For the same reason that we do not use the traditional crossover operator, we can not use the traditional mutation operator. For example if we have a legal tour before mutation
1 2 3 4 5 0
Assuming the mutation site is 3, we randomly change 3 to 5 and generate a new tour
1 2 5 4 5 0
This new tour is illegal because city 5 appears twice while city 3 does not appear. Instead of using the traditional mutation operator, we randomly select two bits in one chromosome and swap their values. Thus, we still have legal tours after swap mutation as shown in Figure 4.
