Identification of Groundwater Parameter Structure Using Harmony Search Algorithm - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 134

3.2 Comparison of the Identified Results

Table 1 and 2 list the results of GA [10] and HS [11]. After comparing both tables, it
can be seen that RE values decrease with the increase of the zone numbers. However,
the improvement of the RE is not significant after Ω 3 . As can be seen, HS finds better
results than GA (+ grid search + BFGS) in terms of the final RE values. Also, HS re-
quires fewer simulation runs than GA. Although the obtained transmissivities are
nearly same in Ω 1 , they are different at the others. The reason of this is related to the
differences of the identified zone structures.

Table 1. Identified results for different zone structures using HS

Structures RE # of Simulations T 1 T 2 T 3 T 4 T 5

Ω 1 275.95 3,690 208 − − − −

Ω 2 60.46 12,732 281 56 − − −

Ω 3 2.50 23,486 585 233 58 − −

Ω 4 2.33 29,370 499 259 218 57 −

Ω 5 2.31 33,363 541 557 284 214 56

Table 2. Identified results for different zone structures using GA

Structures RE # of Simulations T 1 T 2 T 3 T 4 T 5

Ω 1 280.11 10,000 207 − − − −

Ω 2 71.60 15,000 253 46 − − −

Ω 3 3.55 25,000 517 228 52 − −

Ω 4 2.62 40,000 501 299 164 54 −

Ω 5 2.61 50,000 520 279 172 48 51

80 60

(a) (b)

70

50

60

40

50

40

30

30

20

20

10

10

0 0

1

1

2 2

HS
GA

3 HS

GA

3

4 4

5

5

Number of Zones

Number of Zones

(a) (b)

Fig. 5. Variation of the PU values for different zone structures; (a): for the trace of the covari-
ance matrix; (b): for the norm of the covariance matrix