Overview of Applications and Developments in the Harmony Search Algorithm - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 21

node with the rest of the grid points being demand nodes. The decision is whether or
not to place a pipe between adjacent nodes. No loops were permitted.
The location of a leak in a pipeline can be estimated from the transient pressure or
flow rate response to the sudden closure of a downstream valve. Leak detection was
investigated using HS and GA in [37, 38]. The rehabilitation of pipe networks was
studied in [39, 40] with a modified HS method. The problem was to select the year
and type of rehabilitation work undertaken to minimise the total cost over the net-
work's lifetime.
A water pump switching problem was investigated in [41] and briefly in [42]. Ten
pump stations, each containing four pumps in series, were located along a pipeline.
The problem was to decide which pumps should operate to minimise the energy cost
subject to constraints on the pump suction and discharge pressures. The optimal
scheduling of a system of four dams was studied in [43]. The aim was to find the wa-
ter release schedule that maximised both hydropower and irrigation benefits. There
were constraints on the dam outflows, and instantaneous and final storage levels.
Several water-related studies involve parameter estimation. Parameters for the
nonlinear Muskingum model, which can be used in the prediction of volumetric water
flow rates for flood routing, were fitted in [1, 44] and also discussed in [4, 32]. Paik
and co-workers [45] developed a rainfall-runoff model that required estimation of 16-
40 continuous parameters. Ayvaz [14] combined HS with fuzzy C -means clustering to
estimate the zone structure and zonal transmissivities for a heterogeneous aquifer.
3.2 Structural Design
Typical structural design problems involve selecting the best cross-sectional areas or
designation codes for beams making up a structure to minimise the structure's weight.
The configuration and lengths of beams forming the structure and any applied exter-
nal loads are specified. There are constraints on the maximum tensile and compres-
sive stresses that beams should experience, and on the maximum deflections of
selected nodes. Both continuous variable and discrete variable problems have been
studied. Considerable use is made of symmetry in the structure to reduce the number
of decision variables required.
Continuous variable applications using basic HS include two-dimensional (plane)
trusses with 10-200 bars, three-dimensional (space) trusses with 22-72 bars, and a
120-bar dome truss [8]. Discrete variable problems, namely a 52-bar plane truss, 47-
bar power line tower, and 25- and 72-bar space trusses, were reported in [9]. Saka
[46] presented optimised designs for geodesic domes having three to six rings (75-
285 bars). Erdal and Saka [47] optimised 24-264-member grillages, which are
frameworks of longitudinal and transverse beams used to support platforms. De-
gertekin [48, 49] reported designs for several frame structures, including a 1-bay,
8-storey plane frame and a 4-storey, 84-bar space frame. Brief results on structural
optimisation are also reported in [4, 50]. A hybrid PSO-HS algorithm was used to op-
timise various structures: 10- and 17-bar plane trusses, and 22-, 25- and 72-bar space
trusses [51-53].
A few structural design studies go beyond optimisation of beam cross-sections. Both
cross-sectional area or designation and nodal positions were optimised for an 18-bar
plane truss in [4] and a 25-bar space truss in [13]. Lo [29] reported an extensive study