=Paper=
{{Paper
|id=Vol-1829/iStar17_paper_3
|storemode=property
|title=Dealing with Goal Models Complexity using Topological Metrics and Algorithms
|pdfUrl=https://ceur-ws.org/Vol-1829/iStar17_paper_3.pdf
|volume=Vol-1829
|authors=Lucía Méndez Tapia,Lidia López,Claudia P. Ayala
|dblpUrl=https://dblp.org/rec/conf/istar/TapiaLA17
}}
==Dealing with Goal Models Complexity using Topological Metrics and Algorithms==
https://ceur-ws.org/Vol-1829/iStar17_paper_3.pdf
Dealing with Goal Models Complexity using
Topological Metrics and Algorithms
Lucía Méndez Tapia1, 2, Lidia López1, Claudia P. Ayala1
1Universitat Politècnica de Catalunya (UPC)
c/Jordi Girona, 1-3, E-08034 Barcelona, Spain
emendez@lsi.upc.edu, {llopez, cayala}@essi.upc.edu
2Universidad del Azuay (UDA)
Av. 24 de Mayo 7-77 y Francisco Moscoso, Cuenca, Ecuador
lmendez@uazuay.edu.ec
Abstract. The inherent complexity of business goal-models is a challenge for
organizations that has to analyze and maintaining them. Several approaches are
developed to reduce the complexity into manageable limits, either by providing
support to the modularization or designing metrics to monitor the complexity
levels. These approaches are designed to identify an unusual complexity
comparing it among models. In the present work, we expose two approaches
based on structural characteristics of goal-model, which do not require these
comparisons. The first one ranks the importance of goals to identify a manageable
set of them that can be considered as a priority; the second one modularizes the
model to reduce the effort to understand, analyze and maintain the model.
Keywords: i* Framework, iStar, Complexity, Metrics, PageRank, Clustering.
1 Introduction
The envisioned state that all organizations desire to achieve, is represented by a set of
strategic goals, which in turn are related to each other through semantic links that
denote the participation that a specific goal as a support of others. The particular goal
arrangement and goal relationships of an organization, constitute its business goal
model. It is well-known the extensiveness and complexity inherent to business goal-
models [1]. And according to [2] its complexity can be seen from a general point of
view as “the difficultly of handling a system, as it is hard to estimate the outcome of an
action”, that involves specific properties [3] like understandability (it is difficult to
understand and verify) and high interaction among its components. Hence, it is crucial
to managing the complexity in an effective way [4].
Several approaches has been developed to address the complexity problem, among
them we refer to [4], where the authors defines the set of metrics to evaluate the
accidental complexity (originated by the modeling way) of KAOS goal models while
building those models; the StarGro approach [5] that contains three requirements
management metrics which also be applied to goal-model complexity. In [6], the
authors propose a metrics suite to take advantage of the modularity given by the actor's
boundaries in i* models. The metrics of all of these approaches generate a set of values
that must be compared with datasets of other models, in order to identify if they are an
‘unusual behaviors’ or if they are ‘normal’. On the other hand, the work presented in
[7] proposes different types of modules associated with a specific semantic (Data
Warehouse domain), and the work of [8] shows 3 types of Strategic Rationale modules
(task-decomposition, means-end, and contribution) as a composition of elements.
To reduce the complexity, we propose two approaches from the Graph Theory
perspective, which are based on topological characteristics of the model, and unlike the
aforementioned, they do not require to be compared with any dataset and are not
associated with a specific semantic or based on goals relationship. We apply these
approaches to an organization’s goal model created to support the analysis of OSS
adoption implications. The complexity hinders the analysis and management of the
model. Our first proposed approach is the Ranking, which identifies a manageable set
of goals that are relevant for a specific analysis; this approach allows us to focus the
effort on goals that can be considered as high priority. Our second proposed approach
is the Clustering, which seeks to decrease the complexity creating modules of goals
(clusters) that can integrate a hierarchy with different levels of abstraction; this
hierarchy facilitates the analysis and maintenance tasks because the effort is centered
in one subset of goals at a time.
The rest of the paper is structured as follows: Section 2 introduces the characteristics
of our goal model; Section 3 presents the ranking approach; Section 4 presents the
clustering approach; finally Section 5 shows the conclusions.
2 The goal model
With the business goals catalogs presented in our previous work [9], we built a Strategic
Rationale diagram that represents the goal model of a software-intensive organization
(who develops software and/or offers services related to software), that incorporates
Open Source Software (OSS) as part of its customer offer. These business goals have
been extended including the strategic goals related to the OSS Integration adoption
strategy defined by [10], characterized by the active participation of the organization
in an OSS community in order to share and co-create OSS. The complexity of our
diagram can be appreciated in Fig. 1, it is hard to visualize, manage and maintain a
model with 80 goals and more than 120 links.
In the context of our research, we need to analyze the importance of the goals from
the organization’s point of view. The resulting model contains a unique root element
representing the organization’s vision (1BG01 Vision, the main business goal to reach)
located at the upper level; from this root are disaggregated all other goals. Our example
only includes those business goals that are involved in OSS adoption.
Fig. 1 Strategic Rationale diagram
3 Identifying More Impacted Goals
As aforementioned, the large number of goals and its relationships increases the
complexity of the model and, therefore, the effort and resources required for its
analysis. For this reason, a selective analysis is more efficiently that an exhaustive one,
because the first one allows focusing on a manageable set of highly impacted goals.
With this perspective, the first of our approaches proposes to identify this
manageable set through a goal importance ranking. This ranking allows us to know the
business goals that receive more cumulative impact from its offspring (all its sub-goals
down to OSS adoption strategy goals). This ranking also considers the total size of the
goal model, because, for example, a goal does not have the same importance if it
belongs to a model of 200 goals or if it belongs to a model of 20,000 goals, even if its
offspring is the same. It is important to emphasize that our analysis is topologic, not
semantic, and therefore do not consider the type of link.
