Abstract:
In this project we build on research that has been done by Joubert and Axhausen (2013), who
built a commercial vehicle complex network for Gauteng. Two shortcomings are identi ed in
the approach they followed. The rst shortcoming is the approximations used to determine
whether an activity formed part of a cluster. These approximations resulted in some activities
to be assigned to the wrong clusters, and other activities to not be assigned to any cluster.
The second shortcoming is that the completeness of the complex network was never explicitly
considered when they evaluated the di erent combinations of input clustering parameters.
We address the rst shortcoming by generating a concave hull for each cluster. The concave
hull envelopes all points in the cluster, and one can accurately determine whether an activity
forms part of a cluster. To generate the concave hulls, we integrate the Duckham Algorithm
with the existing clustering algorithm used by Joubert and Axhausen (2013). The rst step
of the Duckham Algorithm is to generate the Delaunay triangulation of the cluster. For some
combinations of input clustering parameters, more than 2% of the clusters were degenerate. A
degenerate Delaunay triangulation occurs when three or more points in a cluster are colinear
(lie on a straight line), or when four points in a cluster are cocircular (lie on the circumference
of a circle). No valid Delaunay triangulations can be generated for these clusters. We suggest
to deal with these degeneracies by using the weighted average of the points as a reference to the
cluster, instead of simply ignoring it.
We consider the completeness of the complex network as part of a multi-objective problem:
we cannot maximise completeness without making a trade-o with computational complexity.
We address this multi-objective problem by conducting a multiple response surface experiment
and performing multi-objective evaluation by constructing two e cient frontiers. From the
multiple response surface experiment, we found that the input clustering parameters ( , pmin)
that optimises the completeness of the complex network, while minimising the computational
complexity, is (1, 2). From the multi-objective evaluation, we determined that in general, using
= 1 will result in an e cient point.
To conclude, we use input clustering parameters (1, 2) to build a commercial vehicle complex
network in the Nelson Mandela Bay Municipality, and perform various network analyses on this
network.
