  We construct an integrable sigma model with a generalized $\mathcal{F}$
structure, which involves a generalized Nijenhuis structure $\mathcal{J}$
satisfying $\mathcal{J}^{3}=-\mathcal{J}$. Utilizing the expression of the
generalized complex structure on the metric Lie group manifold $G$ in terms of
operator relations on its Lie algebra $\mathfrak{g}$, we formulate a
Yang-Baxter sigma model with a generalized complex structure. Additionally, we
present multi-Yang-Baxter sigma models featuring two and three compatible
Nijenhuis structures. Examples for each of these models are provided.
