The preliminary stage of a design process usually includes an iterative process of generating alternative concepts, evaluating and selecting them. In the case of a multi-objective design task, it is suitable to employ a systematic and hierarchical way of decision-making. Although there have been successful accomplishments in developing computational methods and tools in conceptual design, the prior step of problem structuring needs more consideration. A designer may spend several hours to build a parametric model and explore the suitable solutions through an iterative process of generation, evaluation, and modification of design alternatives while the parametric model does not initially include some determining features. One may experience such disruption specifically when the design objectives are in contradiction. Then, the designer may either give privilege to only one design criterion or compromise (trade-off) solutions. Some scholarly works suggest bringing implicit search goals, higher-level information into account. In this research, the contribution of the Theory of Innovative Problem Solving (TRIZ) along with a genetic algorithm in the framework of ParaGen method is studied to resolve such design complication. The outcome of the research is a map of the design process which is validated by accomplishing the design of a folded plate dome.