This article presents the partial results obtained in the first stage of the research, which sought to answer the following questions: (a) What is the role of intuition in university students' solutions to optimization problems? (b) What is the role of rigor in university students' solutions to optimization problems? (c) How is the combination of intuition and rigor expressed in university students' solutions to optimization problems? (d) Is there really an optimizing intuition? In the first part, we provide reasons that make it plausible to consider intuition as a vector (metaphorically speaking) with three components: idealization, generalization, and argumentation. In the second part, we present the experimental design of the research and analyze the data to answer the questions previously asked. The experimental design does not allow us to falsify the hypothesis that some students have an optimizing intuition.