Complex computer codes are frequently used in engineering to generate outputs based on inputs, which can make it difficult for designers to understand the relationship between inputs and outputs and to determine the best input values. One solution to this issue is to use design of experiments (DOE) in combination with surrogate models. However, there is a lack of guidance on how to select the appropriate model for a given data set. This study compares two surrogate modelling techniques, polynomial regression (PR) and kriging-based models, and analyses critical issues in design optimisation, such as DOE selection, design sensitivity, and model adequacy. The study concludes that PR is more efficient for model generation, while kriging-based models are better for assessing max-min search results due to their ability to predict a broader range of objective values. The number and location of design points can affect the performance of the model, and the error of kriging-based models is lower than that of PR. Furthermore, design sensitivity information is important for improving surrogate model efficiency, and PR is better suited to determining the design variable with the greatest impact on response. The findings of this study will be valuable to engineering simulation practitioners and researchers by providing insight into the selection of appropriate surrogate models. All in all, the study demonstrates surrogate modelling techniques can be used to solve complex engineering problems effectively.