Photonic crystal is a periodic lattice of dielectric structure. Studies of photonics crystal bandgap and its applications have forged a new interdisciplinary scientific field called "bandgap engineeringh with promising technological revolution possibilities. Bandgap is a range of frequencies at which the propagation of light is forbidden in all directions. Photonic crystals with large bandgaps can be used to control the flow of light in new ways and result in various novel applications such as on-chip waveguiding, perfectly reflecting mirrors, and high-quality resonant cavities. Several photonic crystal structure parameters need to be suitably determined to achieve the largest bandgap. We will discuss how surrogates assisted tuning framework can be incorporated to solve this structure optimal design problem efficiently. To construct the surrogates, we consider the uncertainty quantification models based on Kriging and co-Kriging. By using co-Kriging, we integrating low- and high-fidelity results and get high-fidelity predictions with reduced costs. Numerical simulation results will be demonstrated to show the performance of the proposed algorithms.