A 2-Dimensional Search Space Representation for Combinatorial T-Way Test Suite Generator Using the Whale Optimization Algorithm

Metaheuristic algorithms reduce the size of combinatorial test suites, lowering testing costs. Researchers have developed several combinatorial test suite generators in the literature that adopt metaheuristic algorithms, such as particle swarm optimization (PSO), harmony search strategy (HSS), and whale optimization algorithm (WOA). Although many studies report near-optimal results, some do not address the representation of combinatorial optimization. This paper models combinatorial optimization in a two-dimensional (2D) search space using WOA to address the limitations of 1D representations, which may limit search capability, especially in bio-inspired algorithms. The proposed model represents the combinatorial optimization problem in a 2D search space. To evaluate effectiveness, a bio-inspired WOA is adopted, as it mimics living organisms’ behavior beyond 1D space, enabling exploration of multidimensional combinatorial configurations. Metaheuristic algorithms update candidate solutions as position vectors in a multidimensional space. In WOA, each agent updates its position relative to the best solutions using vector-based distance calculations. Representing solutions using spatial coordinates improves neighborhood-based search by enabling spatial proximity between candidate solutions. In contrast, linear index representations in combinatorial testing may limit this spatial interpretation, motivating the proposed 2D model. Results show that 53% of experiments achieve smaller test suite sizes with the 2D representation. Statistical analysis using the Wilcoxon signed-rank test (p<0.05) indicates a significant difference between 1D and 2D representations. These findings demonstrate that the 2D model improves the ability of WOA to reduce test suite size. This study presents a 2D combinatorial model using WOA that outperforms most existing strategies in producing smaller test suites. The implications of applying the model extend beyond the current algorithm, offering significant advantages over other algorithms that generate near-optimal numbers of test suites.