Robust Differential Evolution via Nonlinear Population Size Reduction and Adaptive Restart: The ARRDE Algorithm

This study is motivated by a robustness issue in numerical optimization of bound-constrained problems: many algorithms that perform well on a particular benchmark suite, such as the IEEE CEC2017 problems, struggle to maintain the same level of performance when applied to other suites that differ in dimensionality, landscape complexity, or the maximum number of function evaluations ($N_{\text{max}}$). To address this issue, we propose the Adaptive Restart--Refine Differential Evolution (ARRDE) algorithm, a variant of Differential Evolution (DE) built on jSO. ARRDE is centered on two main design contributions: an adaptive restart--refine mechanism, which includes final-stage refinement and local exclusion during restart, and a nonlinear population-size reduction strategy whose shape depends on problem dimensionality. We evaluate ARRDE on five benchmark suites: CEC2011, CEC2017, CEC2019, CEC2020, and CEC2022. To the best of our knowledge, this is one of the most comprehensive experimental studies conducted in this context. Because the official metrics of these benchmark suites emphasize different performance aspects, we additionally introduce a bounded accuracy-based scoring metric derived from relative error for cross-suite robustness assessment. Using both the official suite-specific metrics and the proposed robustness-oriented metric, ARRDE consistently demonstrates top-tier performance and one of the most stable aggregate profiles across all benchmark suites. These results support ARRDE as a competitive and robust DE variant across heterogeneous benchmark regimes.