Wireless Network Design: Optimization Models and Solution ...

134 Jeff Kennington, Jason Kratz, and Gheorghe Spiride
Minimize ∑ Wi jIi j
(i, j)∈E
The third version is identical to the second with all weights set to 1. The third model
is the well-known graph coloring problem and the second is the weighted graph coloring
problem. They present two distributed algorithms for problem solution. Their
simulation experiments indicate that the use of overlapping channels can yield improvements
over the restricted use of only 3 non-overlapping channels. Some of
the simulation results indicated improvements of up to 30%. It should be noted
that channel assignment is not required for some design problems. Some AP vendors
(see [15]) design their equipment so that it can choose the best frequency for
communication. Each AP listens for traffic on the various frequencies and selects a
frequency that results in the best reception.
6.2.4 Access Point Placement
Sherali et al. [18] developed a set of nonlinear optimization models to determine
optimal access point location. Mobile devices are placed at grid points and standard
models are used to determine gi(x,y,z), the path loss at grid point i associated
with a access point at (x,y,z). One objective function is to minimize the sum of
all weighted path losses. A penalty term may be defined for mobiles at grid points
where communication is not possible. A second objective function is to minimize
the maximum path loss plus the aforementioned penalty. The third model is a combination
of the first two. The authors evaluate three nonlinear techniques for solution
(Hooke and Jeeves, a quasi-Newton method, and a conjugate gradient method) and
report solving several small problems successfully.
Adickes et al. [1] use a genetic algorithm based on a circle covering heuristic to
solve the transceiver placement problem. Three objective functions are developed
and a Pareto ranking is used to evaluate solutions. The first objective is the fraction
of covered grid points. The second uses the Shannon-Hartley law (http://www.factindex.com/s/sh/shannon
hartley law.html) to estimate capacity, while the third model
involves average signal strength over the set of grid points. Using a population size
of 30, the authors develop the Genetic Algorithm Optimizer (GAO) software tool
for problem solution.
6.2.5 Proprietary Design Tools
The problem of determining the location, number, and power of a set of access
points that will provide coverage for a given building at minimum cost was investigated
by Fortune et al. in [3]. They developed the Wireless System Engineering
(WISE) software tool to assist design personnel with this problem. WISE is de-