An adaptive modified Newton-Raphson-based optimizer for efficient optimal power flow performance under multiple operating conditions.

In particular, the comparison between MNRBO and NRBO shows a highly significant improvement with a mean difference of 7.978 and a p-value of 3.1894 × 10 –25 .

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These studies illustrate a clear trend toward hybrid, Levy-enhanced, and bio-inspired metaheuristics that overcome the limitations of traditional solvers.

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