In engineering application heuristics are widely used for dis- crete optimization tasks.We report two cases (in DenseWavelength
Divi- sion Multiplexing and High Level Synthesis), where a recent “intelligent” heuristic (STAGE) performs excellently by
learning a value-function of the states. We have found that if a global structure of local minima is found by the function approximator
then search time may not have to scale with the dimension of the problem in the exponent, but it may become a polynomial function
of the dimension.