Recently, the importance of design process with unknown parameter increased. On the other hand, the design of Autonomous Underwater Vehicles (AUVs) is a difficult challenge since it requires the consideration of various aspects such as mission range, controllability, energy source, and carrying capacity. A design process for novel type of AUV constructed using an origami-based structure that includes active material actuators and solar panels is proposed in this paper. To increase the efficiency in the three-dimensional shape modeling of the AUV, the shape of the outer surface is parameterized by a finite set of variables using shape functions. Here, the AUV should operate underwater via electrical power with the batteries being charged periodically using solar panels. The ability of the AUV to transport cargo such as instrumentation is also addressed. The design parameters include the total height and width of the AUV. As these dimensions of the AUV might vary in a non-preferential manner based on particular mission goals, these dimensions are considered as design parameters in a multi-objective optimization setting. The Predictive Parameterized Pareto Genetic Algorithm (P3GA) is selected as the optimization method to determine a Pareto frontier of design options with desired characteristics for a variety of missions for the AUV. The evaluation of each AUV design entails quantitative assessment of the origami fold pattern determined using a method developed by the authors and Computational Fluid Dynamics (CFD) analysis. The development of a design process that addresses the design optimization of the AUV considering its hydrodynamic performance and origami aspects is the main topic of this paper.