Multi-objective general variable neighborhood search for software maintainability optimization

The quality of software projects is measured by different attributes such as efficiency, security, robustness, or understandability, among others. In this paper, we focus on maintainability by studying the optimization of software modularity, which is one of the most important aspects in this regard. Specifically, we study two well-known and closely related multi-objective optimization problems: the Equal-size Cluster Approach Problem (ECA) and the Maximizing Cluster Approach Problem (MCA). Each of these two problems looks for the optimization of several conflicting and desirable objectives in terms of modularity. To this end, we propose a method based on the Multi-Objective Variable Neighborhood Search (MO-VNS) methodology in combination with a constructive procedure based on Path-Relinking. As far as we know, this is the first time that a method based on MO-VNS is proposed for the MCA and ECA problems. To enhance the performance of the proposed algorithm, we present three advanced strategies: an incremental evaluation of the objective functions, an efficient exploration of promising areas in the search space, and an analysis of the objectives that better serve as guiding functions during the search phase. Our proposal has been validated by experimentally comparing the performance of our algorithm with the best previous state-of-the-art method for the problem and three reference methods for multi-objective optimization. The experiments have been performed on a set of 124 real software instances previously reported in the literature.