Preliminary study on the correlation of objective functions to optimize product-line architectures

The Product Line Architecture (PLA) is one of the most important artifacts of a Software Product Line (SPL). The Multi-Objective Approach for PLA Design (MOA4PLA) aims at optimizing the PLA design by using search algorithms easing the design activity. From an original PLA, MOA4PLA automatically obtains alternative designs to improve the original one in terms of the objectives selected for optimization. The use of search algorithms is an incipient research topic, which includes several open research questions. The evaluation model of MOA4PLA is composed of various objective functions, which use software metrics to evaluate different factors that influence on the PLA design. However, the simultaneous optimization of all objective functions is a computationally complex task. In this sense, it is worthwhile to investigate the possible correlation between objective functions because the discovery of correlated functions allows to reduce the number of objectives to be optimized by the search algorithm. Hence, in this paper we perform a preliminary study to investigate the correlation among five objective functions related to metrics that provide indicators on conventional architectural properties, such as coupling, cohesion and size. To accomplish the objective of this paper, four controlled experiments were carried out with four different PLA designs. Empirical results provide preliminary evidence that two pairs of functions are positively correlated and two other pairs of functions are negatively correlated. From such findings, several guidelines were derived to help architects to both reduce and select the objectives related to conventional architectural properties to be tackled during the PLA design optimization.