This work introduces Inter-DS, a blackbox optimization algorithmic framework for computationally expensive constrained multi-fidelity problems. When applying a direct search method to such problems, the scarcity of feasible points may lead to numerous costly evaluations spent on infeasible points. Our proposed algorithm addresses this issue by leveraging multi-fidelity information, allowing for premature interruption of an evaluation when a point is estimated to be infeasible. These estimations are controlled by a biadjacency matrix, for which we propose a construction. The proposed method acts as an intermediary component bridging any non multi-fidelity direct search solver and a multi-fidelity blackbox problem, giving the user freedom of choice for the solver. A series of computational tests are conducted to validate the approach. The results show a significant improvement in solution quality when an initial feasible starting point is provided. When this condition is not met, the outcomes are contingent upon specific properties of the blackbox.
