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JANUS: Online Jacobian-Aligned Infill for Black-Box Optimization

Population optimizers such as CMA-ES, DE, and multi-objective evolutionary algorithms drive search mainly through selection signals that are scalar or rank based: such a signal indicates that one candidate outperforms another, but not the local direction responsible for the improvement. JANUS (\emph{Jacobian-Aligned Newton-Unified Search}) is a plug-and-play infill module that extracts this missing local geometric signal without replacing the host optimizer. It estimates a local Jacobian from the recent evaluation trace; the same Jacobian yields both a damped Gauss--Newton exploitation candidate and a trace-preserving exploration metric, reserving a fraction of the host's per-generation candidate slots for geometry-guided infill rather than spending evaluations on top of the host's budget. Unlike MetaBBO methods, JANUS needs no offline training or task distribution, estimating this geometry on the fly from the current run alone, while the host keeps full control of selection, survival, covariance adaptation, and step-size control. Under same-protocol comparisons, JANUS improves the CMA-ES host on \textbf{11--15/16} BBOB functions across $d\in\{30,100,500\}$. It also attains the best mean error on \textbf{13 of the 16} functions at $d{=}500$ in the complete NN-BBO/MetaBBO baseline comparison, with no training cost, and yields a $936\times$ geometric-mean improvement over the host on a $d{=}1000$ BBOB subset. On structured and multi-objective tasks, JANUS gives the best mean cost on 1135-dimensional UAV path planning ($-12.8\%$ vs.\ the strongest baseline), and it improves SMS-EMOA/AGE-MOEA2 hosts on 12/38 multi-objective tasks with zero significant regressions. Code is available at https://github.com/hongyuanyu/JANUS.

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