Appling the Roulette Wheel Selection Approach to Address the Issues of Premature Convergence and Stagnation in the Discrete Differential Evolution Algorithm

Table 13

Example of the process to generate the new solution (offspring) by crossover stage in the EDDE and DDE algorithms.

Process	Solution												Nonmatching degree
EDDE algorithm
Select best solution (πBest)	4	5	11	3	7	10	12	9	8	6	1	2	—
Mutation stage to select the parent 1	4	3	11	5	7	10	12	9	8	6	1	2	2
Select individual as parent 2 from the group that selection by RWS	4	2	11	6	12	1	7	5	9	3	10	8	10
Crossover stage between parent 1 and parent 2	4	2	11	6	7	1	12	9	8	3	10	5	6
DDE algorithm
Select best solution (πBest)	4	5	11	7	1	8	12	10	9	3	6	2	—
Mutation stage to select the parent 1	4	5	1	7	11	8	12	10	9	3	6	2	2
Select individual from a population as parent 2	4	5	11	7	1	8	12	10	9	3	6	2	0
Crossover stage between parent 1 and parent 2	4	5	11	7	1	8	12	10	9	3	6	2	0

It can be noted that the new solution (offspring) generated by the EDDE algorithm (bold) by the crossover stage has a high degree of nonmatching with the best solution which means the diversity of the population will be increased. While the opposite is in the DDE algorithm that generated offspring (italic) by the stage of crossover that degree of nonmatching was zero compared with the best solution, which means that the new solution is matched with the best solution which leads to loss of diversity.