Geoscience Reference
In-Depth Information
Table 1.
Comparison of the original and enhanced SCE-UA algorithms.
Original SCE-UA
Enhanced SCE-UA
No. of complexes;
Function name
population size
NF
AFE
θ
NF
AFE
Goldstein-Price (2D)
(2; 10)
2
162
0.5
0
86
Rosenbrock (2D)
(2; 10)
0
274
0.2
0
214
6-hump camelback (2D)
(2; 10)
0
162
0.5
0
87
Rastrigin (2D)
(2; 10)
34
340
0.0
20
303
Griewank (2D)
(2; 10)
12
355
0.2
9
289
Schwefel (2D)
(2; 10)
53
257
0.3
14
177
Shekel (4D)
(3; 27)
23
494
0.2
0
415
Hartman (6D)
(6; 78)
10
673
0.4
0
469
Neumaier (10D)
(50; 1,050)
0
20,989
0.6
0
9,760
Griewank (10D)
(50; 1,050)
0
28,843
0.6
0
15,438
Note
: NF: number of failures in 100 runs and AFE: average function evaluations.
in the range 0.1-0.5 and values higher than this lead to an increase in
the number of failures. It is clearly seen that the proposed enhancements
significantly reduce the NF and also the AFE of the SCE-UA algorithm.
Thus, the proposed enhancements lead to significant improvement in the
robustness and eciency of the SCE-UA.
5. Conclusions
The present study proposes two enhancements to the SCE-UA model-
calibrating algorithm, which is compared with the original SCE-UA on
a suite of test functions. A scheme to systematically, instead of randomly,
generating the initial population leads to much better exploration and a
significant reduction in the number of failures. The second enhancement,
a modification to the downhill simplex search method leads to enhanced
exploitation, which in turn leads to a significant reduction in the func-
tion evaluations to reach the global optimum. Thus, the two proposed
enhancements improve the robustness and eciency of the SCE-UA model-
calibrating algorithm.
Acknowledgments
The authors wish to thank Dr. Q. Duan of the NOAA (National Oceanic
and Atmospheric Administration, USA) for kindly providing the source
code for the SCE-UA (version 2.2).
