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This technical note addresses the discrete optimization of stochastic discrete event systems for which both the performance function and the constraint function are not known but can be evaluated by simulation and the solution space is either finite or unbounded. Our method is based on random search in a neighborhood structure called the most promising area proposed in and a moving observation area. The simulation budget is allocated dynamically to promising solutions. Simulation-based constraints are taken into account in an augmented performance function via an increasing penalty factor. We prove that under some assumptions, the algorithm converges with probability 1 to a set of true local optimal solutions. These assumptions are restrictive and difficult to verify but we hope that the encouraging numerical results would motivate future research exploiting ideas of this technical note.