Adaptive Fitness–Distance-Guided Newton Downhill Optimizer for Dynamic Multi-Target Path Planning

Abstract

The Newton Downhill Optimizer (NDO) combines a derivative-free downhill relation with population differences. However, its Hybrid-Guided Operator uses a random reference and persistent best-solution guidance, which can cause directional fluctuations and premature population contraction. This study proposes the Adaptive Fitness–Distance-Guided Newton Downhill Optimizer (AFDNDO). Fitness–Distance Balance selection identifies guiding individuals that account for both solution quality and spatial diversity. Stage protection, elite protection, and historical success-rate feedback regulate activation of the improved branches. A tripodal heavy-tailed update and a wave-weighted masked differential update reconstruct the two original branches. A non-uniform mutation is also triggered for low-quality individuals when the global best value stagnates. Across 30 independent runs on CEC2017, CEC2020, and CEC2022, AFDNDO attained the lowest mean rank in all six formal benchmark configurations. Its mean ranks on the 10-, 30-, and 50-dimensional CEC2017 tests were 1.172, 1.241, and 1.276, respectively. Dynamic path-planning environments included rigid obstacles, three levels of soft-risk regions, and moving obstacles. In the single-target environments, AFDNDO–DWA achieved a 100% execution success rate without collisions. In the multi-target environments, it reduced the mean objective value by 4.46–6.64% relative to NDO. It also increased the success rate from 63.33% to 70.00% in the most constrained environment. These findings indicate that AFDNDO improves cross-landscape optimization performance while retaining the basic NDO framework. They also support its use as a global planner within the tested dynamic multi-task environments.