Tumbleweed algorithm (TA), as relatively new population intelligence optimization algorithms within the field of evolutionary algorithms, are challenged to deal with the high computationally expensive problems. Thus, within this paper, we introduce a pioneering surrogate-assisted Tumbleweed Algorithm (STA). Here in this paper, we reduce the number of times the objective function is called mainly by introducing a local surrogate mode and a global one. This paper conducts experiments utilizing five benchmark functions. Furthermore the STA has been compared with other excellent population intelligent optimization algorithms, and it is observed that the STA presented in this paper generally outperforms other intelligent optimization algorithms. Subsequent engineering optimization problems serve to validate the efficacy of the algorithm and provide an innovative approach to address high - cost optimization issues.