It is important for superconducting utilization, such as MRI, that sup
erconducting magnets generate a highly homogeneous magnetic field. In
order to enhance the field homogeneity, some notches are placed outsid
e of a solenoid. The optimal design of notched solenoid arrangement be
comes a problem which has both continuous and discrete design variable
s. In this paper, we propose an optimal design method utilizing a modi
fied simulated annealing algorithm to realize the minimum winding volu
me design for notched multi-section superconducting magnets.