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

Robustness across heterogeneous optimization regimes remains a central challenge in bound-constrained continuous optimization. In practice, users often prefer optimizers that remain reliable across different dimensionalities, landscape structures, and evaluation budgets. Yet many Differential Evolution (DE) variants that perform strongly in one regime degrade substantially when transferred to others. To address this issue, we propose the Adaptive Restart--Refine Differential Evolution (ARRDE) algorithm, a DE variant designed explicitly for cross-regime robustness. ARRDE combines an adaptive restart--refine strategy, a nonlinear population-size reduction schedule that depends on problem dimensionality, and a budget-aware population-initialization rule for restricted-budget settings. Because robustness cannot be established credibly from a narrow experimental setting, we evaluate ARRDE on five benchmark suites: CEC2011, CEC2017, CEC2019, CEC2020, and CEC2022. These suites span markedly different dimensions, landscape characteristics, and evaluation budgets, making this, to the best of our knowledge, one of the most comprehensive robustness-oriented evaluations reported for a proposed DE variant in this context. Since their official performance metrics emphasize different aspects and are not directly comparable, 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 unified metric, ARRDE demonstrates consistently strong performance and one of the most stable aggregate profiles across the five suites. These results support ARRDE as a competitive DE variant for robust optimization across heterogeneous benchmark regimes.