On the Exploration and Exploitation Capabilities of Adaptive Differential Evolution: A Case Study Using JADE, L-SHADE, and jDElscop

Differential Evolution (DE) is one of the most successful population-based optimization algorithms, and numerous adaptive variants, such as JADE, L-SHADE, and jDElscop, have been proposed to improve its search performance. Although these methods consistently outperform classical DE variants, whether they genuinely improve the balance between exploration and exploitation remains largely unexamined, since prior evaluations relied on imprecise diversity-based measures. This paper presents a detailed study of DE variants using the recently proposed attraction basin-based measures that distinguish between different types of exploration (successful, failed, deceptive, and successful rejection) and exploitation (successful and unsuccessful). The exploration and exploitation behavior of JADE, L-SHADE, and jDElscop is compared with four classical DE strategies: DE/best/1/bin, DE/best/1/exp, DE/rand/1/bin, and DE/rand/1/exp. The results show that adaptive DE variants prolong the exploration phase and improve the balance between successful and unsuccessful exploitation compared with the classical strategies, though each achieves this through a distinct mechanism. The presented findings improve the understanding of adaptive DE search behavior and demonstrate the usefulness of attraction basin-based measures for analyzing evolutionary optimization algorithms.