TRIDENT-DE: Triple-Operator Differential Evolution with Adaptive Restarts and Greedy Refinement

This paper introduces TRIDENT-DE, a novel ensemble-based variant of Differential Evolution (DE) designed to tackle complex continuous global optimization problems. The algorithm leverages three complementary trial vector generation strategies best/1/bin, current-to-best/1/bin, and pbest/1/bin executed within a self-adaptive framework that employs jDE parameter control. To prevent stagnation and premature convergence, TRIDENT-DE incorporates adaptive micro-restart mechanisms, which periodically reinitialize a fraction of the population around the elite solution using Gaussian perturbations, thereby sustaining exploration even in rugged landscapes. Additionally, the algorithm integrates a greedy line-refinement operator that accelerates convergence by projecting candidate solutions along promising base-to-trial directions. These mechanisms are coordinated within a mini-batch update scheme, enabling aggressive iteration cycles while preserving diversity in the population. Experimental results across a diverse set of benchmark problems, including molecular potential energy surfaces and engineering design tasks, show that TRIDENT-DE consistently outperforms or matches state-of-the-art optimizers in terms of both best-found and mean performance. The findings highlight the potential of multi-operator, restart-aware DE frameworks as a powerful approach to advancing the state of the art in global optimization.