4.3. Global modification of MNMS algorithm
In the MRTOF system, due to the
possible roughness of the objective function, demanding high accuracy
for an optimization in a global search space is usually costly. While
the NMS algorithm is effective in
a local area, it is a challenge to find a reliable global minimum. This
also restricts its applicability in broader situations. Thus, adding
additional random points to the NMS acts as a double check for the
effectiveness of minimum. This re-check validation program is an
alternative function that starts manually.
The flowchart of the global MNMS algorithm is shown in Fig. 5. First,
the variables are transformed by adding a window with a periodic
function. After optimization, they are transformed back to the original
domain. It is similar to the processes of the traditional Fourier
transform and the inverse Fourier transform. Additional re-checks, which
are circled by dotted lines in Fig. 5, are used for global minimum
verification. It compares the values of randomly points with the current
simplex points to validate the current minimum. If the simplex settles
in a local area that is not sufficiently low, the random point will be
adopted as a new simplex point, altering the shape of the simplex and
subsequently moving it out of the current area. Meanwhile, if it
confirms the validity of the simplex after numerous re-checks, we can
consider the solution good enough to be accepted.