Multi-objective Integer Programming Approaches for Solving the Multi-criteria Test-suite Minimization Problem

Abstract

Test-suite minimization is one key technique for optimizing the software testing process. Due to the need to balance multiple factors, multi-criteria test-suite minimization (MCTSM) becomes a popular research topic in the recent decade. The MCTSM problem is typically modeled as integer linear programming (ILP) problem and solved with weighted-sum single objective approach. However, there is no existing approach that can generate sound (i.e., being Pareto-optimal) and complete (i.e., covering the entire Pareto front) Pareto-optimal solution set, to the knowledge of the authors. In this work, we first prove that the ILP formulation can accurately model the MCTSM problem and then propose the multi-objective integer programming (MOIP) approaches to solve it. We apply our MOIP approaches on three specific MCTSM problems and compare the results with those of the cutting-edge methods, namely, NonlinearFormulation_LinearSolver (NF_LS) and two Multi-Objective Evolutionary Algorithms (MOEAs). The results show that our MOIP approaches can always find sound and complete solutions on five subject programs, using similar or significantly less time than NF_LS and two MOEAs do. The current experimental results are quite promising, and our approaches have the potential to be applied for other similar search-based software engineering problems.