Reformulating Branch Coverage as a Many-Objective Optimization Problem

Test data generation has been extensively investigated as a search problem, where the search goal is to maximize the number of covered program elements (e.g., branches). Recently, the whole suite approach, which combines the fitness functions of single branches into an aggregate, test suite-level fitness, has been demonstrated to be superior to the traditional single-branch at a time approach. In this paper, we propose to consider branch coverage directly as a many-objective optimization problem, instead of aggregating multiple objectives into a single value, as in the whole suite approach. Since programs may have hundreds of branches (objectives), traditional many-objective algorithms that are designed for numerical optimization problems with less than 15 objectives are not applicable. Hence, we introduce a novel highly scalable many-objective genetic algorithm, called MOSA (Many-Objective Sorting Algorithm), suitably defined for the many-objective branch coverage problem. Results achieved on 64 Java classes indicate that the proposed many-objective algorithm is significantly more effective and more efficient than the whole suite approach. In particular, effectiveness (coverage) was significantly improved in 66% of the subjects and efficiency (search budget consumed) was improved in 62% of the subjects on which effectiveness remains the same.