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.