarts, “Global optimization and simulated annealing,” Math. Programming, 50, 367–393 (1991).

Djurišic, A. B.

A. B. Djurišić, A. D. Rakić, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

A. B. Djurišić, J. M. Elazar, A. D. Rakić, “Modeling the optical constants of solids using genetic algorithms with parameter space size adjustment,” Opt. Commun. 134, 407–414 (1997).
[CrossRef]

A. D. Rakić, J. M. Elazar, A. B. Djurišić, “Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

Elazar, J. M.

A. B. Djurišić, J. M. Elazar, A. D. Rakić, “Modeling the optical constants of solids using genetic algorithms with parameter space size adjustment,” Opt. Commun. 134, 407–414 (1997).
[CrossRef]

A. B. Djurišić, A. D. Rakić, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

A. D. Rakić, J. M. Elazar, A. B. Djurišić, “Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

Engers, S.

P. Schiebener, J. Straub, J. M. H. Levelt, S. Engers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Fleming, R.

A. Chipperfield, R. Fleming, “Genetic algorithms in control system engineering,” Control Comput. 23, 88–94 (1995).

Franke, A.

A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogeneously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
[CrossRef]

Fry, E. S.

Gallagher, J. S.

P. Schiebener, J. Straub, J. M. H. Levelt, S. Engers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, pp. 671–680 (1983).
[CrossRef]

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine learning (Addison-Wesley, Reading, Mass., 1989).

Gonatann, J.

D. Raynolds, J. Gonatann, “Stochastic modelling of genetic algorithms,” Artif. Intell. 82, 303–330 (1996).
[CrossRef]

Gutowski, M. W.

M. W. Gutowski, “Smooth genetic algorithm,” J. Phys. A Math. Gen. 27, 7893–7905 (1994).
[CrossRef]

Han, T. H.

T. H. Han, W. W. Chang, “Estimation of the Gilbert model parameters using the simulated annealing method,” Electron. Lett. 32, 1256–1258 (1996).
[CrossRef]

Hogg, T.

S. H. Clearwater, T. Hogg, “Problem structure heuristics and scaling behavior for genetic algorithm,” Artif. Intell. 81, 327–347 (1996).
[CrossRef]

Huibers, P. D. T.

Iyengar, S. S.

R. R. Brooks, S. S. Iyengar, J. Chen, “Automatic correlation and calibration of noisy sensor readingsusing elite genetic algorithms,” Artif. Intell. 81, 329–354 (1996).

Kai, F.

M. K. Vai, S. Prasad, N. C. Li, F. Kai, “Modeling the microwave devices using simulated annealing optimization,” IEEE Trans. Electron. Devices 36, 761–762 (1989).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, pp. 671–680 (1983).
[CrossRef]

Levelt, J. M. H.

P. Schiebener, J. Straub, J. M. H. Levelt, S. Engers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Li, N. C.

M. K. Vai, S. Prasad, N. C. Li, F. Kai, “Modeling the microwave devices using simulated annealing optimization,” IEEE Trans. Electron. Devices 36, 761–762 (1989).
[CrossRef]

Majewski, M. L.

A. D. Rakić, M. L. Majewski, “Modeling the optical dielectric function of GaAs and AlAs: Extension of Adachi’s model,” J. Appl. Phys. 80, 5909–5914 (1996).
[CrossRef]

Matthaus, W.

W. Matthaus, “Empirische Gleichungen fúr den Brechungsindex des Meerwassers,” Beitr. Meereskd. 33, 73–78 (1974).

McNeil, G. T.

G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
[CrossRef]

Muhlenbein, H.

H. Műhlenbein, D. Schlierkamp-Voosen, “Predictive models for the breeder genetic algorithm I. Continuous parameter optimization,” Evol. Comput. 1, 25–41 (1993).
[CrossRef]

Parisi, V.

F. Aluffi-Pentini, V. Parisi, F. Zirilli, “Global optimization and stochastic differential equations,” J. Optim. Theory Appl. 47, 1–16 (1985).
[CrossRef]

Prasad, S.

M. K. Vai, S. Prasad, N. C. Li, F. Kai, “Modeling the microwave devices using simulated annealing optimization,” IEEE Trans. Electron. Devices 36, 761–762 (1989).
[CrossRef]

Quan, X.

Rakic, A. D.

A. B. Djurišić, J. M. Elazar, A. D. Rakić, “Modeling the optical constants of solids using genetic algorithms with parameter space size adjustment,” Opt. Commun. 134, 407–414 (1997).
[CrossRef]

A. B. Djurišić, A. D. Rakić, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

A. D. Rakić, M. L. Majewski, “Modeling the optical dielectric function of GaAs and AlAs: Extension of Adachi’s model,” J. Appl. Phys. 80, 5909–5914 (1996).
[CrossRef]

A. D. Rakić, J. M. Elazar, A. B. Djurišić, “Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

Raynolds, D.