In graph theory, the centrality concept manages the importance of a node in the
network. From several centrality metrics, we decided to apply PageRank [11] because
it calculates the importance value for each node based on topological characteristics of
the model (number of goals and links among them) and works with a unique ‘root’
node. An excerpt of PageRank (PR) values for the goal model of our example is
presented in Table 1. They are obtained using Gephi tool (https://gephi.org/) with a
damping factor set in 1 (a value less than one and greater than or equal to zero is
assigned to damping factor when this algorithm is applied to web navigation graphs).
As we appreciate, the most impacted goals are in the first places of the ranking, that is,
goals which achievement depends on the achievement of a major number of sub-goals.
This is the case, for instance, of To ensure that income (revenue streams from the s/p/f)
are obtained as planned, that is the 3rd goal in the ranking with an importance value of
0.0586 and depends on 44 sub-goals, against the goal To offer the p/s/f required, that is
the 25th goal in the ranking with an importance value of 0.0084 and depends on 15 sub-
goals.
Table 1 Excerpt of PageRank values
#Sub
Pos. Goal PR Value Level
goals
1st VISION 0.160799 0 79
2nd To give sustainability to the shareholder value model 0.065000 1st 63
3rd To ensure that income are obtained as planned 0,058618 2nd 44
…
15th To incorporate external innovation inputs into the 0,020421 4th 22
business offering
…
25th To offer the p/s/f required 0,008413 2nd 16
…
67th To establish a patent scheme 0,001985 4th 0
…
80th To ensure the output logistic (customer delivery) 0,001985 4th 0
This ranking may be used to know the most impacted node among nodes that have
the same detail level. For example, at the 4th level of detail, the importance value of To
establish a patent scheme (0.0020), is less than To incorporate external innovation
inputs into the business offering (0.0204): the difference is caused by the number of
sub-goals each has.
4 Discovering Goal Clusters
As we mentioned in the Introduction, an appropriate management of the goal model’s
complexity is a critical success factor to improve the analysis and understanding of goal
model. One way to deal with this issue is to modularize in order to divide an extensive
model into small, more manageable modules that can be analyzed and maintained as a
unit. In this sense, our Clustering approach groups the goals applying a clustering
algorithm to find, if possible, two or more community structures that could constitute
modules. A community structure is a set of nodes that has more connections between
its members than to the remainder of the network [12].
We apply three clustering algorithms: Clauset-Newman-Moore (CNM) [13],
Wakita-Tsurumi (WT) [14], and Girvan-Newman (GN) [15]. In Table 2 we present the
synthesis of results. The CNM algorithm found 6 clusters: Offer & Innovation, Strategy
& Law compliance, Incomings, Oss Community, Human Talent, and Quality. In this
last one, the membership of 4 of its goals it is not quite clear; these goals are: To manage
customer relationships (establish, maintain and expand them), To ensure the output
logistic (customer delivery), To choose a compatible license, and ACQ-Leg (To acquire
legal skills). Over the others clusters, there are not doubts about its members. In the
Fig. 2 we show the clusters identified by the CNM algorithm. For the processes of
clustering and visualization, we use NodeXL Excel Template
(http://www.smrfoundation.org/).
The Wakita-Tsurumi algorithm found 10 clusters, 2 of which are the same as those
found by the CNM algorithm (Human Talent and Community); 3 of them are very
similar (Offer & Innovation, Strategy & Law compliance, and Incomings; they have 3,
4 and 2 goals less than the correspondent CNM groups, respectively); 3 of them are
about Quality (component integration, component selection, and customer issues,
which in total have 4 goals less than CNM Quality group); 1 of them is new: Offer
Delivery; the last group comprises 6 goals (about market, offering, use of OSS
component, working practices) without a clear relationship.
Table 2 Clustering results
Code Cluster Name CNM WT GN
A Quality 23 - -
A1 Quality (component integration) - 8 11
A2 Quality (component selection) - 7 8
A3 Quality (customer issues) - 4 -
B Offer & Innovation 15 12 15
C Strategy & Law compliance 14 10 12
D Incomings 12 10 13
E OSS Community 9 9
15
F Human Talent 7 7
C1 Law compliance (only) - - 6
G Offer delivery - 7 -
H Not clear - 6 -
Fig. 2 Clusters generated by CNM algorithm
The Girvan-Newman algorithm found 7 clusters where the most relevant issues with
regard to CNM classification are: Quality is divided into 2 clusters (component
integration, and component selection); the Human Talent and OSS Community goals
are grouped into a single cluster; and, Legal goals are placed in a cluster with the goal
about to the shareholder value model sustainability.
5 Conclusions
In the present work, we have proposed two approaches to managing the complexity of
goal-oriented models, based on its topological characteristics. The first approach
generates a ranking of the importance that each goal has like part of an entire model
(without considering a goal in isolation); the highest values in the ranking correspond
to the goals with major relative importance, which can be selected to perform a deeper
analysis. The second approach seeks to identify groups of goals that can become
modules; thus, based on the application results of Clauset-Newman-Moore, Wakita-
Tsurumi, and Girvan-Newman algorithms, we found that the adequate goals grouping
is performed by the first of them; this algorithm generates modules which goals have
more affinity.
Acknowledgments. This work is a result of the Q-Rapids project, which has
received funding from the European Union’s Horizon 2020 research and innovation
program under grant agreement N° 732253. Lucía Méndez’s work is supported by a
SENESCYT (Secretaría de Educación Superior, Ciencia, Tecnología e Innovación)
grant from the Ecuatorian Government.
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