Identification of Groundwater Parameter Structure Using Harmony Search Algorithm - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 135

The comparison of the identified zone structures for HS and GA solutions can be
seen in Figure 4. As can be seen from Figure 4, all the zone structures well capture the
true transmissivity field for both HS and GA solutions. Note that Tsai et al. [10] used
the VT as a zonation technique in the GA solution whereas Ayvaz [11] used the FCM
in the HS solution.
As can be seen from Figure 4, both HS and GA can effectively identify the zone
structures of the transmissivity field given in Figure 3. However, the important issue at
that point is to determine the optimum zone structure which best represents the true
transmissivity field. Note that, when the number of zones increases, the number of the
decision variables also increases. For instance, while there are 6 decision variables for
Ω 2 solution ( x and y coordinates of the basis points and embedded transmissivity val-
ues for each zone), the number of them is 15 for Ω 5 solution. As indicated in the previ-
ous section, when the number of decision variables increases, the reliability of them
usually decreases. In other words, uncertainty of the identified parameters usually in-
creases. Hence, uncertainty of the identified parameters is also checked during the
simulation. Figure 5 shows the trace and the norm of the covariance matrix of the iden-
tified parameters which are the two common measures of calculating the PU. As can
be seen from Figure 5, the change in the PU values is not significant for Ω 1 - Ω 4 solu-
tions. However, there is a sudden jump in the Ω 5 solution. This means the reliability of
the identified parameters decreases at that zone structure and the use of Ω 5 as an opti-
mum zone structure is not appropriate in both HS and GA solutions. Therefore, use of
Ω 4 is appropriate as an identified zone structure for both HS and GA.
4 Conclusions
This chapter reviewed the application of the HS algorithm to the solution of parameter
structure identification problems in groundwater modeling. In order to evaluate the
applicability of the HS algorithm to finding the global optimum solution for a parame-
ter structure identification problem, the performance of HS was compared with a GA
based hybrid solution model given in literature. The comparison showed that HS
gives better results than GA in terms of the final objective function values and re-
quires less simulation runs.
Although the identified zone structures of HS well capture the true transmissivity
field for all the zone structures, there are some differences between the identified zone
structures of HS and GA. The reason for this may be associated with a given parame-
terization schemes. Although there are the differences between the identified zone
structures, both the HS and GA based solution models finds the same zone structure
as an optimum one. The results of the comparison also indicate that HS can be effec-
tively used for identifying the parameter zone structures and the associated parameter
values for the solution of the inverse problem.
References
1. Ayvaz, M.T., Karahan, H.: A simulation/optimization model for the identification of unknown
groundwater well locations and pumping rates. Journal of Hydrology 357, 76-92 (2008)
2. Theodossiou, N.: Combined use of simulation and optimization models in aquifer man-
agement: A case study. Transactions on Ecology and the Environment 7, 73-80 (1994)