**6. Conclusions**

In this paper, aiming at the disadvantage of poor local search ability of KH algorithm, we optimized it by simulated annealing strategy and QPSO algorithm, and proposed a new algorithm: AKQPSO. This algorithm was compared with eight other excellent algorithms, and the computational accuracy of AKQPSO was tested by the 100-Digit Challenge problem. As predicted before the experiment, the computational accuracy of AKQPSO algorithm is the highest among these algorithms. Moreover, we also adjusted the parameters of AKQPSO through experiments to further improve the computational accuracy. By calculating the accuracy of the 100-Digit Challenge problem, our experiment provided a new method to study the accuracy of the algorithm, and the paper provided a very high accuracy algorithm. However, the research of this paper still has some limitations. The accuracy of the algorithm in 100-Digit Challenge problem is very high, but it is unclear whether AKQPSO still has high accuracy in general problems.

In the future, we can focus on other aspects. Firstly, besides the simulated annealing strategy and QPSO algorithm, we could look for other metaheuristic algorithms [85] that can be used to improve the search ability of KH and carry out in-depth research such as bat algorithm (BA) [86,87], biogeography-based optimization (BBO) [84,88], cuckoo search (CS) [82,89–92], earthworm optimization algorithm (EWA) [93], elephant herding optimization (EHO) [94,95], moth search (MS) algorithm [96], firefly algorithm (FA) [97], artificial bee colony (ABC) [98–100], harmony search (HS) [101], monarch butterfly optimization (MBO) [102,103], and genetic programming (GP) [104], as well as more recent research. Secondly, for the parameters in the algorithm, besides the proportion of subpopulation, we can also study the influence of other parameters on the computational accuracy of AKQPSO. Thirdly, now we just use two kinds of algorithms to make them cooperate and optimize in a relatively simple way, and we can also study how to make them cooperate more efficiently through other methods. Finally, although the 100-Digit Challenge is a classical problem, it is still less used for testing computational accuracy of algorithms, and there is still a large development space in this area.

**Author Contributions:** Conceptualization, C.-L.W. and G.-G.W.; methodology, C.-L.W.; software, G.-G.W.; validation, C.-L.W.; formal analysis, G.-G.W.; investigation, C.-L.W.; resources, G.-G.W.; data curation, C.-L.W.; writing—original draft preparation, C.-L.W.; writing—review and editing, C.-L.W.; visualization, C.-L.W.; supervision, G.-G.W.; project administration, G.-G.W.; funding acquisition, G.-G.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, gran<sup>t</sup> number U1706218, 41576011, 41706010 and 61503165.

**Conflicts of Interest:** The authors declare no conflict of interest.
