The design of quantisation table is viewed as an optimisation problem because the quantisation table produces the compression/quality trade-off in baseline joint photographic experts group algorithm. In this paper, efforts have been taken to reduce the computation time of the differential evolution (DE) algorithm by using the surrogate model. This paper applies a problem approximation surrogate model (PASM) to assist DE algorithms for optimising the quantisation table. It also analyses the performance of PASM in DE algorithm based on approximation error and evolutionary perspective. In addition, it confirms the results using statistical hypothesis tests. PASM is integrated in classical differential evolution and knowledge-based differential evolution algorithms. Different benchmark images are used to validate the PASM performance in DE algorithms for three target bits per pixel. The result shows that integrated PASM in DE algorithms reduces the computation time and guarantees the similar results as DE algorithms without a model.