Wireless Network Design: Optimization Models and Solution ...

122 Eli Olinick
solution times. Cai et al. [17] found this to be a very effective strategy in their computational
study of the CKKOIP model. For the largest instances in the study this
strategy reduced solution time by an order of magnitude with only a modest loss
in revenue (typically 5%) compared to the best solution found using the full Lm
for each test point. Thus, they were able to find near-optimal solutions to problem
instances with up to 160 potential tower locations, 2,000 test points and 5 candidate
MSTO locations in less than an hour of CPU time on the Compaq AlphaServer
described above.
Rosenberger and Olinick [52] propose a heuristic based on a geographical decomposition
approach whereby a large planning region is subdivided into several
smaller regions. After solving their model for one of the smaller problems they fix
the y variables for all towers that are not near the boundary of the region. They repeat
this for each of the sub-regions and then solve a problem for the entire large
region in which many of the tower location decisions have already been made.
As computing resources continue to become less expensive and more efficient,
the techniques described in this section should enable network planners to “scale up”
the models described in Sections 5.2 and 5.3 to tackle even larger design problems.
For example, it takes only a matter of seconds to solve small AMCIP instances
with newer hardware and a more recent version of CPLEX than the combination
used in [7]. The fact remains, however, that the optimization problem represented
by the core model, and its variations and extensions, is computationally intractable,
and so as wireless technology advances and planners attempt to design larger and
more complex networks the “combinatorial explosion” of the models seems likely to
eventually outstrip the performance gains from advances in computing technology.
Thus, we expect that the development of good, fast heuristics and improvements
to the branch-and-bound process for solving cellular network design problems will
continue to be active areas of research.
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