## 3 Optimization Algorithm
### Mind-Evolved Advanced Genetic Algorithm  
Because of the above-mentioned shortcomings of GA algorithm, this paper proposes MAGA. This MAGA algorithm has a competitive relationship between multiple populations. Its main idea is to transform the single population of GA algorithm into several competing subpopulations based on the mind evolution method [45], and enhance the communication between groups, which can reflect the mind evolutionary characteristics to complicate and deepen a simple mind. Following the principle of survival of the fittest, the superior groups and the best individual are retained, while the substandard sub-populations are eliminated. New sub-populations are generated near the best individual to replace the eliminated ones, so that the individuals participating in GA algorithm can be continuously updated and the search is moving towards the optimal solution. Within the sub-population, the select operator, cross operator and mutation operator in the genetic process are improved. When a new superior individual appears in the sub-population, there is a greater opportunity to break the limitations of the current gene and the balance of certain comparative advantage, and then evolving a more adaptive individual to improve the competitiveness of this sub-population. This strategy not only preserves the individuals with excellent genes, but also ensures individual diversity in the population. In addition, the different search scope near the optimal solution can improve the local search ability in different regions of the global space. This MAGA algorithm uses a rank-base fitness assignment to design the selection operator \(P_{\text{g}}\), which is only related to the ranking of individual fitness values, and is not directly affected by the  
Figure 6: Flow chart of Genetic Algorithm (GA). specific value of fitness values. The individual with the best fitness has the highest probability to live to the next generation, and the second-best individual has the second-highest probability, and so on. The fitness value is only used to determine the ranking of individuals in the population, which can overcome the scale problem of proportional fitness. The select probability of individuals in the sorting space \(P_{g}\) is calculated by Equation (7). \[P_{g}=\left\{ \begin{array}{ll}(1-c)^{g-1}c,&g=1,2,3.\ldots.,d-1\\ (1-c)^{g-1},&g=d\end{array} \right. \tag{7}\]  
It should be ensured that the select probability of the last individual is the smallest, \(c\in(0.5,1)\), and \(\sum\limits_{g=1}^{d}P_{g}=1\). \(g\) is the individual ranking number, \(d\) is the total number of individuals. Cross and mutation operators determine the evolutionary ability of individual genes. This MAGA algorithm presents the improved cross and mutation operators, which are adjusted with the change of fitness value. When the individual fitness value is smaller than the average fitness value, the probability of this individual being changed is appropriately reduced to protect this better individual for the next generation. When the individual fitness value is larger than the average fitness value, the probability of this worse individual being crossed or mutated is increased to keep the diversity. Because the best individual may not be the global optimal solution, a certain minimum cross and mutation probability is also assigned to the best individual to increase the possibility of jumping out of a local optimum. The improved cross operator \(P_{c}\) and mutation operator \(P_{m}\) are updated by Equations (8) and (9). \[P_{c}=\left\{ \begin{array}{ll}P_{c1}-\frac{(P_{c1}-P_{c2})(f^{\prime}-f_{avg })}{f_{min}-f_{avg}},&f^{\prime}\leq f_{avg}\\ P_{c1},&f^{\prime}>f_{avg}\end{array} \right. \tag{8}\]  
\[P_{m}=\left\{ \begin{array}{ll}P_{m1}-\frac{(P_{m1}-P_{m2})}{f_{min}-f_{avg}}, &f\leq f_{avg}\\ P_{m1},&f>f_{avg}\end{array} \right.