SEKE 2012 Proceedings - Knowledge Systems Institute

study was planned and carried out to validate the complexity
metrics; Section IV discusses the results obtained in this
study; and Section V provides the conclusions and directions
for future work.
II. COMPLEXITY METRICS FOR SOFTWARE PRODUCT
LINE ARCHITECTURES
The complexity understanding is essential from the PL
adoption point as a PL manager is able to analyze the
complex of the potential PL products to be produced.
Organizations which have a developed PL core asset
for a certain domain can analyze the complexity of the
distinct configurations and the PL evolution. Therefore, a PL
manager may choose from a set of feasible configurations
which are the most interesting to be produced.
The complexity metrics for PLA were composed based on
the Cyclomatic Complex (CC) [11] and Weighted Methods
per Class (WMC) [6]. The CC metric measures the quantity
of decision logic represented by the number of paths to be
tested in a source code. The WMC metric is the sum of the
CC metric for each concrete method in an object-oriented
class. Abstract methods have WMC value 0.0. Each metric
measures the complexity of class, interface and component
based on one of the following PL variability concepts:
• Variability, according to Bosch [4], is “the ability of
a software or artifact to be changed, customized or
configured for use in a particular context.” Although
a variability can take place at different levels of abstraction
and artifacts, the complexity metrics in this
paper address only class and component UML artifacts
that result from PL activities [14] and represents the
PLA;
• Variation Point is the resolution of variabilities in
generic artifacts of a PL. According to Jacobson et al.
[9], “a variation point identifies one or more locations at
which the variation will occur.” Thus, a variation point
may take place at generic artifacts and at different levels
of abstraction. Basically, a variation point answers the
question: What varies in a PL? [16]; and
• Variant represents the possible elements through which
a variation point may be resolved. It may also represent
a way to directly resolve a variability. Basically, a
variant answers the question: How does a variability
or a variation point vary in a PL? [16].
The complexity metrics taken into consideration in this
paper are as follows:
CompInterface: measures the complexity of an interface.
It always has value 0.0 as an interface has no concrete methods
to calculate the WMC metric. This metric is represented
by the following formula (1):
}
CompInterface(Cls) = WMC(Itf)=0.0,
where:
• n=#ofconcrete methods (Mtd) of an interface (Itf)
(1)
CompClass: measures the complexity of a class. It is the
WMC metric value for a class. This metric is represented
by the following formula:
⎫
n∑
CompClass(Cls) = WMC(Cls)= WMC(Mtd i),
⎪⎬
i=1
where:
• n=#ofconcrete methods (Mtd) of a class Cls
CompVarPointClass: measures the complexity of a variation
point. It is the value of the metric CompClass (Equation
2), for a class which is a variation point, plus the sum of the
CompClass (Equation 2) value for each associated variant
class. This metric is represented by the following formula:
⎫
CompVarPointClass(Cls) = CompClass(Cls) +
n∑
CompClass(Ass i),
⎪⎬
i=1
where:
• n = # of (inclusive + exclusive + optional + mandatory) variant
classes and interfaces associated (Ass)
CompVariabilityClass: measures the complexity of a variability.
It is the sum of the metric CompVarPointClass
(Equation 3), for each variation point. This metric is represented
by the following formula:
⎫
nV P
∑
⎪⎬
CompVariabilityClass(Vbt) =
CompV arPointClass(Cls i),
i=1
where:
• nVP = # of class and interface (Cls) variation points
CompVarComponent: measures the complexity of a variable
PLA component. It is the sum of the metric CompVariabilityClass
(Equation 4), for each variability in a
component. This metric is represented by the following
formula:
CompVarComponent(Cpt) =
nV ar
∑
CompV ariabilityClass(Var i),
i=1
where:
• nVar=#ofvariabilities (Var) in a component (Cpt)
⎪⎭
⎪⎭
⎪⎭
⎫
⎪⎬
CompPLA: measures the complexity of a PLA. It is
the sum of the CompVarComponent (Equation 5) for each
component of a PLA. This metric is represented by the
following formula:
⎫
nCpt
∑
CompPLA(PLA) = CompV arComponent(Cpt i), ⎪⎬
i=1
where:
• nCpt = # of PLA variable components
• Cpt i is the o i th component of a PLA
⎪⎭
⎪⎭
(2)
(3)
(4)
(5)
(6)
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