Harmony Search Algorithms for Water and Environmental Systems - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 119

damage, casualties, epidemics, contamination of water, shortage of harvest, and eco-
nomic hardship, it is important to predict the flood amount along the timespan.
One popular hydrologic model that routes the flood is Muskingum model (Figure 6)
originally developed by McCarthy [36] after his research of the Muskingum river basin
in Ohio. The Muskingum model had two hydrologic parameters. An additional pa-
rameter was added by Gill [37] in order to represent the characteristic of the flood
more accurately. Up to now, various techniques, such as least-square method (LS)
[37], modified Hooke-Jeeves (HJ) pattern search [38], nonlinear technique (NL) [39],
GA [40], HS [41], Lagrange multiplier (LM) method [42], and Broyden-Fletcher-
Goldfarb-Shanno (BFGS) method [43], have tackled the optimal parameter calibration
of the three-parameter Muskingum model. The objective of the approach is to mini-
mize the difference between real-world flood amounts and computed ones in terms of
the residual sum of squares (SSQ).

Fig. 6. Schematic of Muskingum flood routing model

Table 5. Parameter Calibration Results of Muskingum Model

Algorithms SSQ

LS
HJ
NL
GA
HS 1
HS 2
LM
BFGS

145.69
45.61
156.44
38.24
36.78
36.77
130.49
36.77