Designing and optimizing complex systems often requires numerous evaluations of a quantity of interest.
This is typically achieved by querying potentially expensive models in an optimization process.
To alleviate the cost of optimization, surrogate models can be used in lieu of the original model, as they are cheaper to evaluate.
This work presents a strategy to adaptively construct and exploit a surrogate for the optimization of a single truth high-fidelity model.
This is achieved by defining a utility function that quantifies the information gained about the model in regions of interest.
The next design to evaluate is chosen to maximize that utility function.
We also propose leads to extend the formulation to the case where the quantity of interest can be estimated by multiple models (e.g. several numerical models, experimental results, surrogates or historical data).