Surrogate (meta or response surface) models are frequently used to emulate expensive computer simulations. In global optimization, surrogate-based approaches accelerate the optimization process that would otherwise suffer from intractable run times. In many cases, design constraints are also expensive to evaluate and replaced with surrogates. If the constraint functions are poorly modelled, locating the best feasible design becomes difficult to achieve and requires an infill sampling criteria that balances exploration and exploitation of both the objective and all constraint surrogates. Furthermore, by encouraging model updates to be placed in close proximity to the constraint boundaries, regions that are likely to contain the optimum solution can be better modelled. This leads to the development of infill sampling criteria suitable for handling both inequality and equality constraints in surrogate-based optimization.