With the recent developments of autonomous vehicles, extensive studies have been conducted about Adaptive Cruise Control (ACC), which is an essential component of advanced driver-assistant systems (ADAS). The safety assessment must be performed on the ACC system before its commercialization. The validation process is generally conducted via simulation due to insufficient on-road data and the diversity of driving scenarios. Our paper aims to develop an optimization-based reference generation model for ACC, which can be used as a benchmark for assessment and evaluation. The model minimizes the difference between the actual and reference inter-car distance, while respecting constraints about vehicle dynamics and road regulations. ACC sensors can be impacted by external factors such as weather and produce inaccurate data. To handle the uncertainty involved, we also propose a chance-constrained stochastic model to reach results with a high level of confidence. Our numerical results illustrate that the stochastic model outperforms the deterministic model on randomly generated driving scenarios.