With the technology of artificial defects creating, we can tune the band structure and transport properties of many two-dimensional (2D) layered materials. One prototype materials system is the antidoted graphene sheet, where periodical pores are made using focuses ion or electron beams in the nanoscale. We here study the electrical conductivity, thermopower, and active rates of cooling and refrigeration of antidoted graphene samples with different pore-radii and interporous distances. We use a calculation method that takes into consider the sensitivity of transport to charge carrier energy, which can be used to describe the elastic and inelastic scatterings in diffusive, ballistic and quantum hopping regimes. It is found that our results from the new calculational approach are more consistent with the experimental data, compared to some traditional methodologies. It is also interesting to see that the optimized active rates of cooling and refrigeration are very robust against the distribution variations of interporous distance and the pore-radius, which implies easy industrialization and inexpensive manufacturing. The same analysis and investigation can also be extended to many other layered materials, including the transitional metal dichalcogenides (TMD), blue phosphorene, and tellurium.