At the early phase of the engineering design, numerous ideas were generated as many as possible to satisfy the customer needs. Those ideas finally were transformed into a set of design matrices. However, the result of idea generation usually gave abundant of possible design variants. To avoid design conflicts and to obtain potential design variants, the design team must find the possible design variants and evaluate them. This process is considered a time-consuming and iterative work. This paper presents a method to find the possible design variants and to evaluate it complexity. It focuses on the mapping process between the function domain and the design domain. The generated ideas were transformed into design matrices represent a set of functional requirements (FRs) and a set of design parameters (DPs). The possible design variants were stored in the design library. They were then evaluated its complexity with complexity index (Ci). This method supports the design team to avoid design conflicts and to select suitable design variants at the early design phase.