In modern times, antenna design has become more demanding than ever. The escalating requirements for performance and functionality drive the development of intricately structured antennas, where parameters must be meticulously adjusted to achieve peak performance. Often, global adjustments to geometry are necessary for optimal results. However, direct manipulation of antenna responses evaluated with full-wave electromagnetic (EM) simulation models using conventional nature-inspired methods entails significant computational costs. Alternatively, surrogate-based techniques show promise but are impeded by dimensionality-related challenges and nonlinearity of antenna outputs. This study introduces an innovative technique for swiftly optimizing antennas. It leverages a machine learning framework with an infill criterion employing predicted enhancement of the merit function, utilizing a particle swarm optimizer as the primary search engine, and employs kriging for constructing the underlying surrogate model. The surrogate model operates within a reduced-dimensionality domain, guided by directions corresponding to maximum antenna response variability identified through fast global sensitivity analysis, tailored explicitly for domain determination. Operating within this reduced domain enables building dependable metamodels at a significantly lower computational cost. To address accuracy loss resulting from dimensionality reduction, the global optimization phase is supplemented by local sensitivity-based parameter adjustment. Extensive comparative experiments involving various planar antennas demonstrate the competitive operation of the presented technique over machine learning algorithms operating in full-dimensionality space and direct EM-driven bio-inspired optimization techniques.