Crude oil has different characteristics according to its origin, and this difference causes suboptimal operation if not considered. Similar to other refinery operations, hydrodesulfurization suffers from lacking this knowledge. Information on the true boiling point curve of the feed, next to its sulfur concentration, can be used to optimize the operating temperature. In this work, an optimization problem is demonstrated for two manipulated temperatures of the system and solved by using a gradient-based and a gradient-free algorithm. While the gradient based solution has a single objective of minimum sulfur content, the gradient-free solution has three objectives: minimum sulfur, inlet temperature, and secondary hydrogen flow rate. A continuous lumping model is used to predict the temperature and sulfur responses of a real hydrodesulfurization plant. An adaptive approach is preferred for the model to cope with the catalyst deactivation interference on the product sulfur content constraint. The effect of changing feed on optimality is demonstrated by using eight types of feeds with varying true boiling point and sulfur content. In addition to that, the impact of catalyst age is shown on similar feed processed on different dates.