Gradient-based methods are widely used in topology optimization due to their ability to handle a large number of design variables. However, their application to turbulent flow problems remains challenging. The complexity of turbulence models makes accurate sensitivity derivation difficult, and the strong nonlinearity of turbulent flows results in multimodal objective functions, in which gradient-based methods are prone to local optima. While non-gradient methods can address these issues, as they do not require sensitivity information and have global search capabilities, they typically suffer from the curse of dimensionality, where the number of required function evaluations grows rapidly with the number of design variables [1]. To overcome this limitation, this study proposes reducing the number of design variables by using end-constrained spline curves with variable width [2] for the fluid domain representation. This representation uses the widths of the curve components and the coordinates of the control points as design variables. In contrast to density-based approaches that produce blurred interfaces, this representation provides explicit boundaries. Moreover, since non-gradient methods evaluate each design independently, the meshes can be regenerated for each configuration. This flexibility allows for the construction of boundary layer meshes, improving the accuracy of turbulence analysis. For the optimization algorithm, a variant of differential evolution with semi-parameter adaptation [3] is employed to reduce parameter tuning effort and is combined with a local search method to accelerate convergence. The proposed method is applied to several numerical examples to demonstrate its effectiveness.