  This work introduces a novel blackbox optimization algorithm 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
fidelity and interruption controlled optimization 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.
