This study presents a computational framework for optimizing undulatory swimming profiles using a combination of design-by-morphing and Bayesian optimization strategies. The body deformation is expressed as a linear combination of five baseline bio-inspired profiles, including two unconventional shapes to enhance diversity in the design space. The optimization objective is to maximize propulsive efficiency over a wide range of frequency-wavelength combinations. The Arbitrary Lagrangian--Eulerian formulation is employed to simulate the unsteady flow around two-dimensional undulating swimmers. The optimized profile achieves a significantly improved efficiency of 82.4\%, while the second- and third-best profiles achieve efficiencies of 51.8\% and 42.8\%, respectively, outperforming the benchmark anguilliform and carangiform profiles by leveraging advantageous surface stress distributions and effective energy recovery mechanisms. A detailed force decomposition reveals that the optimal swimmer minimizes resistive drag and maximizes constructive work contributions, particularly in the anterior and posterior body regions. Spatial and temporal work decomposition indicates a strategic redistribution of input and recovered energy, enhancing performance while reducing energetic cost. The wake topology associated with the optimized swimmer exhibits organized and coherent vortex structures, reflecting superior fluid-structure interaction characteristics compared to conventional profiles. These findings demonstrate that morphing-based parametric design, when guided by surrogate-assisted optimization, offers a powerful framework for discovering energetically efficient swimming gaits, with significant implications for the design of autonomous underwater propulsion systems and the broader field of bio-inspired locomotion.

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