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An improved Jaya algorithm named surrogate-assisted Jaya algorithm based on optimal directional guidance and historical learning mechanism (SDH-Jaya) is proposed in this study to address the continuous optimization problems. In the SDH-Jaya, a surrogate-assisted model combined with the polynomial model and radial basis model built by the individual with real fitness is introduced to decrease the expensive computational simulations and accelerate the convergence speed. Two co-evolutionary mechanisms, which are named assisted co-evolutionary mechanism and self-learning co-evolutionary mechanism, are proposed to optimize the surrogate model and evolutionary population. Search directions and steps of the SDH-Jaya are adjusted adaptively by the differential vector resulting from the best solution and worst solution in the candidates at each generation. The historical population stored in an archive is selected randomly to provide new search areas for improving the diversity of the population during the evolution process of the SDH-Jaya. The performance of SDH-Jaya is tested on CEC2017 benchmark problems. The experimental results reveal that the effectiveness of the SDH-Jaya algorithm outperforms the classical Jaya algorithm, its variants, and state-of-the-art algorithms in terms of the quality of solution and execution time. • The SDH-Jaya based on optimal directional guidance and historical learning is proposed. • A surrogate-assisted model is introduced in the SDH-Jaya. • The co-evolutionary and self-learning mechanism are incorporated in the surrogate model. • The differential vector is utilized to adjust the search directions and steps. • The historical population stored in the archive is adopted to generate new search areas. [ABSTRACT FROM AUTHOR]