<p>The rapid development of additive manufacturing technology has provided new avenues for the design of multiscale structures, wherein fatigue-resistant design has become one of the key indicators for ensuring structural performance. However, different fatigue strength criteria often yield different assessments of structural failure, introducing significant challenges in structural design optimization based on various fatigue strength criteria. This study introduces a novel concurrent topology optimization framework for two-scale structures that incorporates multiple fatigue strength criteria. The optimization model aims to minimize structural compliance while simultaneously accounting for various fatigue failure modes, as evaluated by the Goodman, Gerber, ASME-elliptic, and Soderberg criteria. To evaluate fatigue performance in multiscale architectures, a microscopic fatigue strength analysis method based on the characterization of microscopic stress fields is employed. Numerical homogenization methods are utilized to assess the equivalent properties of the microstructural configuration. In the optimization model, prescribed volume constraints and fatigue strength constraints are imposed concurrently. The multi-constrained optimization problem is addressed by using the active-set technique, which reduces computational cost by limiting the number of active constraints. Fatigue sensitivity analysis is conducted using the adjoint variable approach, and the method of moving asymptotes (MMA) is employed as the optimization solver. Numerical results demonstrate that the selected fatigue criterion critically influences the final structural topology.</p>