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Software test suites based on the concept of interaction testing are very useful for testing software components in an economical way. Test suites of this kind may be created using mathematical objects called covering arrays. A covering array, denoted by CA(N; t, k, v), is an N × k array over with the property that every N × t sub-array covers all t-tuples of at least once. Covering arrays can be used to test systems in which failures occur as a result of interactions among components or subsystems. They are often used in areas such as hardware Trojan detection, software testing, and network design. Because system testing is expensive, it is critical to reduce the amount of testing required. This paper addresses the Optimal Shortening of Covering ARrays (OSCAR) problem, an optimization problem whose objective is to construct, from an existing covering array matrix of uniform level, an array with dimensions of (N − δ) × (k − Δ) such that the number of missing t-tuples is minimized. Two applications of the OSCAR problem are (a) to produce smaller covering arrays from larger ones and (b) to obtain quasi-covering arrays (covering arrays in which the number of missing t-tuples is small) to be used as input to a meta-heuristic algorithm that produces covering arrays. In addition, it is proven that the OSCAR problem is NP-complete, and twelve different algorithms are proposed to solve it. An experiment was performed on 62 problem instances, and the results demonstrate the effectiveness of solving the OSCAR problem to facilitate the construction of new covering arrays. [ABSTRACT FROM AUTHOR]

Several variable selection algorithms in multivariate calibration can be accelerated using Graphics Processing Units (GPU). Among these algorithms, the Firefly Algorithm (FA) is a recent proposed metaheuristic that may be used for variable selection. This paper presents a GPU-based FA (FA-MLR) with multiobjective formulation for variable selection in multivariate calibration problems and compares it with some traditional sequential algorithms in the literature. The advantage of the proposed implementation is demonstrated in an example involving a relatively large number of variables. The results showed that the FA-MLR, in comparison with the traditional algorithms is a more suitable choice and a relevant contribution for the variable selection problem. Additionally, the results also demonstrated that the FA-MLR performed in a GPU can be five times faster than its sequential implementation. [ABSTRACT FROM AUTHOR]