(c) Paternal selection

There are three common methods of paternal selection: random selection, tournament selectionandroulettebet.Here,weuseroulettemethod,thespecificoperationisasfollows:

 Step 1: The fitness of each individual in the population is calculated *fi* (*i* = 1,2,3, ... *n*), where n is the population size.

Step 2: Calculate the probability *pi* = *fi* ∑*n* 1 *fi* of each individual being inherited into the next generation population.

Step 3: Calculate the probability distribution of each individual:

$$\eta\_i = \sum\_{j=1}^{i} p(x\_j). \tag{6}$$

Step 4: A pseudo-random number (rand) with uniform distribution is generated in the interval (0, <sup>1</sup>).

Step 5: When *rand* < *q*1, *q*1 is chosen; otherwise, if *qk*−<sup>1</sup> ≤ *rand* ≤ *qk*, individual K is chosen.

Step 6: Repeat step 4 and step 5 several times, and the number of repetitions depends on the size of the population.

(d) Cross rate selection

Crossover is the main way to produce new individuals. The crossover rate is the number of chromosomes in the crossover pool. A reasonable crossover rate can ensure that new individuals will be produced continuously in the crossover pool, but it will not produce too many new individuals, so as to prevent the genetic order from being destroyed. This paper adopts the most popular method of the adaptive crossover rate.

### (e) Variation rate selection

The mutation rate is the proportion of the number of genes in a population based on the number of all genes. Because mutation is a way to produce new individuals, we can control the mutation by setting the number of genes or the rate of random mutation. Too low a mutation rate will lead to too few chromosomes involved in the mutation, which leads to the problem that the chromosome containing unique genes cannot be entered into the set. The high mutation rate will cause too many chromosomes involved in the mutation, which will generate some illegal data and increase the time cost. After the experiment and model tuning, the final mutation rate is 0.5.
