Before revision:  We describe a new approach to this optimization problem, based on embedding the discrete parameter space into an extended continuous space . Optimization is then carried out over the extended continuous space using standard descent based continuous optimization schemes. The embedding is performed using a novel simulation-based ergodic interpolation method that produces the interpolated value in a single simulation run .
After revision:  We describe a new approach to this optimization problem, based on embedding the discrete parameter space into an extended continuous space so that continuous space techniques can be applied to the embedded problem using cycle accurate simulation for evaluating the objective function. This embedding is implemented using simulation-based ergodic interpolation method that produces the interpolated value in a single simulation run .