The output of permanent-magnet-assisted synchronous machines is maximized under constant permanent magnet (PM) volume and machine size by optimizing rotor shape. An automatic shape optimization method combining Rosenbrock's method and adaptive finite-element method is applied for the optimization. Then, a prototype machine is manufactured due to the result of the optimization in order to confirm the validity. It is clarified that the output of the optimized machine significantly increases without decrease in efficiency, increase in PM volume, and increase in machine size compared with that of the conventional machine.