Constraint Handling in NSGA-II for Solving Optimal Testing Resource Allocation Problems

In software testing, optimal testing resource allocation problems (OTRAPs) are important when seeking a good tradeoff between reliability, cost, and time with limited resources. There have been intensive studies of OTRAPs using multiobjective evolutionary algorithms (MOEAs), but little attention has been paid to the constraint handling. This paper comprehensively investigates the effect of the constraint handling on the performance of nondominated sorting genetic algorithm II (NSGA-II) for solving OTRAPs, from both theoretical and empirical perspectives. The heuristics for individual repairs are first proposed to handle constraint violations in NSGA-II, based on which several properties are derived. Additionally, the Z-score based Euclidean distance is adopted to estimate the difference between solutions. Finally, the above methods are evaluated and the experiments show several results. 1) The developed heuristics for constraint handling are better than the Existing Strategy in terms of the capacity and coverage values. 2) The Z-score operation obtains better diversity values and reduces repeated solutions. 3) The modified NSGA-II for OTRAPs (called NSGA-II-TRA) performs significantly better than the existing MOEAs in terms of capacity and coverage values, which suggests that NSGA-II-TRA could obtain more and higher quality testing-time-allocation schemes, especially for large, complex datasets. 4) NSGA-II-TRA is robust according to the sensitivity analysis results.