D. Raynolds, J. Gonatann, “Stochastic modelling of genetic algorithms,” Artif. Intell. 82, 303–330 (1996).
[CrossRef]

Schiebener, P.

P. Schiebener, J. Straub, J. M. H. Levelt, S. Engers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Schlierkamp-Voosen, D.

H. Műhlenbein, D. Schlierkamp-Voosen, “Predictive models for the breeder genetic algorithm I. Continuous parameter optimization,” Evol. Comput. 1, 25–41 (1993).
[CrossRef]

Schwefel, H.-P.

T. Bäck, H.-P. Schwefel, “Evolution strategies I: variants and their computational application,” in Genetic Algorithms in Engineering and Computer Science, G. Winter, J. Periaux, M. Galan, P. Cuesta, eds. (Wiley, New York, 1995), pp. 111–126.

Stendal, A.

A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogeneously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
[CrossRef]

Stenzel, O.

A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogeneously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
[CrossRef]

Straub, J.

P. Schiebener, J. Straub, J. M. H. Levelt, S. Engers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Vai, M. K.

M. K. Vai, S. Prasad, N. C. Li, F. Kai, “Modeling the microwave devices using simulated annealing optimization,” IEEE Trans. Electron. Devices 36, 761–762 (1989).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, pp. 671–680 (1983).
[CrossRef]

Vemuri, R.

R. Vemuri, R. Vemuri, “Genetic algorithm for MCM partitioning,” Electron. Lett. 30, 1270–1272 (1994).
[CrossRef]

R. Vemuri, R. Vemuri, “Genetic algorithm for MCM partitioning,” Electron. Lett. 30, 1270–1272 (1994).
[CrossRef]

von Borczyskowski, C.

A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogeneously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
[CrossRef]

Wong, K. P.

K. P. Wong, Y. W. Wong, “Genetic and genetic/simulated annealing approaches to economic dispatch,” IEE Proc. Gen. Transm. Distrib. 141, 507–513 (1994).
[CrossRef]

K. P. Wong, Y. W. Wong, “Floating-point number coding method for genetic algorithms,” in Proceedings of IEEE Australian and New Zealand Conference on Intelligent Information Systems 93 (University of Perth, Western Australia, 1993), pp. 512–516.

Wong, Y. W.

K. P. Wong, Y. W. Wong, “Genetic and genetic/simulated annealing approaches to economic dispatch,” IEE Proc. Gen. Transm. Distrib. 141, 507–513 (1994).
[CrossRef]

K. P. Wong, Y. W. Wong, “Floating-point number coding method for genetic algorithms,” in Proceedings of IEEE Australian and New Zealand Conference on Intelligent Information Systems 93 (University of Perth, Western Australia, 1993), pp. 512–516.

Zirilli, F.

F. Aluffi-Pentini, V. Parisi, F. Zirilli, “Global optimization and stochastic differential equations,” J. Optim. Theory Appl. 47, 1–16 (1985).
[CrossRef]

Appl. Opt. (2)

Artif. Intell. (3)

D. Raynolds, J. Gonatann, “Stochastic modelling of genetic algorithms,” Artif. Intell. 82, 303–330 (1996).
[CrossRef]

S. H. Clearwater, T. Hogg, “Problem structure heuristics and scaling behavior for genetic algorithm,” Artif. Intell. 81, 327–347 (1996).
[CrossRef]

R. R. Brooks, S. S. Iyengar, J. Chen, “Automatic correlation and calibration of noisy sensor readingsusing elite genetic algorithms,” Artif. Intell. 81, 329–354 (1996).

Beitr. Meereskd. (1)

W. Matthaus, “Empirische Gleichungen fúr den Brechungsindex des Meerwassers,” Beitr. Meereskd. 33, 73–78 (1974).

Control Comput. (1)

A. Chipperfield, R. Fleming, “Genetic algorithms in control system engineering,” Control Comput. 23, 88–94 (1995).

Electron. Lett. (2)

R. Vemuri, R. Vemuri, “Genetic algorithm for MCM partitioning,” Electron. Lett. 30, 1270–1272 (1994).
[CrossRef]

T. H. Han, W. W. Chang, “Estimation of the Gilbert model parameters using the simulated annealing method,” Electron. Lett. 32, 1256–1258 (1996).
[CrossRef]

Evol. Comput. (1)

H. Műhlenbein, D. Schlierkamp-Voosen, “Predictive models for the breeder genetic algorithm I. Continuous parameter optimization,” Evol. Comput. 1, 25–41 (1993).
[CrossRef]

IEE Proc. Gen. Transm. Distrib. (1)

K. P. Wong, Y. W. Wong, “Genetic and genetic/simulated annealing approaches to economic dispatch,” IEE Proc. Gen. Transm. Distrib. 141, 507–513 (1994).
[CrossRef]

