The individual time trial discipline (ITT) in professional cycling is dubbed the race of truth as the cyclists are racing alone against the clock. These stages can be very close and they often play a decisive role in the Grand Tours. At the first ITT stage of the Tour de France 2022, the first and second places were separated by 5 seconds corresponding to a 0.5% difference in the finishing times. This makes the discipline highly interesting from an optimization perspective. A pacing strategy defines how a cyclist distributes their power output along a course and hence also their velocity. We have developed a numerical design methodology for computing optimal pacing strategies-i.e. the pacing strategy that minimizes the finishing time for a given cyclist racing on a given course. We apply the method to four hypothetical courses of 2 km simulating various gradients and wind conditions. The optimized pacing strategies led to improved finishing times ranging from 0.45% to 2.84% compared to benchmark pacing strategies. We also show how the method can be applied to compute an optimized pacing strategy for a complex real world course. The result is closely related to a pacing strategy derived from data from professional cyclist and ITT specialist Martin Toft Madsen, with the optimized strategy being 1.2% faster over 21.3 km. We believe that the method presented here constitutes a promising framework for computing optimal pacing strategies and with further research and a more accurate physiological model, this could prove an important tool for strategizing in professional cycling.