  Existing efforts are dedicated to designing many topologies and graph-aware
strategies for the graph Transformer, which greatly improve the model's
representation capabilities. However, manually determining the suitable
Transformer architecture for a specific graph dataset or task requires
extensive expert knowledge and laborious trials. This paper proposes an
evolutionary graph Transformer architecture search framework (EGTAS) to
automate the construction of strong graph Transformers. We build a
comprehensive graph Transformer search space with the micro-level and
macro-level designs. EGTAS evolves graph Transformer topologies at the macro
level and graph-aware strategies at the micro level. Furthermore, a surrogate
model based on generic architectural coding is proposed to directly predict the
performance of graph Transformers, substantially reducing the evaluation cost
of evolutionary search. We demonstrate the efficacy of EGTAS across a range of
graph-level and node-level tasks, encompassing both small-scale and large-scale
graph datasets. Experimental results and ablation studies show that EGTAS can
construct high-performance architectures that rival state-of-the-art manual and
automated baselines.
