Polling systems are multi-queue systems served by a single server according to a prescribed visiting scheme and service discipline. There are five typical service disciplines: exhaustive, gated, limited, k-limited and time-limited. Each service discipline represents a decision strategy to achieve a certain performance of the polling system, for example the mean waiting time. We will focus on the problem of finding the optimal service limits in a G/G/1/K polling system with the k-limited service discipline. Since it is hardly to get any analytical formula for evaluating the system's performance using the existing service discipline, it would be more practical to design a service discipline that can obtain better system's performance for the G/G/1/K polling system. To accommodate a more realistic G/G/1/K polling system, we need to formulate an optimization problem and choose the most beneficial k-limited service discipline as the decision variable to optimize, say, the mean waiting cost for the polling system. First, we model the G/G/1/K polling systems and formulate as a stochastic simulation optimization problem. In addition, we apply the proposed ordinal optimization algorithm to G/G/1/K polling systems to solve for a good enough k-limited service discipline to minimize the expected cost of operating the system. We have compared our results with those obtained by the existing service disciplines and found that our approach outperforms the existing ones.