Goal models are an efective mechanism for elicitation and analysis in early Requirements Engineering, improving communication with stakeholders. However, in real scenarios, goal models become a complex network of actors and evaluating them can be dificult. Some tools assess the level of achievement of actors and intentional elements, which alleviate this limitation. However, using tools to evaluate models has some limitations, like the dificulty of integrating goal models with other models, the training required to use these tools, and the impossibility of assessing models when tools become outdated. In this work, we propose a formalization of iStar 2.0 models in the form of linear constraints that makes it possible to evaluate and optimize models using linear programming. This formalization allows the evaluation of goal models on existing tools and facilitates integration with other approaches.
are propagated on the contrary from leaves to roots. The third type of analysis of the level of achievement is by optimising goal models, which intends to assign values to intentional elements that maximise the model’s satisfaction level.
The evaluation based on frameworks presents some issues that limit the use of goal models in practice. Firstly, existing frameworks strongly depend on specific tools that belong to academia. So, their maintenance is discontinued and they frequently become outdated; therefore, their use for evaluating goal models is rather inadvisable. In addition, these tools are usually closed systems, so integrating goal models with other approaches is almost impossible. The resolution algorithms depend on the specific implementation of the models, so it is necessary to adapt them to similar systems. Another important aspect is the training required to use these tools.
Recently, it has been proposed the formalisation of goal models using arithmetic semantics
[
This work is structured as follows: Section 2 presents some related work; Section 3 introduces the formalization of the goal model in the form of ILP; Section 4 shows our proof of concept tool; and the paper concludes with some conclusions and future work.
The work presented here is related to many contributions that study how to analyse goal models using alternative representations.
GRL models use the GRL satisfaction analysis [13], a family of algorithms propagating
satisfaction values in goal models. Internally, these algorithms work with mathematical expressions
of goal models. The work [
The work in [
The iStar 2.0 language does not specify how users have to evaluate models. Indeed, for the case
of i* (the ancestor of iStar 2.0), frameworks take guidelines from other goal modelling languages
like GRL for the evaluation [
2 + elements, the constraint would be − ∑ =1 ∗ = 0.
Our objective function is the level of satisfaction of the entire model, which is the weighted sum of the satisfaction of the actors in the model ( ) and the , ℛ, , , ℬ constraints derived from the model in the form of ∗ <= or ∗ =
are the linear
. We have a single
weight because we consider each actor equally important. We will use diferent weights if
actors have diferent importance in the model. Constraints
model the satisfaction value of an
agent, which is the weighted sum of the satisfaction value of its intentional root elements. We
have a linear constraint for each agent, for example for the agent that has root intentional
ℛ represents constraints derived from AND and OR refinements. In previous contributions
[
1, 2), we define a binary decision variable , which
is 1 if 1 > 2 and 0 otherwise, and a variable , which is bigger than 1 and 2 in any solution
of the problem. Then we define several constraints to enforce the value of , ( 1 − 2 <=
and 2 − 1 <= (1 − )
), and the value of ( >=
1, >=
2, <= 1 + (1 − )
and
). This approach can be generalized for refinements with more than two leaf
represents constraints derived from contributions to qualities. We model this as a weighted
sum in which the weights depend on the kind of link. So, for make links the weight is 1, for help
the weight is 0.75, for hurt links the weight is 0.25 and for break links is 0. These weights for
the diferent kinds of contributions are aligned with the proposal of [
∑ =1 − 0.75 ∑ =1 ℎ − 0.25 ∑ =1 ℎ = 0.
represents constraints derived from dependencies between actors. In this kind of relationship, we have five entities: the depender, the depender element, the dependum, the dependee and the dependee element. According to the iStar 2.0 specification, the satisfaction of the depender elements depends on the dependum. So, we use an equality constraint to enforce this issue with the form − = 0 . On the other hand, if the dependee element is not satisfied, the dependum cannot be satisfied as well. This is modeled using the linear constraint − <= 0 . Where there is no depender or dependee element, we use its actor’s satisfaction level.
The ℰ represents these variables in the model that we want to set to a specific value. In a forward analysis, we would like to know the configuration of the model to achieve a certain level of satisfaction in an entity. We model this issue using equality constraints. Finally, ℬ represents the boundings of the model entities that should have a value between 0 and 100.
To validate our approach, we have implemented a command-line utility in Java (available in https://github.com/iayalavinas/istar20) that takes models from the piStar tool1 and generates a Matlab script. The piStar tool permits the export of models in JSON format. We use the json-simple library to parse piStar models. Matlab has diferent libraries to optimise linear programs, we use intlinprog2.
We have validated our utility for models of diferent sizes. We see that even for models of more than 100 elements, Matlab and our scripts provide solutions in less than 10 seconds. This time is reasonable for a program not intended for user interaction or real-time interaction. For example, for the initial model of the piStar tool (see Figure 1), we obtain the Matlab script that appears in the screenshot of Figure 2. In line 2 appears the objective function, and as Intlinprog only supports minimisation problems, we multiply its weights by −1. Intlinprog requires to indicate what variables of the model are integers. We do so in line 3 using the vector intcon. The script sets the equality and inequality constraints of the ILP using vectors A, b, Aeq and beq (lines 4-7). We set between 0 and 100 the satisfaction level of intentional elements in lines 8 and 9. The Intlinprog function is called in line 10. Finally, we print the index of the variable to interpret the results (lines 11-28).
In this work, we have presented a formalisation of iStar 2.0 models in linear constraints that allows optimising these models using ILP. IStar 2.0 models, which are modeled using the piStar tool, are then converted into an ILP problem using our proof of concept tool and resolved in Matlab. Our formalisation considers most iStar 2.0 entities such as intentional elements, agent dependencies, contributions and refinements. Although similar approaches exist for other goal modelling languages like GRL, KAOS or RELAX, they use other formalism that requires specific solvers like SMT or SAT or does not permit the model optimisation. Other work uses ILP for goal models, but it only considers a limited sub-set of the entities and does not evaluate 1https://www.cin.ufpe.br/~jhcp/pistar/ 2https://es.mathworks.com/help/optim/ug/intlinprog.html the model’s satisfaction level. In future work, we plan to integrate this formalisation into our approach for Proactive Dynamic Software Product Lines.
This work is supported by the European’s H2020 research and innovation programme under grant agreement DAEMON 101017109, by the projects co-financed by FEDER funds LEIA UMA18-FEDERJA-15, MEDEA RTI2018-099213-B-I00 and Rhea P18-FR-1081, the PRE2019087496 grant from the MICINN and by DISCO B1-2012 12 funded by Universidad de Málaga. [13] D. Amyot, S. Ghanavati, J. Horkof, G. Mussbacher, L. Peyton, E. Yu, Evaluating goal models within the goal-oriented requirement language, International Journal of Intelligent Systems 25 (2010) 841–877. [14] C. M. Nguyen, R. Sebastiani, P. Giorgini, J. Mylopoulos, Multi-objective reasoning with constrained goal models, Requirements Engineering 23 (2018) 189–225. [15] A. J. Ramirez, B. H. C. Cheng, Automatic derivation of utility functions for monitoring software requirements, in: Model Driven Engineering Languages and Systems, Springer Berlin Heidelberg, 2011, pp. 501–516.