Harmony Search Algorithm for Transport Energy Demand Modeling - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 166

4.2 HASTEDE Applications

For the application of each HASTEDE model for estimating transport energy de-
mand, the HS parameters are set as in Table 1. Lee et al. [39] have recommended
the HS parameter values: HMCR range between 0.7 and 0.95; PAR values range
between 0.2 and 0.5; and HMS values range between 10 and 50 to produce good
performance of the HS algorithm. Thus, they are taken within the bounds of rec-
ommended values.

Table 1. HS parameters for HASTEDE models

HASTEDE lin HASTEDE exp HASTEDE quad

HMS 20

HMCR 0.90

PAR 0.40

Number of weighting variables 4 7 7

Number of improvisations 100,000

The solution of the linear form of the HASTEDE model is:

HASTEDE lin = 0.0077 X 1 - 0.0351 X 2 + 0.2473 X 3 + 2.999 (6)

The solution of the exponential form of the HASTEDE model is:

HASTEDE exp = 1.7727 X 1 0.1822 - 0.3796 X 2 0.7974 + 0.4525X 3 0.9297 + 4.2140 (7)

The solution of the quadratic form of the HASTEDE model is:

HASTEDE quad = 0.0888X 1 - 0.9775X 2 - 0.0718X 3 - 0.0019X 1 X 2
+ 0.0008X 1 X 3 +0.0062X 2 X 3 + 4.8984

(8)

Solution of the above models is performed for 20 solution vectors and it is per-
formed according to the procedure defined Section in 3 for the period of 1970-1995 in
order to obtain weighting parameters for each of the HASTEDE models. Convergence
of models is given in Figure 3 in logarithmic scale. As can be seen in the figure, the
HASTEDE models showed a steady convergence for this problem.
About two-thirds of the data are used for estimating weighting parameters and one-
third of the data are used for testing the HASTEDE models. The relative errors ob-
tained for the example in 2001 is about 12, 16, 31, 45 percent for linear, exponential,
quadratic, and MENR, respectively, but relative errors in 2005 are respectively 14, 12,
17, 42 percent.
The values of the objective function (Eq. 5) are given in Table 2. The quadratic
form of the HASTEDE model provides the lowest SSE, and it may be used for future
energy prediction for planning purposes.