An Adaptive Fractional Newton-Derived Optimizer for Global Optimization and 3D UAV Path Planning

The performance of an optimization algorithm can be limited when the same search behavior is maintained throughout the optimization process. Fractional Newton-Derived Optimization (FNDO) uses a fixed fractional order and does not adapt its main search mechanisms during the run. To address this limitation, this study introduces SA-FNDO, an adaptive extension of FNDO that retains the original fractional order while incorporating archive-assisted guidance based on JADE, covariance-based crossover derived from CoBiDE, and CMA-ES refinement around the current best solution. SA-FNDO is evaluated on the CEC2017 and CEC2022 benchmark suites and on three static 3D UAV path-planning environments. The ablation study shows that archive guidance and CMA-ES refinement provide the clearest contributions, while the effect of covariance crossover is more problem-dependent. Across the CEC test conditions, SA-FNDO obtains the best overall mean rank among the nine compared methods, ranking first on CEC2017 and CEC2022 at D=10 and second on CEC2022 at D=20. In the UAV case study, SA-FNDO obtains feasible paths in all 90 runs and achieves the lowest feasible-run median geometric cost in all three environments. These results support SA-FNDO as an effective extension of the publicly available FNDO implementation under the tested conditions.