# Self-adaptive Artificial Bee Colony with a Candidate Strategy Pool
## 5 Conclusions  
In this paper, we proposed a new self-adaptive ABC algorithm with candidate strategies (SAABC-CS) to balance the exploration and exploitation of the evolution. Compared with the original ABC, SAABC-CS has three modifications, without adding any extra parameters: (1) five strategies are selected and assembled in a strategy pool; (2) a self-adaptive mechanism was designed to make the algorithm universal; (3) three neighbor mutations work together to enhance the scout phase. The aforementioned additions enhance ABC's overall performance by allowing it to tackle complicated issues with more features, while balancing its exploration and development capabilities. Comprehensive experiments were performed on two groups of functions: 22 basic benchmark functions and CEC2013 test suites. The experiment results for the 22 basic test functions showed that SAABC-CS obtained a much better performance than an ABC with one strategy. Furthermore, the self-adaptive selection mechanism in SAABC-CS was well-turned to select an appropriate strategy for facing problems of a different nature. For the complex and difficult CEC2013 benchmark suite, SAABC-CS still achieved promising results and surpassed four state-of-the-art ABCs. With the increasing dimensions of CEC2013, the performance of SAABC-CS did not deteriorate. The method also produced positive results when it was used to tackle real-world engineering challenges, demonstrating that it can solve real-world optimization problems as well as test functions. Although extensive experiments were conducted to demonstrate the performance of SAABC-CS, we hope to theoretically analyze the algorithm, inspired by the literature [40; 41; 42]. We also wish to extend the use of SAABC-CS to certain large and expensive problems in the future. Y.H. : Conceptualization, Methodology, Software, Validation, Formal analysis, Writing--Original Draft. Y.Y. : Conceptualization, Methodology, Writing--Original Draft, Supervision, Project administration. J.G. : Conceptualization, Methodology, Writing--Original Draft, Supervision, Project administration. Y.W. : Methodology, Supervision, Project administration. All authors have read and agreed to the published version of the manuscript. This work was part funded by the National Natural Science Foundation of China (No. 61966019), and the Fundamental Research Funds for the Central Universities (No. CCNU20 TS026). \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & \multicolumn{6}{c}{**The Best Value of Six Parameters**} & \multirow{2}{*}{**Error Variance**} \\ \cline{2-2} \cline{4-7}  & \(\mathbf{a_{1}}\) & \(\mathbf{\omega_{1}}\) & \(\mathbf{a_{2}}\) & \(\mathbf{\omega_{2}}\) & \(\mathbf{a_{3}}\) & \(\mathbf{\omega_{3}}\) & \\ \hline ABC & 0.3559 & 0.0316 & 1.0678 & 0.1394 & 5.0670 & 4.9233 & 1.659715 \(\times\) 10\({}^{1}\) \\ ABCNG & 0.5546 & 0.0627 & 1.5207 & 0.1437 & 4.3253 & 4.9361 & 1.460573 \(\times\) 10\({}^{1}\) \\ KFABC & 0.1414 & 0.2657 & 0.1414 & 0.1414 & 0.1414 & 0.1414 & 2.901492 \(\times\) 10\({}^{1}\) \\ MGABC & 0.6894 & 14.6861 & 0.7746 & 9.7434 & 1.0506 & 5.1230 & 1.226273 \(\times\) 10\({}^{1}\) \\ SABC-GB & 0.7306 & 14.5462 & 0.6579 & 4.6106 & 5.7068 & 4.8736 & 1.177162 \(\times\) 10\({}^{1}\) \\ SAABC-CS & 0.3370 & 4.7477 & 0.4820 & 0.2280 & 1.2430 & 3.2447 & **1.024282 \(\times\) 10\({}^{1}\)** \\ \hline \hline \end{tabular}
\end{table} 
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