An Enhanced Newton Downhill Optimizer for High-Dimensional Optimization and Thermal–Pumped-Storage Economic Dispatch

Abstract

The Newton Downhill Optimizer (NDO) provides a compact derivative-free search framework, but its random dimension mask, uniform treatment of individuals, and limited use of supplementary global-best candidates may restrict performance on high-dimensional problems. This study proposes an Enhanced Newton Downhill Optimizer (ENDO) that incorporates three mechanisms: an adaptive dimension mask, a DE/rand/2-based greedy mutation for inferior individuals, and dynamic-boundary opposition-based best guidance. ENDO was evaluated on the CEC2017 benchmark at 10, 30, 50, and 100 dimensions. The primary comparison involved nine representative optimizers, and an additional 100-dimensional comparison was conducted with six advanced optimizers. In the primary 100-dimensional tests, ENDO ranked first on 18 of 29 functions, remained among the top three on 26 functions, and achieved an average rank of 1.79. In the additional comparison, ENDO ranked third with an average rank of 3.52. Across the four dimensions, its average ranks were 1.79, 1.66, 1.38, and 1.79, indicating stable performance under changes in problem scale. ENDO was further applied to a 168-dimensional thermal–pumped-storage economic dispatch problem, where it achieved the lowest mean operating cost, the best average rank of 1.87, and a feasibility rate of 100% over 30 independent runs. Statistical analyses further supported the competitiveness of ENDO across the benchmark and engineering evaluations. These results show that ENDO improves the sustained search capability of NDO and provides competitive performance for complex high-dimensional and constrained optimization problems.