According to the discussions above, DEMR can get a relatively better solution with a high stability.
It is obvious that DEMR can also achieve a relatively better result in all of the evaluation indexes with a good stability.
For other three algorithms, the performances of SaDE and DEMR are not only equally matched but also top-notch for all of the evaluation indexes, while the performance of SHADE is slightly inferior compared to these two, especially for the stability.
It can be found that SaDE, SHADE, and DEMR can be very successful in the optimization of the problem.
To further confirm the effectiveness of DEMR, another group of experiments between DEMR and the same algorithms used in experiments for Earth-Moon low-energy transfer trajectory optimization (CMA-ES, LBBO, GL-25, SaDE, MPEDE, and SHADE) is conducted on 25 benchmark functions from CEC2005 special session  on real parameter optimization.
The parameters in DEMR are set the same with those in the former experiment for Earth-Moon low-energy transfer trajectory optimization, except the maximum evaluations MaxNFEs and the maximum number of randomly reinitialization [R.sub.max], which are set as MaxNFEs = 10,000 * D and [R.sub.max] = 20.
The symbols "-," "+," and "="denote that the performance of the corresponding algorithm is, respectively, worse than, better than, and similar to DEMR, respectively, according to the Wilcoxon rank-sum test at [alpha] = 0.05.
The [R.sup.+] in Table 11 is a measure of the case where DEMR outperforms the compared algorithm and the greater the [R.sup.+] value is, the greater difference between DEMR and the compared algorithm is.
It can be observed that, DEMR can achieve both a fast convergence speed and a high search accuracy for multimodal functions, but for the unimodal functions f1 and f5, DEMR converges a little early.
It shows that DEMR ranks the second with Ranking = 3.22, behind SHADE with Ranking = 2.70.
DEMR introduces its own parameters [[rho].sub.1,max], [[rho].sub.2,max], and [R.sub.max], of which [[rho].sub.1,max] and [[rho].sup.2max] determine the time to trigger the local search algorithm SQP, and [R.sub.max] controls the maximum number of random reinitialization.
And it can be seen that, for CEC2005 benchmark functions, Rmax = 20 is the most appropriate choice, while for the design of EarthMoon low-energy transfer trajectory, the performance of DEMR ranks the first when [R.sub.max] = 5.