Applied Computational Intelligence and Soft Computing

Research Article

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

Table 12

Comparison between the DDE and EDDE algorithms and the illustration of the stagnation situation for DDE and how EDDE avoids it.


DDE algorithm solutions													Cost	Gap	Nonmatching degree	Solution stagnation start	Waiting for solution improvement

π_Best	4	5	11	7	1	8	12	10	9	3	6	2	272700	3.84	—	—
π₁	4	5	11	7	1	8	12	10	9	3	6	2	233040	3.84	0	113 iteration
π₂	4	5	11	7	1	8	12	10	9	3	6	2	233040	3.84	0	98 iteration
π₃	4	5	11	7	1	8	12	10	9	3	6	2	233040	3.84	0	101 iteration
π₄	4	5	11	7	1	8	12	10	9	3	6	2	233040	3.84	0	103 iteration
π₅	4	5	11	7	1	8	12	10	9	3	6	2	233040	3.84	0	99 iteration
π₆	4	5	11	7	1	8	12	10	9	3	6	2	233040	3.84	0	85 iteration

EDDE algorithm solutions													Cost	Gap	Nonmatching degree	Group

π_Best	4	5	11	3	7	10	12	9	8	6	1	2	230704	2.80	—	—	—
π₁	4	12	11	3	2	7	5	8	9	6	1	10	232164	3.45	7	1	9 times
π₂	4	5	11	7	1	8	12	10	9	3	6	4	233040	3.84	8	2	7 times
π₃	4	5	11	3	7	10	12	9	8	6	1	2	230704	2.80	0	—	1 times
π₄	4	5	11	10	1	7	12	8	3	6	9	2	235704	5.03	7	1	4 times
π₅	4	2	11	6	12	1	7	5	9	3	10	8	243100	8.33	10	3	3 times
π₆	6	5	1	7	2	4	8	12	3	11	10	9	315722	31.95	11	4	Regenerated

π_Best: the π_Best (bold) is the best solution in the population of the DDE and EDDE algorithms. Cost: the best value of the objective function obtained by DDE and EDDE algorithms by using equation (1). Nonmatching is the number of different facility locations between two solutions and calculated by using Algorithm 1. Group: a set of individuals with the same nonmatching degree as the best individual in EDDE algorithm. Gap: the best value obtained by equation (12). Solution stagnation start: the number of iterations that the solution has not changed (not improved) in the DDE algorithm, where max iteration is 1000. Waiting for solution improvement: the number of trials the EDDE algorithm waits for before considering the solution is stagnated and should be regenerated randomly (italic) the default value is 10 trials.