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Other 9%
Medical 3%
Water 25%
Thermal / energy 4%
Transport 6%
IT 8%
Structural 17%
Soil 14%
Benchmark 14%
Fig. 3.
Approximate Breakdown of HS Applications by Discipline Area as of November 2008
3 Applications of HS by Discipline Area
Many applications, excluding benchmark problems, have been summarised in [3]. A
significant portion of publications compare the performance of HS with other optimi-
sation algorithms; some also report the sensitivity of the results to the parameters of
the HS algorithm. More detail on specific issues in each discipline area is provided in
the other chapters of this topic.
3.1 Water-Related Applications
Several studies have focussed on the design of municipal water distribution networks,
in particular the selection of optimal pipe diameters [1, 7, 10, 24, 30, 31]. Brief results
are also reported in [20, 32-34]. Typically there is one fixed-pressure supply node in
the network and many demand nodes, with the structure (connectivity) of the distribu-
tion network being given. The elevations and distances between nodes (pipe lengths)
are also specified. The aim is to select the diameter for each pipe segment that mini-
mises the total capital cost of the network, given that pipes come in certain standard
diameters and smaller-diameter pipes cost less. The problem is constrained by the
laws of fluid mechanics—mass and energy conservation equations—and there are
also customer requirements at each demand node for some minimum water pressure.
A hydraulic simulator, such as EPANET, is used to perform the fluid mechanics cal-
culations. The networks considered range in size from the 8-pipe 'two-loop' network
[10] to the 454-pipe Balerma network in Spain [24]. A related study is the design of
coffer dam drainage pipes by [35].
Geem [36] considered the optimal sizing of both the pipes and the water supply
pump in a distribution network. The objective was to minimise the total cost, compris-
ing capital costs for the pump and pipes, plus the operating cost for the pump.
The optimal structure (layout) of rectilinear branched pipe networks has been stud-
ied for 3×3 and 8×8 regular grids of nodes [22, 23]. This problem has one supply
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