**6. Time complexity analysis of RGSGCS algorithm**

10 Will-be-set-by-IN-TECH

*RP*(*c*) = *Rank*(*c*) ∑*<sup>N</sup>*

RRWS determines how many and which individuals will be kept in the next generation. Next,

Two-point crossover operator (figure 7) controls how to exchange genes between individuals. Two chromosomes are selected randomly from mating pool. Where the middle part in each chromosome is reversed between two parent chromosomes. It is applied to the chromosomes from selection phase. After that, the mutation operator allows for random gene alteration of

In this phase, single exchange mutation operator (figure 8) is applied to the output of crossover phase. Mutation operator exchanges only two genes according to a mutation rate

Besides the standard genetic operators (i.e., crossover and mutation operators). The elitism Phase is used finally to preserve the best candidates for the next generation, so that the algorithm always converges to the global optimum. It combines the parent population with the modified population (the candidates generated by crossover and Mutation operators), and

**5.6 Single exchange mutation operator of RGSGCS algorithm**

*Pm*. It is useful to avoid premature convergence of GA.

*<sup>n</sup> Rank* ; (7)

based on cumulative proportion.

 

an individual.

Fig. 7. Two-Point Crossover Operator

Fig. 8. One Exchange Mutation Operator

**5.7 Elitism of RGSGCS algorithm**

crossover operator and mutation operator are explained.

**5.5 Two-point crossover operator of RGSGCS algorithm**

Time complexity analysis of RGSGCS algorithm can be analyzed step by step as shown in table 1. From table 1 time complexity of RGSGCS algorithm is expressed as: O(*Q*.*PS*.*N*.*M*). Where *PS* is population size, and *Q* is Maximum number of iterations of RGSGCS algorithm.


Table 1. Time complexity analysis of RGSGCS algorithm
