The goal of an on-line ontology-based question-answering system is to automatically derive answers from ontology knowledge bases without demanding additional information or intervention from users. This paper focuses on the problem of automatically mapping the tokens of a question into OWL elements, as an important step towards the further construction of answers. This problem can be essentially viewed as that of question understanding. The basic ideas underlying our method can be stated as follows: first we translate the tokens of a question as well as their syntactical and semantic relations (as in NLP) into constrained question variables and functions, and thereafter, we utilize an optimization-based assigning mechanism to substitute the question variables with the corresponding constructs in OWL knowledge bases. In the paper, we will discuss our preliminary studies using the questions collected from, and the knowledge base built at, the International WIC Institute (WICI).