Efficiently scheduling multiprocessor tasks on two dedicated processors is a complex challenge. This is particularly true when navigating task dependencies and resource constraints. This paper investigates the impact of a skewed strategy within population-based metaheuristics. This strategy introduces a controlled tolerance for accepting degraded solutions. As a result, the exploration of the solution space is significantly enhanced. The proposed approach hybridizes a modified Grey Wolf Optimizer (GWO) with a skewed local search strategy. This combination takes advantage of the robust global search capabilities of the GWO while utilizing the skewed local search to maintain diversity. Consequently, the algorithm avoids premature convergence, which is a common issue in purely stochastic methods. A customized constructive procedure initializes the population. Solutions are then refined using specialized operators, such as a shaking mechanism and a “fix-and-complete” procedure. These components create a balance between exploration and exploitation. This balance allows the search to target promising regions while escaping local traps. Further- more, the skewed acceptance criterion enables the exploration of slightly inferior paths. Such divergence from current trajectories reduces the risk of stagnation. To ensure stability across various problem instances, the algorithm’s parameters were calibrated using the Taguchi method. This design of experiments framework systematically optimized key factors, including population size, iteration limits, and skewness tolerance. Experimental results on benchmark instances show that the proposed method outperforms existing state-of-the-art approaches. The achieved results were confirmed through rigorous statistical validation. The analysis included rank tests, the Wilcoxon signed-rank test, and analysis of variance.
Baatout et al. (Tue,) studied this question.