In conventional windmills, the high tip speed creates aerodynamic noise, and when they are used at very low Reynolds numbers, their performance deteriorates due to laminar separation. These are important issues in modern windmills. Present study deals with a new windmill concept, the “flapping wing power generator,” which would solve such problems. The concept is to extract energy via the flutter phenomena and the concept has been developed by some researchers. In 2003, Isogai et al. 2003, “Design Study of Elastically Supported Flapping Wing Power Generator,” International Forum on Aeroelasticity and Structural Dynamics, Amsterdam) proposed a new system. The system utilizes dynamic stall vortices efficiently and generates high power. The dynamic stall vortex is something that should be avoided in conventional windmills. They optimized the system to maximize the efficiency and obtained the set of design parameters, which achieved best efficiency. The system works at low frequencies and it enables high efficiency. To realize the system, it is necessary to consider the power and the efficiency. Thus, the present study optimized the system to maximize both the power and the efficiency. To obtain nondominated solutions, which are widely distributed in the design space, adaptive neighboring search, which is one of evolutionary algorithms, has been extended to handle multiple objectives and was used in the present study. Self-organizing map was used for the data mining. The trade-off between the power and the efficiency has been visualized. The trade-off curve was shaped by the constraints on the reduced frequency and the phase delay angle, which were imposed so that the dynamic stall phenomenon gives favorable effects on the power generation. The heaving amplitude was a parameter correlated to the objective functions. The reduced frequency and the phase delay angle change to control the heaving amplitude. Consequently, when the power is emphasized, the system undergoes a large heaving motion with a low frequency. On the other hand, when the efficiency is emphasized, the system undergoes a small heaving motion with a high frequency. Multiobjective optimization and data mining revealed the trade-off of the objective functions and the parameters correlated to the objective functions. The power obtained was comparable to that of present windmills at low tip-speed ratio region.