A determining method of movement sequence and a positioning apparatus of the
invention
are arranged in such a manner that, in order to measure positions of plural marks
as being measurement targets provided on a wafer within a shorter time, a group
including executable movement sequences is generated out of a group of movement
sequence candidates, each indicating a measurement order of these marks, and a
movement sequence that accomplishes a movement operation between the marks within
the shortest time is obtained from the group thus generated.
For efficiently searching an optical system as a globally optimal solution within
a shorter computation time, independently of an initial solution given, a designing
method of optical system of the invention obtains the optimal solution of the optical
system to be designed, using an evolutionary computation method (genetic algorithm)
having a genetic operator for handling continues values explicitly. Particularly,
from a partial space defined by a predetermined continuous occurrence probability
distribution of occurrence probabilities set based on parent individuals, child
individuals to be candidates in the next generation population are generated according
to the occurrence probabilities.
