Harmony Search Algorithms for Water and Environmental Systems - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 120

Table 5 shows the computational results of various algorithms. HS found the near-
optima (SSQ = 36.78 and 36.77) that are very close to global optimum reached by
BFGS (SSQ = 36.77). In Table 5, HS 1 indicates the discrete-version of the HS algo-
rithm [41], and HS 2 is a continuous version [44].
Although the BFGS was able to arrive at the global optimum, only 26.7% of the
randomly generated starting parameter values reach this level. A hybrid model, re-
cently reported in [45], that integrated HS and gradient-based algorithms may enhance
the performance of the parameter calibration problem. This will be investigated in the
future.

5 Planning of Biological Conservation

Excessive urban area expansion is increasingly causing the loss or degradation of
wildlife habitat. The protection of wildlife in the face of urban growth and other de-
velopment pressures is an important and challenging task in biological conservation.
If current trends continue, precious species of flora and fauna will be subject to grow-
ing risks of extinction. The HS algorithm may be used to help protect wildlife in gen-
eral, including at-risk species by identifying effective and efficient plans for saving
critical habitat [46].
There are at least five different optimization models [47] for optimally selecting
ecological reserves: species set covering problem (SSCP), maximal covering species
problem (MCSP), maximal multiple-representation species problem (MMRSP),
chance constrained covering problem, and expected covering problem.
Among these five models, MCSP, which maximizes the number of species con-
served, while limiting the number of reserves operated, is one of the more commonly
used models. The MCSP is formulated as follows:
∑
∈ I

Maximize

y

(1)

i

∑
∈

s . t . x ≥ y , all i ∈ I , (2)

j i

j M

i

∑
∈

x

j P

= , (3)

j J

where i and I are the index and set of species, respectively; y is a binary variable
representing whether species i is covered or not (it is one if species i is covered); j
and J are the index and set of candidate reserves, respectively; M is the set of can-
didate reserves that include species i ; x is a binary variable for reserve selection (it
is one if candidate reserve j is selected); and P is the number of candidate reserves
to be selected.
The MCSP model was applied to real-world ecological conservation problem in
Oregon, USA, as shown in Figure 7. Total 426 vertebrate species were identified for
this data set, which consists of 441 hex parcels (candidate reserves). Each parcel con-
tains one or more of the 426 listed species [48].