IEEE Trans. Electron. Devices (1)

M. K. Vai, S. Prasad, N. C. Li, F. Kai, “Modeling the microwave devices using simulated annealing optimization,” IEEE Trans. Electron. Devices 36, 761–762 (1989).
[CrossRef]

Int. J. Electron. (1)

F. Curatelli, “Implementation and evaluation of genetic algorithms for system partitioning,” Int. J. Electron. 78, 435–437 (1995).
[CrossRef]

J. Appl. Phys. (1)

A. D. Rakić, M. L. Majewski, “Modeling the optical dielectric function of GaAs and AlAs: Extension of Adachi’s model,” J. Appl. Phys. 80, 5909–5914 (1996).
[CrossRef]

J. Optim. Theory Appl. (1)

F. Aluffi-Pentini, V. Parisi, F. Zirilli, “Global optimization and stochastic differential equations,” J. Optim. Theory Appl. 47, 1–16 (1985).
[CrossRef]

J. Phys. A Math. Gen. (1)

M. W. Gutowski, “Smooth genetic algorithm,” J. Phys. A Math. Gen. 27, 7893–7905 (1994).
[CrossRef]

J. Phys. Chem. Ref. Data (1)

P. Schiebener, J. Straub, J. M. H. Levelt, S. Engers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Math. Programming (1)

A. Dekkers, E. Aarts, “Global optimization and simulated annealing,” Math. Programming, 50, 367–393 (1991).

Opt. Commun. (1)

A. B. Djurišić, J. M. Elazar, A. D. Rakić, “Modeling the optical constants of solids using genetic algorithms with parameter space size adjustment,” Opt. Commun. 134, 407–414 (1997).
[CrossRef]

Opt. Eng. (1)

G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
[CrossRef]

Phys. Rev. E (2)

A. B. Djurišić, A. D. Rakić, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

A. D. Rakić, J. M. Elazar, A. B. Djurišić, “Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

Pure Appl. Opt. (1)

A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogeneously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
[CrossRef]

Science (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, pp. 671–680 (1983).
[CrossRef]

Other (4)

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine learning (Addison-Wesley, Reading, Mass., 1989).

K. P. Wong, Y. W. Wong, “Floating-point number coding method for genetic algorithms,” in Proceedings of IEEE Australian and New Zealand Conference on Intelligent Information Systems 93 (University of Perth, Western Australia, 1993), pp. 512–516.

T. Bäck, H.-P. Schwefel, “Evolution strategies I: variants and their computational application,” in Genetic Algorithms in Engineering and Computer Science, G. Winter, J. Periaux, M. Galan, P. Cuesta, eds. (Wiley, New York, 1995), pp. 111–126.

“Optical Constants,” in Group III: Condensed Matter, Vol. 38A of Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, New Series, K.-H. Hellwege, O. Madelung, eds. (Springer-VerlagBerlin, 1996), pp. 17–22.

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Figures (9)

Fig. 1
Fig. 1

Illustration of GA: shades of gray represent fitness: the lighter the shade, the more fit the gene.

Fig. 2
Fig. 2

Multiminima test function g of two variables.

Fig. 3
Fig. 3

Comparison of the algorithms for the function g of x i ∈ [-10, 10], i = 1, n v , for n v = 20, 50, 100 variables.

Fig. 4
Fig. 4

Index of refraction as a function of temperature.

Fig. 5
Fig. 5

Index of refraction versus wavelength for t = 20 °C.

Fig. 6
Fig. 6

Family of curves for index of refraction versus wavelength for t equal to 0, 20, 40, 60, and 80 °C.

Fig. 7
Fig. 7

Family of curves for index of refraction versus wavelength for t equal to 10, 30, 50, 70, and 90 °C.

Fig. 8
Fig. 8

Family of curves for index of refraction versus wavelength curves for t equal to 15, 25, 35, 45, 55, 65, 75, 85, and 95 °C.

Fig. 9
Fig. 9

Family of curves for index of refraction versus temperature for λ equal to 289.4, 404.7, 435.8, and 589.3 nm.

Tables (2)

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Table 1 Values of Model Parameters

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Table 2 Average Absolute Errors between Calculated and Experimental Values of the Refractive Index of Water

Equations (7)

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pk=plk+puk-plkr,
Fi=fii=1N fi,
pnew-uk=pold-uk-cpold-uk-μˆk,
pnew-lk=pold-lk+cμˆk-pold-lk,
gx=πnk1 sin2πy1+i=1n-1yi-k22×1+k1sin2πyi+1+yn-k22,
nλ=A+Bλ2+Cλ4+.
nλ, t=A0+A1t+A2t2+B0+B1t+B2t2λ2+C0+C1t+C2t2λ4.

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