## 4 SMC Parameters Tuning Based on PACSA
### Optimal Tuning Process of SMC based on PACSA  
#### 4.2.1 Brief Introduction of PACSA  
The natural biological immune system has greatly influenced the development of computational intelligence in recent years, and many scholars have proposed many intelligent computing technologies based on immune systems. The artificial immune algorithm is abstracted from the mechanism of the biological immune system. The biological principles like clone generation, proliferation, and maturation are mimicked and incorporated into an artificial immune-based algorithm termed as the clonal selection \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**r** & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline
**RI** & 0 & 0 & 0.58 & 0.9 & 1.12 & 1.24 & 1.32 & 1.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Reference criterion (RI) values. algorithm (CSA) [34]. Many concepts and operators in the algorithm have a corresponding relationship with the concepts and mechanisms in the immune system, which should be introduced. Antigen is a substance that can stimulate the body to produce specific antibodies, such as to viruses or bacteria. Antibodies can bind to an antigen that invades from the outside and then help destroy these antigens to keep the body healthy. However, the extent of binding of different antibodies to antigens is different, and the higher the matching extend, the stronger the ability of antibodies to destroy such antigens. Antibody-antigen affinity is used to describe the matching extent between the antibody and the antigen. In the immune algorithm, the corresponding meanings of the antigen, antibody, and antibody-antigen affinity correspond respectively to: (1) the objective function and constraints of the optimization problem; (2) the optimal solution of the optimization problem; (3) the matching between the solution of the optimization problem and the objective function. PACSA is proposed on the basis of ACSA. 'P' stands for the parallel computing, and the first letter 'A' represents the tune of the parameters is adaptive, which improves the running speed and convergence of the CSA, respectively. Parallel computing can greatly reduce the running time of optimization operations and improve the performance of CSA through sacrificing hardware resources [16; 17]. ACSA enables the cloning operator to adjust the population evolution strategy dynamically based on the evolution of the population. PACSA refers to random mapping of antibodies induced by antibody-antigen affinity, where the meaning of cloning corresponds to the generation of new antibodies based on genetic operators. The main idea of the PACSA could be described as follows: only the antibodies recognized by the antigen are cloned during the process of optimization; in other words, the antibody is selected according to the antibody-antigen affinity in each generation for the cloning operation in each generation to generate a new population. The core operation of PACSA is the cloning operator, which ensures the algorithm converges quickly in the direction of the global optimal solution based on the cloning operation and selection mechanism. The clonal selection operation not only expands the spatial range for the algorithm to search for the optimal solution, but also increases the diversity of antibodies through the mutation operation, helps prevent premature convergence, avoids plunging into a local optimum, and accelerates the convergence of the group through selection operations. According to the principle of self-adjusting, the mutation rate of PACSA can be obtained from Equation (30) based on antibody-antigen affinity. It can be seen that the closer the number of iterations to the maximum set algebra, the smaller the mutation rate. As a consequence, the mutation rate is higher at the beginning of optimization, so that the antibody can jump out of the local extreme point and move to the global maximum point quickly.