## 5 Networking Parameter Adjustment Method for Optimized Systematic Performance
### Optimization Method Based on a Genetic Algorithm  
A genetic algorithm simulates the bio-evolution process of genetic choice and natural selection and combines the rule of survival of the fittest and the mechanism of stochastic information exchange of part of the chromosomes in a group. It is an effective parallel searching method that can achieve global optimal solutions. Aiming at meeting the optimal demand proposed in this thesis, the optimization method based on genetic algorithm is presented as follows:  
(1) Individual encoding and initial population  
Encode: Real encoding is employed. We set six parameters \(k_{b}\), \(d_{b}\), \(n_{b}\), \(c_{b}\), \(r_{b}\), and \(p_{b}\) as \(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{4}\), \(x_{5}\), and \(x_{6}\). We regard \(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{4}\), \(x_{5}\), and \(x_{6}\) as six pieces of a gene which construct a chromosome, and as an individual. (2) Evaluation of fitness  
(a) The fitness  
The fitness function is the key to evaluate individual and determines the evolution strategy. The optimal objective function: \(f(x)=x_{1}^{2}\cdot x_{6}\), so the fitness function is shown as Equation (22):  
\[Fit(f(x))=\frac{1}{1+c+f(x)},c\geq 0,c-f(x)\geq 0 \tag{22}\]  
In the equation, \(Fit\) denotes the fitness function, and \(c\) is a constant. (b) Constraint conditions  
The constraint conditions process is achieved by independently defining a measure for these constraint conditions or a measure characterizing the degree of individual violation of the constraint conditions. Then, a better individual is selected by comparing and competing the fitness value with the unfitness values of the individuals. The degree of violation of the constraint conditions is defined by Equation (23):  
\[obj(x)=\sum_{j=0}^{l}\max(0,g_{i}(x)),1\ll j\ll l \tag{23}\]In the equation, \(obj(x)\) is the function of individual violating the constraint conditions; \(g_{i}(x)\) is the constraint conditions in formula (21); \(l\) is the number of constraint conditions. Selection  
Set a threshold \(\varepsilon>0\) as a given degree of violating the constraint conditions, and the following rules are used to compare two individuals \(A\) and \(B\):  
(a) When the two individuals \(A\) and \(B\) are feasible, the individual with a larger fitness value is regarded as optimum by comparing the values \(f(A)\) and \(f(B)\). (b) When the two individual \(A\) and \(B\) are unfeasible, the individual with a smaller unfitness value is regarded as optimum by comparing the values \(obj(A)\) and \(obj(B)\). (c) When individual \(A\) is feasible but \(B\) is not, if \(obj(B)\leq\varepsilon\), the individual with a larger fitness value is regarded as optimum by comparing the values \(f(A)\) and \(f(B)\). Otherwise, \(A\) is regarded as a better individual. Evidently, the bigger the values of \(\varepsilon\), the higher the proportion of unfeasible solutions. In order to keep the proportion of unfeasible solutions in the population at a given rational level \(p>0\), an adjusted strategy for \(\varepsilon\) is shown as indicated by Equation (24):  
\[\left\{ \begin{array}{c}\epsilon^{\prime}=1.2\cdot\varepsilon,\quad p_{i} \leq p,1\leq i\leq K\\ \epsilon^{\prime}=0.8\cdot\varepsilon,\quad p_{i}>p,1\leq i\leq K\\ \varepsilon^{\prime}=\varepsilon,\text{others}\end{array} \right. \tag{24}\]  
For a given positive integer, from the first generation of produced feasible solutions in the population, we compute the proportion \(p_{i}\) (\(1\leq l\leq K\)) of unfeasible solutions in the population of every generation in \(K\) generations and rectify \(\varepsilon\) as \(\varepsilon^{\prime}\). Through the above selection operation, better individuals can be identified. Meanwhile, a proper and better unfeasible solution can be reserved in the new population. (4) Crossover  
Based on the above process of constraint conditions, an arithmetic crossover operation of feasible solutions and unfeasible solutions is employed, that is, two new individuals are produced by linear combination.