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We propose a gradient-based optimization procedure consisting of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In the first phase a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to a feasible region. In the second phase a tunneling function is constructed at this local minimum in order to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle the search for the global optimum commences again using this new found point as the starting state. The search continues until no improvement in function the result is found. Results from the proposed optimization method are presented and compared with those from the gradient method involving 3 n enumeration proposed earlier, as well as with other published results.