Influence of Initializing Krill Herd Algorithm With Low-Discrepancy Sequences

Abstract

The krill herd (KH) algorithm is a global metaheuristic algorithm that was initially proposed for solving continuous optimization problems. The KH algorithm, since inception, has generated considerable real-world application interests in the research community. The standard algorithm solution implementation steps follow the initialization mechanism, which relies mainly on educated guesses or random initialization solution generation. Therefore, to improve the performance of the KH algorithm, the current study is set to investigate the influence of initializing the KH algorithm with three low-discrepancy sequences, such as the Faure sequence, Sobol sequence, and Van der Corput sequence. These low-discrepancy sequences are known to be more uniformly distributed across the problem search space than the commonly used random number initialization method. The study also evaluates the influence of population size on the performance of the proposed variants of the improved KH algorithms. The experimental results show significant improvements for the enhanced KH algorithms in terms of performance and the quality of solutions obtained; particularly on standard benchmarked high-dimension test problem instances, where the enhanced KH variants outperformed the existing basic KH algorithm for all the test functions evaluated. Similarly, the results for low dimension test cases showed less sensitivity to the initialization schemes, as the performance of our proposed improved scheme was comparable to that of the basic KH algorithm. However, in most cases, as the problem dimension was scaled up, the enhanced KH outperformed the basic KH. Evaluation results based on the population size of the algorithm, revealed that when the number of Krill is set at 25, the Sobol based KH initialization scheme performed better than did the other methods. Although, the Van der Corput and Faure based KH initialization schemes showed similar sensitivity when the dimension was set at 20. As we varied the population size of Krill, it was observed that the performance of the Sobol based KH initialization scheme deteriorated, whereas the other two methods showed superior performance. Overall, the findings from this study revealed that there are significant improvements in the performance of KH algorithm when initialized with low-discrepancy sequences.