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In this paper, we propose a coordinate search algorithm to solve the optimization-via-simulation problems with integer-ordered decision variables. We show that the sequence of solutions generated by the algorithm converges to the set of local optimal solutions with probability 1 and the estimated optimal values satisfy a central limit theorem. We compare the coordinate search algorithm to the COMPASS algorithm proposed in Hong and Nelson (2004) through a set of numerical experiments. We see that the coordinate search has a better performance.