B. Reproduction

The reproduction operator aims at copying chromosomes from parents to offspring, where the roulette-wheel mechanism is employed in IGA. Each chromosome is assigned a proportion value, namely the fitness value of the chromosome to the sum of fitness values of the population. The chromosome with a large proportion of value is reproduced with high probability.

## C. Crossover

The crossover operator is employed after the reproduction operator, where parent chromosomes are selected with a crossover probability defined as 0.6. The order, the two points, and the two-point crossover mechanisms are applied to the first, second, and third parts of every two selected and paired parent chromosomes, respectively. Figure 8 represents the crossover operation of two parent chromosomes and the offspring, where Par1 and Par2 denote two parent chromosomes, while Off1 and Off2 denote chromosomes after crossover operation. f2

**Figure 8.** Two parent chromosomes and offspring after crossover operation.

#### D. Mutation

Mutation probability is defined as 0.15. For the first part of each chromosome, two genes are randomly selected to exchange values. Simultaneously, two random genes of the second part of the chromosome are selected, and the value of each selected gene is changed from  1 to  0 and vice versa. The mutation mechanism of the second part also works for the third part of the chromosome. Figure 9 shows the mutation operation of a chromosome, where Par denotes a selected parent chromosome, while Off denotes the chromosome after the mutation operation. le denotes after

**Figure 9.** Parent chromosome and chromosome after mutation operation.
